Multiobjective Resource Allocation Problems By Multistage Hybrid Genetic Algorithm

　　Multiobjective Resource Management Problems (m-RMP) involves deciding how to divide a resource of limited availability among multiple demands in a way that optimizes current objectives. RMP is widely used to plan the optimal allocating or management resources process among various projects or business units for the maximum product and the minimum cost. “Resources” might be manpower, assets, raw materials, capital or anything else in limited supply. The solution method of RMP, however, has its own problems; this book identifies four of them along with the proposed methods to solve them. Mathematical models combined with effective multistage Genetic Algorithm (GA) approach help to develop a method for handling the m-RMP. The proposed approach not only can solve relatively large size problems but also has better performance than the conventional GA. And the proposed method provides more flexibility to m-RMP model which is the key to survive under severely competitive environment. We also believe that the proposed method can be adapted to other production-distribution planning and all m-RAP models.
In this book, four problems with m-RMP models will be clearly outlined and a multistage hybridized GA method for finding the best solution is then implemented. Comparison results with the conventional GA methods are also presented. This book also mentions several useful combinatorial optimization models in process system and proposed effective solution methods by using multistage GA.

　　Note：Part of this book, once published in international journals SCI (Science Direct) inside, be accepted have five articles.

作者簡介：

林吉銘 (Chi-Ming Lin)

　　電子信箱：chiminglin.tw@gmail.com

　　學歷
　　日本國立兵庫教育大學 教育學碩士
　　日本早稻田大學資訊生產系統研究所5年研究
　　日本公立前橋工科大學工學研究所 工學博士

　　經歷
　　教育部 專員
　　國立台北教育大學 兼任講師
　　台北市立教育大學 兼任講師
　　中央警察大學 兼任講師
　　國立台南師範大學 兼任講師
　　美和技術學院 專任講師
　　長庚技術學院 專任講師
　　桃園縣公、私立托兒所 評鑑委員
　　開南大學 專任講師(現職)

Acknowledgements3
Absract of Chinese 4
Abstract8

Chapter 1 Introduction2
1.1 Background of the Study2
1.2 Related Work7
1.2.1 Genetic Algorithm7
1.2.2 Multiobjective Genetic Algorithm36
1.3 Resource Management Problems54
1.4 Problems in this Dissertation58
1.4.1 A Solution Method for Human RMP Optimization58
1.4.2 A Solution Method for Asset RMP Optimization58
1.4.3 A Solution Method for Capital RMP Optimization58
1.4.4 A Solution Method for Staff Training RMP Optimization59
1.5 Organization of the Dissertation59

Chapter 2 Multistage Genetic Algorithm in Resource Management System65
2.1 Introduction65
2.2 Basic Idea67
2.2.1 Basic Idea Description67
2.2.2 Structure of Resource Management Solution System71
2.2.3 Multistage Network Framework74
2.2.4 Linearization76
2.2.5 Local Search78
2.3 Mathematical Formulations78
2.4 Constructing Multistage Network Structure81
2.4.1 Example One82
2.4.2 Example Two84
2.5 Solving Method by Multistage Genetic Algorithm90
2.5.1 Example Three93
2.5.2 Example Four99
2.6 Experimental Results102
2.6.1 Facility Allocation Problem102
2.6.2 Problem Description of Multiobjective Human RMP104
2.6.3 Experimental Results of Multiobjective Human RMP105
2.7 Summary110

Chapter 3 Optimization for Multiobjective Assets RMP by Multistage GA112
3.1 Introduction112
3.2 Problem Description113
3.2.1 There is Assets Resources Now113
3.2.2 The Data in the Past113
3.2.3 The Problem of Enterprise Boss Expects to be Solved114
3.3 Mathematical Model of Multiobjective Assets RMP115
3.4 Experimental Results and Discussion in First Part122
3.4.1 Experiments Results in the First Part122
3.4.2 Discussion in First Part125
3.5 Experimental Results and Discussion in Second Part134
3.5.1 Experimental Results in Second Part134
3.5.2 Discussion in Second Part139
3.6 Summary144

Chapter 4 Multistage GA for Optimization of Multiobjective Capital RMP149
4.1 Introduction149
4.2 Mathematical Model of Multiobjective Capital RMP153
4.3 Solution Approaches for Multiobjective Capital RMP155
4.3.1 Candidate Mutual Funds Selection155
4.3.2 Multistage Hybrid GA of Multiobjective Capital RMP156
4.3.3 Pareto Optimal Solution159
4.3.4 Adaptive Weight GA161
4.4 Numerical Example of Multiobjective Capital RMP164
4.4.1 Problem Description164
4.4.2 The Goal of the Problem Reached in Research166
4.4.3 Numerical Example of Multiobjective Capital RMP167
4.5 Discussion of Multiobjective Capital RMP175
4.6 Summary178

Chapter 5 Optimization of Staff Training RMP by Multistage GA182
5.1 Introduction182
5.2 Concepts of Competence Set183
5.3 Mathematical Model187
5.4 Solution Approaches by Multistage Hybrid GA191
5.4.1 Genetic Representation191
5.4.2 Evaluation193
5.4.3Selection193
5.5 Numerical Examples195
5.5.1 Problem Description195
5.5.2 The Goal of the Problem Reached in Research196
5.6 Summary209

Chapter 6 Conclusions and Future Research 213
6.1 Conclusions213
6.2 Future Research219

Glossary220
Notations220
Abbreviations222
Bibliography223
List of Publications231
International Journal Papers231
International Conference Papers with Review232

Index235

List of Figure
Figure 1.1: The Flow Chart of Genetic Algorithm11
Figure 1.2: Procedure-code of Basic GA12
Figure 1.3: Coding Space and Solution Space17
Figure 1.4: Feasibility and Legality18
Figure 1.5: The Mapping from Chromosomes to Solutions21
Figure 1.6: An Example of One-cut Point Crossover Operation24
Figure 1.7: Procedure-code of One-cut Point Crossover Operation25
Figure 1.8: An Example of Mutation Operation by Random27
Figure 1.9: An Example of Mutation Operation by Random27
Figure 1.10: Procedure-code of Multiobjective GA54
Figure 2.1: Proposed Structure of Resource Management Solution System72
Figure 2.2: Proposed a Flowchart of Resource Management Solution System73
Figure 2.3: An Example of Complex Multistage Network Framework74
Figure 2.4: Representation of Multistage Network Approach for RMP75
Figure 2.5: Representation Process for RMP83
Figure 2.6: Representation Process for RMP84
Figure 2.7: A Multistage Network of Human RMP90
Figure 2.8: The Code of Random Key-based Encoding in Procedure 194
Figure 2.9: The Code of Weight Generating in Procedure 295
Figure 2.10: An Example of Weight Generating96
Figure 2.11: An Example of One-cut Point Crossover Operator96
Figure 2.12: The Example of Insertion Mutation98
Figure 2.13: Proposed Structure of a Chromosome100
Figure 2.14: An Example   of Optimal Allocation Path101
Figure 2.15: Proposed Chromosome Structure for Four Stages Allocation Path101
Figure 2.16: The Pareto Optimal Solutions of Weighted-sum Method107
Figure 2.17: The Pareto Optimal Solutions of Proposed Method108
Figure 3.1: An Example of Complex Multistage Network Framework114
Figure 3.2: The Path Process of Two Objectives in Each Node119
Figure 3.3: Simulation Results for Multiobjective Assets RMP121
Figure 3.4: The Simulation Results of pri-GA124
Figure 3.5: The Simulation Results of msh-GA124
Figure 3.6: Preference Solutions with Pareto Optimal Solutions by pri-GA137
Figure 3.7: Preference Solutions with Pareto Optimal Solutions by msh-GA137
Figure 4.1: Simple Case with Two Objectives160
Figure 4.2: The Procedure of Pareto GA161
Figure 4.3: Adaptive Weights and Adaptive Hyperplane163
Figure 4.4: The Process Path of Two Objectives in Each Node168
Figure 4.5: An Example for Multiobjective Capital RMP169
Figure 4.6: Experiment Results by Two Methods172
Figure 5.1: The Cost Function of CSE184
Figure 5.2: CSE in Multistage Network Model186
Figure 5.3: An Example of State Permutation Encoding for CSE Operation.192
Figure 5.4: An Example of State Permutation Decoding for CSE Operation.192
Figure 5.5: An Example of Evaluation for CSE193
Figure 5.6: An Example of Selection for CSE193
Figure 5.7: The Procedure of msh-GA for Multistage CSE194
Figure 5.8: An Example of CSE for Staff Training RMP198
Figure 5.9: The Process Path of Two Objectives in Each Arc199
Figure 5.10: A Solution Example of Pareto Optimal Solutions for CSE200
Figure 5.11: Simulation Results of CSE for Staff Training RMP205

List of Table
Table 2.1: Transportation Costs102
Table 2.2: Maintenance Costs of Each Facility102
Table 2.3: The Parameters Setting of Experiment102
Table 2.4: Transportation Amounts from Each Facility to Each Consumer103
Table 2.5: Total Cost of Facility Allocate Transportation by Two Methods103
Table 2.6: An Example of Expected Wage of Programmer (Workers)106
Table 2.7: An Example of Expected Product Number of Task (Job)106
Table 2.8: The Parameter Settings of Experiment106
Table 2.9: Experiment Results of Two Methods108
Table 2.10: Experiment Results of Overall Average by Two Methods109
Table 3.1: The Data of the Company in the Past 4 Years117
Table 3.2: An Example of Expected Cost in 4 Districts  118
Table 3.3: An Example of Expected Selling Goods in 4 Districts118
Table 3.4: The Total Number of Feasible Solutions for Process Planning120
Table 3.5: The Parameter Settings of Experiment122
Table 3.6: Experiment Rs of the Pareto Optimal Solutions123
Table 3.7: Experiment Result of Two Methods125
Table 3.8: Same Preference Solution for Minimum Cost127
Table 3.9: Same Preference Solution for Maximum Selling Goods Number129
Table 3.10: Preference for Golden Mean within Pareto Optimal Solutions131
Table 3.11: The Parameter Settings of msh-GA136
Table 3.12: Experiment Results for Pareto Optimal Solutions138
Table 3.13: Preference for Golden Mean within Pareto Optimal Solutions141
Table 4.1: 3-months and 12-months Return Rates for 60 Sample Companies165
Table 4.2: Reordering Data Sets of Mutual Funds165
Table 4.3: The Total Number of Feasible Solutions for Process Planning169
Table 4.4: The Covariance Matrix170
Table 4.5: The Parameters Setting of Experiment170
Table 4.6: Experiment Results of Pareto Optimal Solutions by Two Methods171
Table 4.7: Experiment Results for the Optimal Portfolio174
Table 4.8: The Optimal Portfolio Solution of Sharpe Ratio174
Table 5.1: Total Numbers of Feasible Solutions for CSE200
Table 5.2: An Example of Data for CSE203
Table 5.3: Parameters Settings204
Table 5.4: Pareto Optimal Solutions for Multiobjective CSE204
Table 5.5: Experiment Results of the Pareto Optimal Solutions207
Table 5.6: Experiment Results of Pareto Optimal Solutions208

Abstract

　　Multiobjective Resource Management Problems (m-RMP) involves deciding how to divide a resource of limited availability among multiple demands in a way that optimizes current objectives. RMP is widely used to plan the optimal allocating or management resources process among various projects or business units for the maximum product and the minimum cost. “Resources” might be manpower, assets, raw materials, capital or anything else in limited supply.

　　The solution method of RMP, however, has its own problems; this thesis identifies four of them along with the proposed methods to solve them. Mathematical models combined with effective multistage Genetic Algorithm (GA) approach help to develop a method for handling the m-RMP. The proposed approach not only can solve relatively large size problems but also has better performance than the conventional GA. And the proposed method provides more flexibility to m-RMP model which is the key to survive under severely competitive environment. We also believe that the proposed method can be adapted to other production-distribution planning and all m-RAP models.

　　In this thesis, four problems with m-RMP models will be clearly outlined and a multistage hybridized GA method for finding the best solution is then implemented. Comparison results with the conventional GA methods are also presented. This study also mentions several useful combinatorial optimization models in process system and proposed effective solution methods by using multistage GA. In the areas of future research, the methods outlined in this study might be applied to combinatorial optimization of m-RMP involving areas of education, portfolio selection or areas of industrial engineering design, product process planning system amongst many others.