El-Ghazali Talbi (Ed.) Metaheuristics for Bi-level Optimization. ^ Springer

Transcription

1 El-Ghazali Talbi (Ed.) Metaheuristics for Bi-level Optimization ^ Springer

2 Contents 1 A Taxonomy of Metaheuristics for Bi-level Optimization 1 El-Ghazali Talbi 1.1 Introduction Bi-level Optimization Concepts Bi-level Optimization Problems Complexity and Optimality Conditions Relationships with Other Problems Bi-level versus Stackelberg Games Bi-level versus Multi-objective Problems Bi-level versus Set-Valued Optimization Problems Applications of Bi-level Optimization Metaheuristics S-metaheuristics P-metaheuristics Metaheuristics for Bi-level Optimization Metaheuristics Based on Nested Approach Metaheuristics Based on Reformulation to Single-Level Optimization Problems Metaheuristics Based on Transformation to Multi-objective Optimization Problems Co-evolutionary Metaheuristics Performance Assessment of Bi-level Metaheuristics Performance Indicators Conclusions and Perspectives 33 References 34 2 A Genetic Algorithm for Power System VulnerabUity Analysis under Multiple Contingencies 41 Jose M. Arroyo, Francisco J. Fernandez 2.1 Introduction Power System Vulnerability Analysis Attacker-Defender Models 44

3 XII Contents 2.4 Genetic Algorithm: An Evolutionary Metaheuristic Structure of a Genetic Algorithm Proposed Genetic Algorithm for Attacker-Defender Models Application: Maximum Vulnerability Model with Line Switching Problem Formulation Particular Features of the Genetic Algorithm Approach Numerical Results Conclusions 63 References 65 3 A Bilevel Particle Swarm Optimization Algorithm for Supply Chain Management Problems 69 Yannis Marinakis, Magdalene Marinaki 3.1 Introduction Bilevel Programming Supply Chain Management Problems Vehicle Routing Problem Location Routing Problem Bilevel Particle Swarm Optimization Algorithm General Description of the Bilevel Particle Swarm Optimization Algorithm (PSOBilevel) Particle Swarm Optimization Expanding Neighborhood Search Results Conclusions and Future Research 90 References 90 4 CoBRA: A Coevolutionary Metaheuristic for Bi-level Optimization 95 Frangois Legillon, Arnaud Liefooghe, El-Ghazali Talbi 4.1 Introduction Bi-level Optimization General Principles of Bi-level Optimization Meta-heuristic Approaches for Bi-level Optimization CoBRA, a Coevolutionary Meta-heuristic for Bi-level Optimization General Principles CoBRA Components General Algorithm Performance Assessment and Bi-level Optimization Motivations Rationality Discussion 103 ' 101

4 Contents XIII 4.5 Application to Bi-level Transportation A Bi-level Multi-depot Vehicle Routing Problem A Multi-objective Bi-level Multi-depot Vehicle Routing Problem : Experimental Analysis Experimental Design CoBRA instantiation for BiMDVRP an M-BiMDVRP Experimental Results Conclusions and Future Works 112 References A Matheuristic for Leader-Follower Games Involving Facility Location-Protection-Interdiction Decisions 115 Deniz Aksen, Necati Aras 5.1 Introduction and Background Man-Made Attacks as a Source of Disruption Preliminary Interdiction Models Recent Network and Power Grid Interdiction Models Protection-Interdiction Models Location-Interdiction and Network Design-Interdiction Models The Triple Problem of Facility Location-Protection-Interdiction Two Service Network Design Models A Location-Protection-Interdiction Model for Coverage-Type Networks A Location-Protection-Interdiction Model for Median-Type Networks A Tabu Search Based Matheuristic for the BFCLP Background of Tabu Search Key Features of the Tabu Search Algorithm TSH Partial Validation of TSH Solutions with Exhaustive Search Computational Results Random Generation of Test Instances Preliminary Analysis of the Neighborhood Structure Test results of TSH Comparison of the Best TSH Solutions with the ESV-p Results Sensitivity of the TSH Solutions to Problem Parameters Effect of the Protection Costs on the Best Facility Configuration Conclusions 147 References 148

5 XIV Contents 6 A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications 153 Andrew Koh 6.1 Introduction The Bi-level Programming Problem A General BLPP Mathematical Programs with Equilibrium Constraints Solution Algorithms for the BLPP Differential Evolution for Bi-Level Programming (DEBLP) Differential Evolution Control Parameters of DE Implicit Assumptions of DEBLP Applications to Transportation Systems Management The Lower Level Program in Transportation Continuous Optimal Toll Pricing Problem (COTP) Continuous Network Design Problem Applications to Parameter Estimation Problems Formulation of EIV Model Examples Handling Upper Level Constraints Overview of Constraint Handling Techniques with Meta-Heuristics Stochastic Ranking Revised DEBLP with Stochastic Ranking Applications to Generalised Nash Equilibrium Problems The Generalised Nash Equilibrium Problem Nikaido Isoda Function Solution of the GNEP Examples Discussion Summary and Conclusions Summary Further Research 179 References Matheuristics and Exact Methods for the Discrete (r p)-centroid Problem 189 Ekaterina Alekseeva, Yury Kochetov 7.1 Introduction The Problem Statement The Bi-level Mixed Integer Linear Formulation The Min-Max Formulation The Single-Level Mixed Integer Linear Formulation The Brief Overview of Related Works Complexity Status 198

6 Contents XV 7.4 Heuristics for the Discrete (r p)-centroid Problem Median Heuristics Alternative Heuristics Hybrid Heuristics : Exact Methods The Branch-and-Cut Method An Iterative Exact Method Computational Experiments Conclusions 216 References Exact Solution Methodologies for Linear and (Mixed) Integer Bilevel Programming 221 Georgios K.D. Saharidis, Antonio J. Conejo, George Kozanidis 8.1 Introduction Description of the Bilevel Problem Solution Approaches for the Linear Bilevel Problem Solution Approaches for the Mixed Integer Bilevel Problem Bilevel Programming Applications Summary 241 References Bilevel Multi-Objective Optimization and Decision Making 247 Ankur Sinha, Kalyanmoy Deb 9.1 Introduction Multi-objective Bilevel Optimization Problems Real World Problems Existing Classical and Evolutionary Methodologies Theoretical Developments Algorithmic Developments Evolutionary Methods Development of Tunable Test Problems Hybrid Bilevel Evolutionary Multi-Objective Optimization (H-BLEMO) Algorithm Update of Population Sizes Termination Criteria Step-by-Step Procedure Algorithmic Complexity Results on Test Problems Scalability Study Comparison with a Nested Algorithm Incorporating Decision Maker Preferences in H-BLEMO Progressively Interactive Hybrid Bilevel Evolutionary Multi-Objective Optimization Algorithm (PI-HBLEMO) Step 3: Preference Elicitation and Construction of a Value Function 273

7 XVI Contents Termination Criterion Modified Domination Principle Results Accuracy and DM Calls Conclusions 280 References 281 Index 285