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Evolutionary Algorithms for Bi-level Programming Problems with Integer Variables

Author: SongQiGang
Tutor: LinDan
School: Tianjin University
Course: Operational Research and Cybernetics
Keywords: Genetic Algorithms Bi-level programming NSGA-II Pareto-optimal frontier
CLC: O221
Type: Master's thesis
Year: 2009
Downloads: 29
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Abstract


The bi-level programming problem (BLPP) is an optimization problem arising from hierarchical decision-making. In this model, decision-makers, whose position in the decision-making is different, can be divided into the upper level decision-maker (UDM) with a higher decision-making power (Leader) and the lower level decision-maker (LDM) (Follower). The upper and lower levels constitute the programming problems with their own objective function and decision-making variables respectively. The UDM’s decision-making affects the LDM’s directly and its decision-making mechanism is Stackelberg positive master-slave strategy. The BLPP with some integer decision variables in the upper level exists in the investment decision-making, resource allocation, production management and the other practical fields, and as a result of the complexity of practical problems, the upper level is often a multi-objects programming problem.The most simple single-object bi-level linear programming problem of bi-level programming model has been proved to be a NP-hard problem, so heuristic algorithm is used to solve the problem as inevitable choice. With its various advantages, evolutionary algorithm (EA) has been applied to the bi-level linear or nonlinear programming in order to solve the problem. But only the traditional continuous variable models are considered, and the problems are limited to single-object case. Multi-objects BLPPs are first translated into single-object problems, and then solved in evolutionary strategy algorithm. There are no works that are solved in multi-objects evolutionary algorithm directly.Based on extensive and thorough reading of the literature both at home and abroad, this thesis makes an in-depth theoretical study on the fundamental theories and methods of Genetic Algorithms and we apply GA to design a valid algorithm for bi-level programming problems with some integer decision variables in the upper level. The gist is as follows:i. A systematic and detailed introduction of the general procedure, fundamental theories and methods of Genetic Algorithms.ii. A brief introduction of bi-level programming problems’ concepts, an analysis of the BLPP’s research status, and some algorithms for BLPP.iii. An algorithm based on ordinary EAs for BLPP with some integer decision variables in the upper level, utilizing existing constraint handling strategy and selection mechanism.iv. The effectiveness of the suggested methods is demonstrated by performing some numerical experiments on some problem instances and comparing the results to those published in literature

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CLC: > Mathematical sciences and chemical > Mathematics > Operations Research > Planning Theory ( mathematical programming)
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