Application of the Strength Pareto Evolutionary Algorithm (SPEA2) Approach to Rail Repair Investments

Transcription

1 CENTER FOR NATION RECONSTRUCTION AND CAPACITY DEVELOPMENT June 2016 United States Military Academy West Point, New York Application of the Strength Pareto Evolutionary Algorithm (SPEA2) Approach to Rail Repair Investments Prepared By Gene Lesinski Department of Systems Engineering United States Military Academy Prepared For C/NRCD Internal Research and Development Project Report

2 The views and opinions expressed or implied in this publication are solely those of the authors and should not be construed as policy or carrying the official sanction of the US Army, the Department of Defense, United States Military Academy, or other agencies or departments of the US government. The cover photo was downloaded at

3 The Superintendent of the United States Military Academy (USMA) at West Point officially approved the creation of the Center for Nation Reconstruction and Capacity Development (C/NRCD) on 18 November Leadership from West Point and the Army realized that the US Army, as an agent of the nation, would continue to grapple with the burden of building partner capacity and nation reconstruction for the foreseeable future. The Department of Defense (DoD), mainly in support of the civilian agencies charged with leading these complex endeavors, will play a vital role in nation reconstruction and capacity development in both pre and post conflict environments. West Point affords the C/NRCD an interdisciplinary and systems perspective making it uniquely postured to develop training, education, and research to support this mission. The mission of the C/NRCD is to take an interdisciplinary and systems approach in facilitating and focusing research, professional practice, training, and information dissemination in the planning, execution, and assessment of efforts to construct infrastructure, networks, policies, and competencies in support of building partner capacity for communities and nations situated primarily but not solely in developing countries. The C/NRCD will have a strong focus on professional practice in support of developing current and future Army leaders through its creation of cultural immersion and research opportunities for both cadets and faculty. The research program within the C/NRCD directly addresses specific USMA needs: Research enriches cadet education, reinforcing the West Point Leader Development Systems through meaningful high impact practices. Cadets learn best when they are challenged and when they are interested. The introduction of current issues facing the military into their curriculum achieves both. Research enhances professional development opportunities for our faculty. It is important to develop and grow as a professional officer in each assignment along with our permanent faculty. Research maintains strong ties between the USMA and Army/DoD agencies. The USMA is a tremendous source of highly qualified analysts for the Army and DoD. Research provides for the integration of new technologies. As the pace of technological advances increases, the Academy's education program must not only keep pace but must also lead to ensure our graduates and junior officers are prepared for their continued service to the Army. Research enhances the capabilities of the Army and DoD. The client-based component of the C/NRCD research program focuses on challenging problems that these client organizations are struggling to solve with their own resources. In some cases, USMA personnel have key skills and talent that enable solutions to these problems. For more information please contact: Center for Nation Reconstruction and Capacity Development Attn: Dr. John Farr, Director Department of Systems Engineering Mahan Hall, Bldg. 752 West Point, NY John.Farr@usma.edu Page i

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5 Abstract The Department of Defense (DoD) manages approximately $850 Billion in infrastructure. As part of their basic infrastructure, most installations, posts, or garrisons have short haul rail systems used to mobilize and transport supplies and equipment. These rail systems are strategically linked to the national rail network to facilitate transportation of equipment and supplies to key ports and terminals. Fort Smith, the notional installation used to illustrate this research, is a typical World War II era facility with approximately >110 miles of rail organized and managed as 104 rail segments. Fort Smith s rail is aging and in poor condition. In fact, roughly 2/3rds of the 104 rail segments were recently issued safety restrictions due to their degraded condition. The fundamental problem for Fort Smith leadership is to determine a repair strategy that maximizes the overall condition of the rail yard while minimizing cost. DoD recognized that they did not have a good accounting of installation rail inventory, condition, or cost to improve rail yard condition to an established threshold. In response, the U.S. Army Construction Engineer Research Lab (CERL) developed a decision support tool called RAILER. RAILER inventories installation rail assets, documents its condition, and generates cost maintenance and repair estimates [24]. RAILER also generates a prioritized rail segment repair list utilizing a prioritized worst first strategy. In this research we apply a frequently cited, commonly benchmarked, multi-objective evolutionary algorithm; the Strength Pareto Evolutionary Algorithm (SPEA2) and compare the results obtained against those generated by RAILER. The SPEA2 is a multi-objective, Paretobased EA approach that employs a count and rank-based dominance fitness measure to drive solutions toward the Pareto optimal front. SPEA2 employs an elitist strategy in that it maintains an external archive of solutions and exclusively produces new solutions from the archive members. SPEA2 also utilizes a nearest neighbor density estimation technique that is used to differentiate solutions and maintain solution spread (diversity) within the archive. Utilizing the RAILER prioritized worst first scheme, the best condition achieved is a score of 768 at a cost of $12.9M. Each of the non-dominated solutions generated by the SPEA2 algorithm exceed the RAILER condition score at a cost well under the $12.9M RAILER cost. The general rail repair strategy highlighted by the SPEA2 generated non-dominated solutions is to recommend doing nothing to low priority/high condition rail segments, swap low priority/low condition segments, and upgrade high priority low to mid condition segments. The collection of non-dominated solutions provided by this multi-objective Pareto technique give decision makers increased flexibility and the ability to evaluate whether an additional cost solution is worth the increase rail condition. Page iii

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7 Table of Contents Chapter Topic Page Abstract... Introduction.... Technical Details.... Model Development Results Summary iii List of Appendices Appendix Topic Page A B C D E F G H References Acronyms Rail Segment Cost and Condition Data... Rail Segment Volume and Normalized Traffic Score..... Rail Segment Priority Scores... Rail Evolutionary Algorithm Code SPEA2 Rail Model Output... RAILER Prioritized Repair List List of Figures Number Title Page Solution Representation Scheme SPEA2 Pseudo Code Sample Solution Chromosome. SPEA2 Strength and Raw Fitness.. Density Estimate to Truncate Archive. Single Point Crossover.. SPEA2 Solution Evolution. Final Archive Solution vs. RAILER Page v

8 List of Tables Number Title Page Sample Condition and Repair Cost Data Sample Normalized Traffic Score of Rail Segments Rail Segment Purpose/Priority. Sample Track Segment Priority Scores.. Sample Track Segment Costs.. Sample Track Segment Priority Scores.. EA Operational Parameters.. General Output Results Across all Seeds.. General Pattern Across all Non-Dominated Solutions.. RAILER Top 10 Recommended Repairs Single Seed Non-Dominated Archive.. Consistent Rail Recommendations across all ND Solutions General Non-Dominated Solution Patterns Page vi

9 Chapter 1 Introduction 1.1 Background The Department of Defense (DoD) manages a global real property portfolio that consists of more than 562,000 facilities including barracks, commissaries, data centers, office buildings, laboratories, and maintenance depots located on more than 5,000 sites worldwide and covering more than 28 million acres. With a replacement value of about $850 billion, this infrastructure is critical to maintaining military readiness, and the cost to build and maintain it represents a significant financial commitment [21]. As part of their basic infrastructure, most installations, posts, or garrisons have short haul rail systems used to mobilize and transport supplies and equipment. These rail systems are strategically linked to the national rail network to facilitate transportation of equipment and supplies to key ports and terminals. DoD operates and maintains approximately 3000 miles of rail spread across 150 geographically dispersed facilities [28]. Rail infrastructure must compete for funding against other degrading infrastructure to include roads, buildings, utilities, etc. The current DoD budget environment and the criticality of these rail resources necessitate sound analysis of rail infrastructure investments. The fundamental challenge for leadership is to decide what repairs or replacements to make within the rail infrastructure portfolio to improve the condition of the rail infrastructure while minimizing repair costs. 1.2 Purpose The purpose of this research project is to apply a selected computational intelligence methodology to a particular DoD rail infrastructure maintenance and repair problem. Specifically, a multi-objective evolutionary algorithm is used to determine a near Pareto optimal set of rail yard infrastructure repairs for a single installation, Fort Smith. 1.3 Scope An important aspect of any research is to highlight what aspects of the problem space are within scope and those that are outside the scope of the effort. The primary dimensions of scope are: operational focus, level of repair details, time horizon, desired solution type, and operational impacts of repairs. Operational Focus: Although the methodology presented can potentially be applied to other installations, the results of this research are specific to a single notional installation (Fort Smith) with a unique rail condition profile and estimated rail repair or replacement costs. The research does not address groupings of installations rail infrastructure or other DoD rail portfolio groupings. Future research will explore expanded application of the approach. Level of Repair Detail: This research examines rail repair options at the macro-level i.e. rail repair options are limited to the broad categories of: do nothing, repair rail segment in accordance with documented recommended repairs, upgrade rail segment to 115 lb. gauge, and swap the individual rail segment. No attempt is made to dissect the recommended repairs and selectively apply only portions of the recommended repairs. Lastly, individual rail segment swaps are examined only at a macro level with an assumed cost savings. Future research may include the detailed!!! potential individual rail swaps (5408 possible swaps). Time Horizon: One would expect old, poor condition rail to degrade faster than recently repaired or upgraded rail. This research does not assume rail segment degradation rates in an attempt to project or forecast future rail condition at some future time horizon (i.e. 1 year or 5 years). The time horizon of this research is limited to the date the repair or upgrade is made. Solution Type: Other researchers have presented various techniques to identify a single, optimal solution to similar problems. However, a change in an assumption or a budget cut may result in an entirely different solution. This research instead, provides a set of near Pareto optimal solutions. Page 1

10 Multiple Pareto solutions provide decision makers flexibility and the ability to conduct trade space analysis; carefully weighing cost versus benefit (rail complex condition). Repair Scheduling and Traffic Flow: Scheduling of repairs and re-routing of rail traffic, although valid considerations are well outside the scope of this research. 1.4 Context/Background DoD recognized that they did not have a good accounting of installation rail inventory, condition, or cost to improve rail yard condition to an established threshold. In response, the U.S. Army Construction Engineer Research Lab (CERL) developed a decision support tool called RAILER. RAILER inventories installation rail assets, documents its condition, and generate cost maintenance and repair estimates [29]. RAILER also generates a prioritized rail segment repair list utilizing a prioritized worst first strategy. The RAILER recommended rail repair is utilized as a basis for comparison of our algorithm performance. Liden presents a survey of techniques and analysis applied to rail maintenance planning and scheduling [13]. This work highlights application of several mathematical and heuristic techniques, a variety of objectives, and an array of decision variables. The literature reveals numerous potential objective functions with respect to rail maintenance and prioritization to include: life-cycle cost, rail quality improvement, rail quality, weighted rail quality, cost versus rail quality improvement, cost versus rail quality, and down time. Levi utilizes renewal cost as the primary objective to determine rail renewal maintenance scheduling [12]. Track quality improvement is used by Oyama & Miwa to evaluate deterioration-based maintenance scheduling [22]. A weighted track quality index is used by Murakami & Turnquist as an objective function to analyze critical rail resource scheduling [18]. Miwa employs cost and track quality as a multi-objective approach to machine scheduling in a deterioration-based rail maintenance scheme [22]. In this research, we utilize prioritized track condition and cost as the fundamental objectives used to evaluate rail repair investment options. Not all rail segments within a rail network experience equal traffic volume or support similar functions within the installation. Typical maintenance decisions include consideration of some aspect of criticality whether it is traffic volume, mission, purpose, or degree of redundancy. Usarski & Grussing introduce a knowledge based rail inspection prioritization methodology [28]. They develop a mission-based scoring index that is a function of track segment priority, track segment condition, track segment condition degradation rate, and serious defect rate. The track segment priority is a weighted combination of segment transit volume (with consideration of hazardous materials or HAZMAT movements), and track segment mission or purpose. The methodology presented is primarily intended to inform scheduling of rail inspections but also has applicability to prioritizing repair and maintenance. We utilize a variant of the Usarski & Grussing track prioritization scheme in our solution to the Fort Smith rail repair investment problem [28]. Since rail degradation/condition is largely a function of traffic or volume, many large rail companies employ a rail replacement technique called cascading. In a cascading replacement scheme, rail is replaced along high priority, main line segments. The rail that is removed from the main line segments, given it meets a baseline condition threshold, is relayed in secondary line locations to replace a deficient rail segment. The relayed rail segment will have a longer life in its new location due to the lower degradation rate linked to the decreased traffic volume along secondary rail segments. We include consideration of a variant of cascading; swapping good condition, low priority and volume segments for poor condition, high priority segments within the rail complex. Researchers have presented several rail maintenance and repair prioritization techniques in the literature. Some of these techniques include expert systems, optimization-based, and computational intelligence approaches. Martland, McNeill, et al. present an expert system methodology (REPOMAN) that combines expert opinion of rail condition, rail deterioration models, and economic analysis to recommend Page 2

11 scheduling and prioritization of rail repair for Burlington Northern [14]. Melching and Liebman develop a heuristic algorithm for solving rail maintenance budget allocation problems via a binary knapsack approach [17]. Marzouk and Osama create a decision support tool for identifying when to repair groupings of infrastructure (i.e road and sewage, and electrical) that employs fuzzy logic to model the uncertainty in lifetime of each infrastructure sub-component with the objective of minimizing overall lifecycle repair costs [15]. Caetano & Teixeira utilize a genetic algorithm approach coupled with Pareto front analysis to recommend scheduling of rail infrastructure sub-components (rail spot repair, ballast tamping, and sleeper spot repair) to minimize both track unavailability and lifecycle cost [2]. In this research, an evolutionary algorithm solution technique is utilized. Evolutionary algorithms (EA) are a biologically inspired non-gradient optimization technique that allows the rapid and efficient exploration of vast solution space. Evolutionary algorithms (EA) have been successfully applied to multiple problem domains. Major components of an EA are a population of potential solutions (chromosomes), mechanisms to select, mate, and exchange portions of solutions with each other, and a means to evaluate solution fitness. The advantages of EA use are that they work well for objective functions that are noisy or not smooth, avoid being trapped in local optimal solutions, can search multiple points in the solution space simultaneously, and can accommodate very large numbers of objective parameters and decision variables. Multi-objective EAs (MOEA) are a special category of EA that consider multiple, often conflicting, objective functions. In the Fort Smith rail repair problem we attempt to both maximize rail yard condition while minimizing cost. Several literature sources summarize, classify, and critique various MOEA [3,10,19]. Approaches to accommodate multiple objectives in EAs can generally be categorized as aggregation-based or Pareto- based. In an aggregation approach objectives are weighted and combined into a scalar value. The objective weights may be fixed or vary as part of the chromosome as in the Hajela s and Lin s genetic algorithm (HLGA) [9]. Fuzzy inference is a non-linear aggregation approach that has been used in conjunction with EAs [16,1,23,6,8]. Pareto-based MOEA approaches utilize various dominance measures as a means to evaluate solution fitness and guide exploration of the solution space. Pareto optimality excludes from consideration all alternatives or solutions that provide no additional value over other solutions. A solution to a multi-objective problem is non-inferior if there is no other solution that yields an improvement in one objective without causing degradation in at least one other objective. A primary advantage of the Pareto-based approach is the generation of a collection of near Pareto optimal, non-dominated solutions, which allow decision makers to examine and compare the cost vs. benefits of solutions within the non-dominated solution set. Three current, commonly benchmarked, Pareto-based MOEA are Non-Dominated Sorting Genetic Algorithm (NSGAII), Pareto Envelope based Sorting Algorithm (PESA), and Strength Pareto Evolutionary Algorithm (SPEA2) [3,10,19]. The primary differences between these Pareto-based approaches are their fitness assignment scheme, diversity mechanism, and use of an external archive. NSGAII clusters solutions into Pareto fronts and assigns fitness based upon what front the solution belongs to. Crowding distance is used as a means to maintain solution diversity within the population. NSGAII does not maintain an external archive of solutions [5]. PESA utilizes a hyper-grid scheme, evaluating the number of solutions within a particular grid, to control selection and solution diversity. PESA maintains an external archive to preserve non-dominated solutions [4]. SPEA2 utilizes count and strength dominance measures to evaluate solution fitness. Count is reflected in a strength (S) score that indicates the number of solutions a particular solution dominates. Rank is the total number of solutions that dominate a particular solution and the sum of their strength scores. SPEA2 utilizes a nearest neighbor density estimate to fine tune fitness and truncate excess non-dominated solutions. Laumanns et al. compare the performance of SPEA2 against NSGAII and PESA across a suite of problems with extremely positive results [11]. In this research, we apply the SPEA2 algorithm to generate a near Pareto optimal rail repair strategy that maximizes rail yard condition while minimizing cost. Page 3

12 1.5 Approach In this research we formulate the Fort Smith rail repair investment problem as a multi-objective optimization problem that attempts to minimize cost while maximizing the overall rail condition of the complex. We include additional repair investment options not included in the current RAILER system including: do nothing, upgrading the rail to 115 lb., and swapping rail segments. This results in four potential repair options for each of the 104 rail segments within the Fort Smith rail complex. Rail segments are prioritized as a function of normalized traffic volume and transit purpose weighting. A well benchmarked, multi-objective evolutionary algorithm solution approach (Strength Pareto Evolutionary Algorithm) is applied to generate a near Pareto optimal front of solution options. Model results are compared to the RAILER prioritized, worst first output. Page 4

13 Chapter 2 Technical Details 2.1 Problem Description Fort Smith is a typical Army installation and consists of approximately 115 miles of rail, some of which has a manufacture date as far as Fort Smith s rail infrastructure is outdated and in poor condition. Fort Smith rail is 90 gauge - current industry standard for the type of traffic is 115 gauge rail. Recent inspections identified numerous rail condition safety concerns. Of the 104 track segments inspected, 1 was recommended for restricted operations and 66 were recommended closed to traffic. The estimated cost of maintenance and repair to render all current track segments defect-free is approximately $13M. The fundamental challenge for Fort Smith leadership is to decide what repairs or replacements to make in what portions of the facility in order to improve the overall condition of the rail infrastructure while minimizing repair costs. 2.2 Decisions/Tradeoffs The Fort Smith rail repair and maintenance problem is classified as a multi-objective optimization problem and consists of two competing objectives: minimize cost while maximizing the overall condition of the rail yard, considering individual track segment priority. The competing objectives for this problem are highlighted in Equations 1 and 2 below.! Minimize Cost =!!! C!" x!" (1)! Maximize Rail System Future Utility =!!! p! fc! (2) c!" is the cost of repair type j per segment i (i=1,2,3,..104; j=0,1,2,3), fc! is the future condition (after repair/upgrade) of rail segment i (Scale of 0-100: Higher better), x!" is repair type j on rail segment i, and p! is the priority of rail segment i (Scale of 0 to 1: Higher better). Available repair options include: a) do nothing, b) repair the rail segment as recommended by RAILER to improve the condition index to 100, c) completely refurbish the rail segment and upgrade to 115 gauge, and d) swap good condition rail from low traffic/low priority segments to high priority, poor condition segments. The repair options can be represented by the following decision variables: x!! = Do nothing to segment i x!! = Repair rail segment i with 90 lb rail x!! = Upgrade rail segment i with 115 lb rail x!! = Swap rail segment i There are multiple factors that influence rail repair investment decisions. First, track segments within the Fort Smith rail complex have differing purposes. The primary purpose of track segments at Fort Smith can be categorized as storage, production, access, or transit. Track segments that provide access to and from the external rail infrastructure and production lines are considered more important than those primarily utilized for intra-yard transit or storage. Second, given the nature of typical operations at Fort Smith, rail segments within the complex have varied traffic volumes. For example, rail associated with access and production has a much higher traffic volume than segments associated with storage. Lastly, the condition and associated repair costs for each rail segment vary greatly. Each of these factors both informs and increases the complexity of repair and maintenance investment decisions at Fort Smith. Page 5

14 2.3 Technical Details The CERL has developed a decision support tool (RAILER) to inventory, assess condition, and generate cost maintenance and repair estimates for installation rail infrastructure [29]. The purpose of the tool is to inform budget decisions as they relate to future repair and maintenance work. Two key modules of RAILER are rail assessment and repair cost estimation. The rail assessment module evaluates and rates the condition of tracks, track segments and overall rail network. Three components groups of each track segment are assessed on a scale of 0 to 100: ballast, subgrade and roadway index (BSCI); crossties and switch ties (TCI); and rail, joints, and fastenings (RJCI). These condition indices are based upon the number, type, and severity of defects identified during the inspection process and reflect rail capacity to support typical military installation rail traffic. Lastly, an overall track structure condition index (TSCI) is assigned to each rail segment, which is the weighted average of the BSCI, TCI, and RJCI scores. Repair costs are itemized by defect (i.e., tie, tie pins, labor, ballast, etc.) and totaled for each track segment. RAILER provides an inventory of rail assets, assesses its current condition, and estimates costs to repair identified defects. We utilize the Fort Smith RAILER condition and cost data as the fundamental data for the formulation of this problem. The TSCI for all track segments ranged from 52 to 98. A sample of the TSCI scores and estimated repair costs for selected rail segments, as computed by RAILER, are shown in Table 1 below. The entire set of Fort Smith RAILER TSCI scores and estimated repair costs are included at Appendix C. Table 1. Sample of Fort Smith RAILER Condition and Repair Cost Data Segment Code Distance Distance Ft Category RJCI TCI BSCI Cost_0 Cost_1 Cost_2 Cost_3 TSCI_0 TSCI_1 TSCI_2 TSCI_ Excellent Very Good Good Very Good Very Good Very Good Very Good Good Good Good As noted earlier, both traffic volume and track segment primary usage vary throughout the rail complex. We utilize a modified version of the Usarski and Grussing track prioritization scheme [28]. First, we analyzed monthly dispatch reports that detail Fort Smith rail movements within the complex. This data allowed us to determine annual rail segment traffic volume for each rail segment within Fort Smith. The annual rail segment traffic volume is converted to a normalized traffic score (NTS) by dividing the track segment volume by the maximum annual volume for a segment within the complex, which were segments 41 through 45 with 1872 transits per year. The NTS for a sample of Fort Smith rail segments are highlighted in in Table 2 below. The entire set of Fort Smith NTS is included at Appendix D. Page 6

15 Table 2. Sample of Normalized Traffic Scores of Rail Segments Segment Code Distance Distance Ft Yr Volume NTS Next, we categorize each rail segment into one of four categories: access, production, transit, and storage. Fort Smith rail managers prioritized and provided a weighting factor for each track segment category (See Table 3 below). Note that rail segments that primarily provide access in and out of Fort Smith are assigned the highest priority and those primarily associated with storage received the lowest priority and weighting. Table 3. Rail Segment Purpose/Priority Priority Weight Access Production Transit Storage Finally, a rail segment priority score is formed as the product of the normalized traffic score and the rail categorization weighting. Rail Segment Priority Score = NTS Rail Category Weight (3) Rail segment priority scores are then normalized resulting a normalized rail segment score ranging from zero (0) to one (1). A sample of track priority scores are highlighted in Table 4 below. The entire set of Fort Smith track priority scores are included at Appendix E. Page 7

16 Table 4. Sample of Track Segment Priority Scores Segment Code Distance Distance Ft Priority N-Prio Assumptions In this research, several simplifying assumptions are made to address incomplete or missing data and to keep the problem complexity within the intended scope of the course project. Relay Cost - Since there was no cost data available for swapping rail segments, we assume that the cost to relay a segment of rail is 25% of the cost of making the RAILER recommended repairs. Upgrade Cost - It is assumed the cost to upgrade rail to 115 gauge is $1M per mile. Traffic and Scheduling of Repairs- We assume that decisions regarding repair scheduling and traffic adjustment are outside the scope of the problem. Relay swaps We assume that all rail swaps are one for one swaps although track segments are not identical length. Additionally, we do not identify specific rail swaps but whether a swap does or does not occur. Rail Use Classification - We assume that each track segments are only categorized under one primary use category (i.e. access, production, transit, or storage). Switches and Rail Geometry- Switches and geometry specific rail considerations are outside the scope of the problem. Do Nothing Cost - We assume that the cost to not repair or replace a rail segment is 10% of the RAILER calculated cost. Page 8

17 Chapter 3 Model Development 3.1 Solution Design In this research we apply a frequently cited, commonly benchmarked, multi-objective evolutionary algorithm; the Strength Pareto Evolutionary Algorithm (SPEA2). The SPEA2 is a multi-objective, Pareto-based EA approach that employs a count and rank-based dominance fitness measure to drive solutions toward the Pareto optimal front. SPEA2 employs an elitist strategy in that it maintains an external archive of solutions and exclusively produces new solutions from the archive members. SPEA2 also utilizes a nearest neighbor density estimation technique that is used to differentiate solutions and maintain solution spread (diversity) within the archive. SPEA2 was selected because of its common use as a benchmark for multi-objective EAs. SPEA2 is designed for multi-objective problems like the Fort Smith rail repair investment problem. The technique produces a near Pareto optimal front, vice a single solution, which provides the decision maker the opportunity to consider trade space analysis. SPEA2 also works to eliminate solutions that are similar by using its density calculations to maintain diversity or spread along the Pareto front. 3.2 Solution Representation An evolutionary algorithm requires that the solution alternatives be encoded as a string (chromosome). Solution alternatives can be encoded according to several formats including: binary, integer, or numerous other combinations. We encode Fort Smith rail segment repair solution alternatives according to the scheme indicated in Figure 1 below. Bit Segment Figure 1. Solution Representation Scheme Each alternative is encoded as a 208-length string. The entire string is composed of 104- repeated two-bit sub-sequence. The two bit sub-elements are binary encoded representations of 0, 1, 2, or 3, which translate to: do nothing, repair, upgrade, or relay that particular rail segment. The particular alternative depicted in Figure 1 above represents upgrade of rail Page 9

18 segment 1, repair rail segment 2, swap rail segment 3, repair rail segment 4, swap rail segment 5, and do nothing with rail segment SPEA2 Overview The pseudo code for the SPEA2 algorithm is highlighted in Figure 2 below. The SPEA2 algorithm begins with a population and an empty external archive. The external archive is an application of EA elitist strategy in which a collection of high quality solutions are maintained and used exclusively for mating of future generations. Typically, the archive size is equal to the population size. However, that is not necessary and in this research we utilize an archive size less than the population size (i.e. 20). Next, the fitness values, which are Pareto dominance based measures, are calculated for both the population and archive. The specifics of the fitness measure are detailed in the following section. All non-dominated solutions from the population and archive are copied to the subsequent archive. If the number of non-dominated solutions exceeds the archive size, excess non-dominated solutions are deleted from the archive based upon on a nearest neighbor density measure presented in the next section. SPEA2 Algorithm Step 1: Generate initial population and empty archive. Set t = 0. Step 2: Calculate fitness values of individuals in and. Step 3: = non-dominated individuals in and. If size of > N then reduce, else if size of < N then fill with dominated individuals in and Step 4: If t > T then output the non-dominated set. Stop. Step 5: Step 6: Fill mating pool by binary tournament selection with replacement on. Apply recombination and mutation operators to the mating pool and set to the resulting population. Set t = t+1 and go to Step 2. Figure 2. SPEA 2 Pseudo Code A mating pool is formed using binary tournament selection. Members of the mating pool are randomly paired for recombination of genetic material to form new offspring or solutions. We utilize single point crossover and bit flip mutation as the primary recombination operators. The above process is repeated until termination criteria, in this case number of generations, are met. At termination, the output of the algorithm is the final archive. Page 10

19 3.4 Fitness Assessment The competing objectives of the Fort Smith rail repair investment problem are repair cost and rail yard condition. Repair costs are a function of the repair option selected. Doing nothing (0) to a rail segment results in a cost equal to 10% of the RAILER estimated cost to repair the segment. The cost of repairing (1) the rail segment is equal to the RAILER repair estimate. Upgrading a rail segment from 90 lb. to 115 lb. costs approximately $1M per mile of rail. Table 5 below provides pertinent sample cost data for rail segments 1-5 and 104. Table 5. Sample of Track Segment Costs (costs in $1000s) Segment Code Distance Distance Ft Distance Mi Cost_0 Cost_1 Cost_2 Cost_ Segment Figure 3. Sample Solution Chromosome To calculate the cost of the sample solution in Figure 4: Segment 1: Upgrade to 115 lb rail (2) = $226 Segment 2: Repair (1) = $ Segment 3: Swap Rail (3) = $ Segment 4: Repair (1) = $ Segment 5: Swap Rail (3) = $ Segment 104: Do Nothing (0) = $ The second fundamental objective in this research is prioritized rail condition. In Section 2.2 above, we presented the methodology for calculating track segment priority as a function of normalized track score (NTS) or traffic volume and transit purpose. Table 6 highlights the priority and condition information for the rail segments represented by the chromosome in Figure 3. Page 11

20 Table 6. Sample of Track Segment Priority Scores Segment Code Distance Distance Ft Distance Mi Purpose Wt Volume Yr Volume NTS Priority N-Prio TSCI_0 TSCI_1 TSCI_2 TSCI_ Transit Transit Access Access Access Transit The condition score for the sample chromosome is: Condition =.02*(115)+.02*(100)+.133*(87.6)+.133*(100)+.133*(89.6)+.036*(72) (4) SPEA2 employs a count and rank-based dominance fitness measure to quantify the quality of candidate solutions. As such, a strength (S) and raw fitness (R) score are calculated as shown in Equation 5 for each solution. The strength score, highlighted in Equation 4 above, indicates the number of other solutions a particular solution dominates. The objectives in this research are cost and overall rail condition of the complex and we seek to maximize condition while minimizing cost. One solution dominates another if a better condition is generated at a lower or equal cost compared to the competing solution. For example, in Figure 5 below, solution A dominates solution C because it provides a higher condition score at a lower cost. The S column of the table on the right portion of Figure 4 lists the strength scores for solutions A-H. (5) Condition G F B H A E C D Cost S R Dominates Dominated By A 3 0 C,D,E None B 3 0 H,D,E None C 1 3 D A D 0 9 None C,H,A,B E 0 6 None H,A,C F 1 0 E None G 0 0 None None H 2 3 D,E B Figure 4. SPEA 2 Strength (S) and Raw Fitness (R) Illustration The raw fitness (R) score, Equation 6, indicates the total number of other solutions that dominate a particular solution. For example, in Figure 4 above, solution E is dominated by Page 12

21 solutions A, B, C, and H therefore it s raw fitness score is the sum of the strength scores of A,B,C, and H (9). The R column of the table on the right portion of Figure 4 lists the strength scores for solutions A-H. Note that solutions with an R score of zero are non-dominated solutions. Solutions are further differentiated by adding a nearest neighbor density factor to the raw fitness score. The details of which are discussed in the next section. (6) 3.5 Density Estimation, Final Fitness, and Archive Truncation SPEA2 utilizes a nearest neighbor density estimate to both fine tune fitness and delete excess non-dominated solutions from the archive. The calculation of the density estimate (D) is shown in Equation 7 below. K is the square root of the sum of the population size and the archive size. Note that solutions with a larger kth nearest neighbor (farther away from neighbor solutions) will have a smaller density score. where (7) The final fitness of each solution or chromosome is the sum of the density estimate (D) and the raw fitness (R) as indicated by Equation 8. As noted earlier, the density estimate (D) is also used to delete excess members within the archive. For example, Figure 5 below shows seven non-dominated solutions currently in the archive. Assuming that the archive size is five, we must truncate 2 non-dominated solutions from the archive. Solution A and D have the largest and second largest density scores amongst the non-dominated solutions in the archive and are therefore truncated. (8) Page 13

22 Condition XA C Condition C B B F X D F E E G G Cost Cost Figure 5. Density Estimate to Truncate Archive 3.6 Recombination and Mutation Evolutionary algorithms employ various techniques that recombine high quality solutions to generate improved offspring or solutions. Crossover is the most common recombination technique. Crossover techniques include single point, two point, cut and splice, and uniform crossover. In this research, we utilize single point crossover. In single point crossover, two parent chromosomes are paired for mating, a random crossover point along the chromosome string is selected, and the tails of the parent chromosomes are swapped (See Figure 6 below). This results in two new offspring that have genetic material from both parents. Crossover Point Parents Children Figure 6. Single Point Crossover Page 14

23 Mutation is used to randomly change a bit within a chromosome. Mutation is typically assigned a much lower probability of occurring than crossover. However, the purpose of mutation is to assist the algorithm from breaking free of local optima and to introduce diversity within the population of solutions. Simple bit flip mutation is utilized in this research. 3.7 EA Operational Parameters Evolutionary algorithms employ several operational parameters that control the evolution of solutions as subsequent generations are produced. These parameters include population size, archive size, selection technique, crossover rate, mutation rate, and termination criteria. Population size represents how many solution alternatives will be generated, evaluated, and carried forward from generation to generation. The selection function determines which solution alternatives will survive to the next generation. Selection techniques include: proportionate, roulette wheel, and tournament schemes. Crossover entails the exchange of solution segments between paired or mated chromosomes and mutation is the random variation of a gene within a chromosome. An EA can typically be terminated via several criteria to include: number of generations or solution improvement. Under the number of generation termination criteria, the EA is stopped once the max generations are reached. A solution improvement-focused termination criteria identifies a solution improvement threshold. If solution improvement stalls or does not exceed the solution improvement threshold, the EA run is terminated. Note that extensive research has been conducted regarding the appropriate settings for these key operational parameters and is outside the scope of this paper [13,25,27,28,29,30,31,38]. Table 7 below highlights the major operational parameters for our multi-objective EA approach. Table 7. EA Operational Parameters Population Size 50 Archive Size 20 Selection Technique Binary Tournament Crossover Rate 0.9 Mutation rate 0.1 Termination 500 Generations The evolutionary algorithm described above was programmed utilizing MATLAB. The detailed code is included at Appendix F. Page 15

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25 Chapter 4 Results 4.1 Results The multi-objective evolutionary algorithm presented earlier was run with an archive size of twenty and several different random number seeds. Multiple random number seeds (50) were used to ensure the solutions obtained were not merely a result of the randomly generated initial population. It is recognized in the literature that the SPEA2 algorithm has above average computation burden with the inherent requirement to conduct pairwise comparison calculations of the population and archive strength (S) scores, the raw fitness scores (R), and the nearest neighbor density estimates (D). The average algorithm run time for an archive size of 20 was 254 seconds. Finally, we examine the model output in general as well as in comparison to the RAILER generated prioritized, worst first solution. 4.2 Analysis Table 8 below highlights the generalized model output for 50 random number seeds with 500 generations per run, an archive size of 20 and a population size of 50. The Fort Smith as is condition score is out of a maximum possible score of Across all 50 random number seeds, 561 non-dominated solutions were generated. On average, each archive contained approximately 11 non-dominated solutions. The smallest number of non-dominated solutions observed within a final solution archive was 7. The maximum non-dominated solutions observed within a final solution archive was 20. The best condition score, across all random number seeds, was at a cost of $19.659M. The minimum cost, across all random number seeds, was $6.124M with a resulting condition score of Table 8. General Output Results Across all Seeds Archive 20 Max Alg. Condition ($19.659M) Min Alg. Cost $6.124M (760.34) Avg % Non-Dom 56.00% Avg Number Non_Dom 11.2 Avg Run Time sec Current Condition Max Possible Cond ($84.345M) Min Possible Cost $1.291M (560.38) The SPEA2 algorithm is designed to move solutions toward the Pareto optimal front while maintaining spread or diversity along the non-dominated front. Figure 7 below shows the theoretical solution evolution as well as the evolution of solutions for an actual algorithm run with archive snapshots at 50,100, and 500 generations. Note the solution movement toward the Page 17

26 Pareto optimal front and the increased spread along the front between generation 100 and the final output at generation 500. Condition Maximize Diversity Cost Minimize Distance to Pareto Optimal Ideal SPEA2 Movement 50 Generations 100 Generations 500 Generations Figure 7. SPEA2 Solution Evolution Table 9 below summarizes the general pattern across all non-dominated solutions across all random number seeds. In general, non-dominated solutions show a preference for repair or swap of rail segments. The least preferred repair option across non-dominated solutions is upgrade of a rail segment from 90 lb. to 115 lb. likely due to the $1M per mile cost for this upgrade. Page 18

27 Table 9. General Pattern across all non-dominated Solutions Across all Seeds Do Nothing Repair Upgrade Swap 21.74% 30.18% 18.28% 29.80% 4.3 Comparison of Output to RAILER As noted earlier, RAILER recommends repairs based upon a prioritized, worst first strategy. Table 10 below highlights the first several recommended repairs using this strategy. The entire prioritized list of repairs is included in Appendix H. Since RAILER only considers repair or do nothing as options, the best possible condition attainable is at a cost of $12.9M. Table 10. RAILER Top 10 Recommended Repairs Segment Priority Condition Repair Cost Below we analyze the results for the output from a single seed and compare its results to that of RAILER (Table 11). Note that all non-dominated solutions in the final archive generate a higher condition code than RAILER. All but one final archive solution provides a higher condition score at a lower cost. The rail segment-repair recommendations for the 20 non-dominated solutions in Figure 8 are included at Appendix G. Page 19

28 Table 11. Single Seed Non-Dominated Final Archive Solution Cost Condition Figure 8 below further illustrates the stark comparison between the RAILER solution and the SPEA2 final non-dominated archive solutions. Note how the RAILER solution is dominated by all non-dominated solutions in the final archive. Page 20

29 Best Possible RAILER Condition Figure 8. Final Archive Solutions vs. RAILER We examined each individual rail segment across all non-dominated solutions highlighted in Table 11 to see if there was a consistent recommendation for a rail segment across all solutions. The results are highlighted in Table 12. Table 12. Consistent Rail Recommendations Across all Non-Dominated Solutions Segment Do Nothing 1,12,18,20,21,32,34,48,56,57,60,62-64,66,67,69,78 Repair 5-7,11,23,26,42-44,53,71,72,79,81,82,87,91,95,98,104 Upgrade 10,14,39,45,46,52,88,89,90,92,93,101 Swap 16,19,28,35,41,49,55,61,65,68,70,74-77,80,97,99,103 Page 21

30 Further analysis of Table 12 reveals some general patterns across the non-dominated solutions. Non-dominated solution preference is to repair or swap rail segments. Swap of rail segments is generally recommended for low priority/low condition rail segments (See Table 13). Table 13. General Non-Dominated Solution Patterns Do Nothing Repair Upgrade Swap 24.95% 30.58% 16.35% 28.13% Low Priority High Condition High Priority Low-Mid Condition Low Priority Low Condition 4.4 Challenges A primary challenge during this research was the tendency for archives to populate with groupings of identical non-dominated solutions. At times, the entire archive was populated by 3 or 4 groupings of identical non-dominated solutions. The selection technique, binary tournament selection, was not discriminant enough to bias identical non-dominated solutions. The density information only became a factor when deleting excess non-dominated solutions (a rare occurrence). This problem was eliminated once the code was modified to only allow unique non-dominated solutions to enter the archive. The second minor challenge was time required to run repeated repetitions of the algorithm. As noted earlier, the SPEA2 algorithm has above average computation burden with the inherent requirement to conduct pairwise comparison calculations of the population and archive strength (S) scores, the raw fitness scores (R), and the nearest neighbor density estimates (D). At 254 seconds per run it requires about 3.5 hours to run all 50 random number seeds. This will become a bigger factor if one desires to experiment with the EA parameters (i.e. population size, crossover rate, mutation rate, and archive size). Page 22

31 Chapter 5 Summary 5.1 Conclusions In this research, we employ a well-benchmarked Pareto-based MOEA (SPEA2) to the Fort Smith rail repair problem. The solutions generated dominate the RAILER solution. Utilizing the RAILER prioritized worst first scheme, the best condition achieved is a score of 768 at a cost of $12.9M. Additionally, this solution does not include any options other than do nothing or repair. Each of the solutions in the selected archive of 20 non-dominated solutions exceeds the RAILER condition and 19 of the 20 solutions achieve this at a cost well under the $12.9M RAILER solution. The general strategy highlighted within the SPEA2 generated non-dominated solutions is to recommend doing nothing to low priority/high condition rail segments, swap low priority/low condition segments, and upgrade high priority low to mid condition segments. The collection of non-dominated solutions provided by this technique provide the decision makers both flexibility and the ability to evaluate whether an additional cost solution is worth the increase rail condition. 5.2 Future Work There are several areas for additional research related to the Fort Smith rail repair investment problem as well as the algorithms employed to solve it. First, an explicit consideration of the exact rail swaps could be included in the problem formulation and analysis. It was highlighted earlier that this adds!! decision variables to the problem. The problem formulation could also! be modified to include a degradation factor with a look at forecasting the condition of the rail condition at some point in the future. An experimental design examining the EA parameters (archive size, population size, selection technique, crossover rate, and mutation rate) effect on generated solutions may provide fruitful research opportunity. Lastly, the problem could be solved using the NSGAII (Non-Dominated Sort Genetic Algorithm) and PESA (Pareto Envelopebased Selection Algorithm), algorithms to compare results and overall performance. Page 23

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33 Appendix A References [9] [1] S. Agarwal et al., Flexible and Intelligent Learning Architectures for SoS (FILA-SoS): Architectural Evolution in Systems-of-Systems, Procedia Computer Science, vol. 44, pp , [41] [2] L. Caetano and P. Teixeira, Availability approach to optimizing railway track renewal operations, Journal of Transportation Engineering, vol.139 (9), pp , [4] [3] C.A. Coello, "Evolutionary multi-objective optimization: a historical view of the field," IEEE Comput. Intell. Mag., Vol. 1(1), pp , [35] [4] D. Corne et al., The Pareto Envelope-Based Selection Algorithm for Multi-objective Optimisation, Proceedings of the 6th International Conference on Parallel Problem Solving from Nature, London, pp , [14] [5] K. Deb et al., A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II, Lecture notes in computer science, 1917, pp , [15] [6] M.S. Dojutrek et al., A Fuzzy Approach for Assessing Transportation Infrastructure Security, in Complex Systems Design & Management, Switzerland: Springer International Publishing, 2015, pp [13] [7] E. Eiben et al., Parameter control in evolutionary algorithms, IEEE Trans. Evol. Comput. vol. 3(2), pp , [18] [8] M. Gunduz et al., "Fuzzy assessment model to estimate the probability of delay in Turkish construction projects," J. Manage. Eng., vol. 31(4), pp.1-14, July [38] [9] Hajela and C.-Y. Lin, Genetic search strategies in multicriterion optimal design, Structural Optimization, New York: Springer, vol. 4, pp , June [5] [10] A. Konak et al., Multi-objective optimization using genetic algorithms: A tutorial, Reliability Engineering & System Safety, vol. 91(9), pp , [11] M. Laumanns et al., SPEA2: Improving the strength Pareto evolutionary algorithm, Swiss Federal Institute of Technology, Zurich, Switzerland, Tech. Rep. TIK-Report 103, May [42] [12] D. Lévi, "Optimization of track renewal policy," World Congress on Railway Research, Cologne [36] [13] T. Lidén, Railway infrastructure maintenance-a survey of planning problems and conducted research, Transportation Research Procedia, vol. 10, pp , [33] [14] C. Martland et al. "Applications of expert systems in railroad maintenance: scheduling rail relays," Transportation Research Part A: General, vol. 24(1), pp , [39] [15] M. Marzouk and A. Osama, "Fuzzy approach for optimum replacement time of mixed infrastructures." Civil Engineering and Environmental Systems, ahead of print, pp. 1-12, Page 25

34 [8] [16] W.L. McGill and B.M. Ayyub, "Multicriteria security system performance assessment using fuzzy logic," The Journal of Defense Modeling and Simulation: Applications, Methodology, Technology, vol. 4(4), pp , [34] [17] C. Melching and J. Liebman, "Allocating railroad maintenance funds by solving binary knapsack problems with precedence constraints," Transportation Research Part B: Methodological, vol. 22(3), pp , [37] [18] K. Murakami and M. Turnquist, Dynamic model for scheduling maintenance of transportation facilities, Transportation Research Record, (1030), pp. 8 14, [20] [19] T. Murata and H. Ishibuchi, MOGA: multi-objective genetic algorithms, Evolutionary Computation, vol. 1, pp , November [30] [20] K. Nag and T. Pal, A new Archive based Steady State Genetic Algorithm, IEEE World Congr. Comput. Intell., Brisbane, Australia, pp. 1-7, June [43] [21] Office of Secretary of Defense for Installation and Environment, Real Property Inventory Requirements Document, [40] [22] T. Oyama and M. Miwa, Mathematical modeling analyses for obtaining an optimal railway track maintenance schedule, Japan Journal of Industrial and Applied Mathematics, vol. 23(2), pp , [10] [23] L. Pape et al., A fuzzy evaluation method for system of systems meta-architectures, Procedia Computer Science, vol. 16, pp , [29] [24] A. Petrowski, A Clearing Procedure as a Niching Method for Genetic Algorithms, Int. Conference Evol. Comput., pp , May [27] [25] N. Sangkawelert and N. Chaiyaratana, Diversity control in a multi-objective genetic algorithm, Congr. Evolutionary Computation, vol. 4, pp , [28] [26] B. Sareni and L. Krahenbuhl, Fitness Sharing and Niching Methods Revisited, IEEE Trans. Evol. Comput., vol. 2(3), pp , September [25] [27] A. Shukla et al, "Comparative Review of Selection Techniques in Genetic Algorithm," 1st Intl. Conf. on Futuristic trend in Computational Analysis and Knowledge Management, pp , [23] [28] D. Uzarski and M. Grussing, Beyond mandated track safety inspections using a missionfocused, knowledge-based approach, International Journal of Rail Transportation, vol. 1(4), pp , [24] [29] D. Uzarski et al., The RAILER System for Maintenance Management of US Army Railroad Networks: RAILER 1 Description and Use, Construction Engineering Research Lab (CERL), Champaign, IL, Tech. Rep. CERL-TR-M-88/18, [31] [30] L. Wang et al., An improved elitist strategy multi-objective evolutionary algorithm, Proc. Intl. Conf. Mach. Learning and Cybern., Dalian, pp , August Page 26

35 Appendix B Acronyms Acronym BSCI CERL DoD EA HAZMAT MOEA NSGAII NTS PESA R RCI RJCI S SPEA2 TCI TSCI USACE Name Ballast and Subgrade Condition Index Construction Engineering Research Laboratory Department of Defense Evolutionary Algorithm Hazardous Materials Multi-objective Evolutionary Algorithm Non-Dominated Sort Genetic Algorithm Normalized Traffic Score Pareto Envelope Based Search Algorithm SPEA2 Raw Fitness Score Rail Condition Index Rail, Joints, and Fastenings SPEA2 Strength Score Strength Pareto Evolutionary Algorithm Tie and Crosstie Condition Index Track Structure Condition Index United States Army Corps of Engineers Page 27

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37 Appendix C Rail Segment Cost and Condition Data Segment Code Distance Distance Ft Distance Mi Category RJCI TCI BSCI Cost_0 Cost_1 Cost_2 Cost_3 TSCI_0 TSCI_1 TSCI_2 TSCI_ Excellent Very Good Good Very Good Very Good Very Good Very Good Good Good Good Good Good Good Very Good Very Good Good Good Good Good Good Good Good Good Very Good Very Good Good Very Good Good Very Good Very Good Very Good Very Good Very Good Fair Very Good Very Good Very Good Very Good Very Good Very Good Very Good Very Good Excellent Excellent Very Good Very Good Very Good Very Good Excellent Very Good Very Good Very Good Excellent Excellent Excellent Excellent Very Good Excellent Excellent Very Good Very Good Very Good Very Good Very Good Very Good Very Good Very Good Very Good Excellent Good Very Good Very Good Good Good Good Good Very Good Excellent Good Good Very Good Good Good Very Good Very Good Good Good Good Very Good Very Good Very Good Very Good Excellent Very Good Very Good Good Good Good Good Good Good Very Good Good Very Good Page 29

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39 Appendix D Rail Segment Volume and Normalized Transit Score Segment Code Distance Distance Ft Distance Mi Volume Yr Volume NTS Priority Page 31

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41 Appendix E Rail Segment Priority Scores Segment Code Distance Distance Ft Priority N-Prio Page 33

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43 Appendix F Rail Evolutionary Algorithm Code clear close all %% %% I. Set GA parameters maxgen=5; % maximum number of iterations (for stopping criteria) popsize=100; % set population size mutrate=0.01; % set mutation rate crossrate=.5; %crossover rate nbits=2; % number of bits in each parameter npar=104; % number of parameters in each chromosome Nt=nbits*npar; % total number of bits in a chromosome %Import supporting cost and condition data from spreadsheet cost_cond_data=xlsread('c:\users\rail data.xls'); %pull appropriate cost and condition data from rail v2 spreadsheet a=cost_cond_data(1:npar,9:12); a(1:npar,5:9)=cost_cond_data(1:npar,19:23); min_cost=1.2e3; max_cost=8.5e3; min_cond=1450; max_cond=2100; %% %%II. Generate initial population %Generate initial population of 50 chromosomes of 0 and 1 clear pop pop=round(rand(popsize,nt)); %% %%Main Loop for gen=1:maxgen clear matepool; clear cross_pop; clear mut_pop; %% %Transform the 2 bit sequences of each chromosome string into decimal %values of 0,1,2,or3 for n=1:popsize%population size or number of chromosomes for j=1:npar%number of segments pop2(n,j)=bin2dec(int2str(pop(n,(2*j-1):2*j))); end end %% %%III. Calculate Costs %Calculate cost and weighted condition fitness of each chromosome and append %to each chromosome as last 2 bits Page 35

44 for n=1:popsize%population size or number of chromosomes sum_cost=0; sum_cond=0; for j=1:npar sum_cost=sum_cost+a(j,1+pop2(n,j)); sum_cond=sum_cond+a(j,5)*a(j,6+pop2(n,j)); end pop(n,nt+1)=sum_cost; pop(n,nt+2)=sum_cond; end w=pop(1:popsize,(nt+1):(nt+2)); %%Prepare for Pa % %Calculate Pareto Strength (S) archive=zeros(popsize,2); archive(:,1)=84400; clear dominate dominate=false(popsize*2); temp=[w;archive]; n=length(temp); %% %Determine which solutions dominate others and populate domination matrix for j=1:n for k=1:n if(temp(j,1)<temp(k,1)) & (temp(j,2)>temp(k,2)); dominate(k,j)=true; end end end %% %Calculate Strength Score (S) for i=1:n S(i)=sum(dominate(:,i)); end %% %Calculate Raw Fitness (R) for i=1:n R(i) = sum(s(dominate(i,:))); end %% %Calculate and sort distance distance=zeros(2*popsize); for i=1:n for j=1:n distance(j,i)=(((temp(i,1)-temp(j,1))^2)+((temp(i,2)- temp(j,2))^2))^.5; end Page 36

45 end closest_neighbor = round(sqrt(popsize*2)); %Sort Distance distancesort=sort(distance,1,'ascend'); for i=1:n d(i)=(1/(distancesort(closest_neighbor,i)+2)); end %Calculate fitness for i=1:n F(i)=R(i)+d(i); end %Sort Fitness [b,i]=sort(f,'ascend'); %Fill Archive num_nd=max(find(b<1)); % num_nd=min(num_nd,20); clear archive2; if num_nd<=popsize archive2(1:popsize,:) = [pop(i(1:popsize),:), R(I(1:popsize))',F(I(1:popsize))']; else archive2(1:num_nd,:)=[pop(i(1:num_nd),:),r(i(1:num_nd))',f(i(1:num_nd))']; temp1=distance(i(1:num_nd),i(1:num_nd)); for k = 1:num_nd-popsize size_a2 = size(archive2); d2 = sort(temp1); range_temp = [1:length(temp1)]; j=1; while j < num_nd range_temp2 = find(d2(j,range_temp)<=min(d2(j,range_temp))); range_temp = range_temp(range_temp2); if(length(range_temp)==1) j = num_nd; end j= j+1; end row_to_del = min(range_temp) rows_to_keep = [1:(row_to_del-1) row_to_del+1:size_a2(1)]; rows_to_keep2 = [1:(row_to_del-1) row_to_del+1:length(temp1)]; temp_archive = archive2(rows_to_keep,:); temp2 = temp1(rows_to_keep2, rows_to_keep2); archive2 = temp_archive; Page 37

46 temp1 = temp2; end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %Create mating pool num=size(archive2,1); matepool=zeros(num,size(archive2,2)); for i=1:num comp=randsample(num,2); if archive2(comp(1),nt+4)<archive2(comp(2),nt+4) matepool(i,:)=archive2(comp(1),:); else matepool(i,:)=archive2(comp(2),:); end end %Pair mates=zeros(num/2,2); for i=1:num/2 mates(i,:)=randsample(num,2); end %% %Perform Crossover % Crossover using single point crossover matepool_size=size(matepool,1); rand_cross=rand(1,matepool_size/2); cross_point=ceil(rand(1,matepool_size/2)*(nt-1)); % crossover point for i=1:matepool_size/2; if rand_cross(i)<crossrate cross_pop(2*i-1,:)=[matepool(mates(i,1),1:cross_point(i)) matepool(mates(i,2),cross_point(i)+1:nt+4)];% % first offspring cross_pop(2*i,:)=[matepool(mates(i,2),1:cross_point(i)) matepool(mates(i,1),cross_point(i)+1:nt+4)];% % second offspring else cross_pop(2*i-1,:)=matepool(mates(i,1),:); cross_pop(2*i,:)=matepool(mates(i,2),:); end %if end %% %Mutate the population nmut=ceil((matepool_size-1)*nt*mutrate); % total mutations mut_row=ceil(rand(1,nmut)*(matepool_size-1))+1; % row to mutate mut_col=ceil(rand(1,nmut)*nt); % column to mutate mut_pop=cross_pop; for i=1:nmut mut_pop(mut_row(i),mut_col(i))=abs(cross_pop(mut_row(i),mut_col(i))-1);% flips bits end Page 38

47 pop=mut_pop(:,1:nt); %% %Plot Final Results figure; plot(archive2(:,nt+1),archive2(:,nt+2),'k.') axis([1e4 8.5e ]); end Page 39

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49 Appendix G SPEA2 Rail Model Output R a i l S e g m e n t Solution Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing 1 Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do 2 Repair Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 3 Upgrade Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 4 Upgrade Upgrade Upgrade Upgrade Swap Swap Upgrade Upgrade Swap Swap Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade 5 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 6 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 7 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 8 Upgrade Upgrade Upgrade Upgrade Swap Swap Swap Upgrade Swap Swap Upgrade Upgrade Upgrade Swap Swap Upgrade Upgrade Upgrade Upgrade Upgrade 9 Repair Repair Repair Repair Repair Repair Nothing Repair Repair Repair Repair Repair Repair Nothing Nothing Repair Repair Repair Repair Repair Do Do Do 10 Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade 11 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 12 Upgrade Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 13 Do Nothing Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 14 Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade 15 Do Nothing Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Do Nothing Upgrade Upgrade Do Nothing Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade 16 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 17 Repair Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do 18 Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 19 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 20 Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do 21 Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 22 Upgrade Swap Swap Swap Swap Swap Swap Repair Swap Swap Repair Swap Swap Swap Swap Swap Swap Swap Swap Swap 23 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 24 Repair Repair Repair Repair Repair Repair Repair Swap Repair Repair Swap Repair Repair Repair Repair Repair Repair Repair Repair Repair 25 Upgrade Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 26 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 27 Swap Swap Swap Swap Swap Swap Swap Repair Swap Swap Repair Swap Swap Swap Swap Swap Swap Swap Swap Swap 28 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 29 Upgrade Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 30 Upgrade Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 31 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 32 Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do 33 Repair Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 34 Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 35 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 36 Repair Repair Nothing Repair Repair Repair Nothing Nothing Repair Repair Nothing Repair Repair Nothing Nothing Nothing Nothing Nothing Nothing Repair Do Do Do Do Do Do Do Do Do Do 37 Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Do Nothing Do Nothing Upgrade Upgrade Do Nothing Upgrade Upgrade Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 38 Swap Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 39 Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade 40 Do Nothing Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 41 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 42 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 43 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 44 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 45 Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade 46 Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade 47 Upgrade Repair Repair Upgrade Upgrade Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 48 Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 49 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 50 Swap Repair Repair Swap Swap Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 51 Do Nothing Repair Repair Do Nothing Do Nothing Do Nothing Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 52 Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade 53 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 54 Repair Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 55 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 56 Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do 57 Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 58 Repair Repair Do Nothing Repair Repair Repair Repair Repair Repair Do Nothing Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 59 Do Nothing Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 60 Do Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do 61 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 62 Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 63 Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 64 Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 65 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 66 Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 67 Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing Do Nothing 68 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 69 Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do 70 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 71 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 72 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 73 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Upgrade Swap Swap Swap Swap Swap Swap Upgrade Swap 74 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 75 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 76 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 77 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 78 Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Nothing Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do Do 79 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 80 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 81 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 82 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 83 Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Swap Upgrade Upgrade Upgrade Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 84 Repair Repair Repair Repair Repair Repair Swap Repair Repair Repair Repair Swap Repair Swap Repair Swap Swap Swap Swap Swap 85 Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Swap Upgrade Upgrade Upgrade Upgrade Swap Upgrade Swap Upgrade Swap Swap Swap Swap Swap 86 Repair Repair Repair Repair Repair Repair Swap Repair Repair Repair Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 87 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 88 Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade 89 Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade 90 Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade 91 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 92 Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade 93 Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade 94 Swap Repair Repair Swap Swap Swap Repair Repair Repair Repair Repair Swap Repair Repair Repair Repair Swap Repair Swap Repair 95 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 96 Repair Swap Swap Repair Repair Repair Swap Swap Swap Swap Swap Repair Swap Swap Swap Swap Repair Swap Repair Swap 97 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 98 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair 99 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 100 Repair Upgrade Upgrade Repair Upgrade Upgrade Repair Upgrade Upgrade Upgrade Upgrade Repair Upgrade Upgrade Upgrade Upgrade Repair Repair Repair Repair 101 Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade Upgrade 102 Do Nothing Repair Repair Do Nothing Repair Repair Do Nothing Repair Repair Repair Do Nothing Do Nothing Do Nothing Repair Do Nothing Repair Do Nothing Do Nothing Do Nothing Do Nothing 103 Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap Swap 104 Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Repair Cost Condition Page 41

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51 Appendix H RAILER Prioritized Repair List Segment Priority Condition Repair Cost Page 43

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54 Department of Systems Engineering United States Military Academy West Point, New York DISTRIBUTION C. Distribution authorized to U.S. Government agencies and their contractors only; operational use; December Other requests for this document shall be referred to the Product Director Joint Services PD-JS, Picatinny, New Jersey