Multiobjective fitness landscape analysis and the design of effective memetic algorithms

For a wide variety of combinatorial optimization problems, no efficient algorithms exist to exactly solve the problem unless P= NP. For these problems, metaheuristics have come to dominate the landscape. Encompassing several widely used techniques such as simulated annealing, tabu search, evolutionary algorithms, alit colony optimization, and other methods, metaheuristics provide the state of the art for many such problems. In recent years, researchers in these areas have begun to consider problems with multiple objectives. As the number of algorithms proposed to solve multiobjective optimization problems has increased, it has become apparent that there is a general lack of understanding of the issues governing the performance of different types of algorithms. The primary motivation for this work is to improve the state of multiobjective optimization by providing a means by which practitioners may obtain a better understanding of the important issues governing multiobjective optimization algorithm performance. The goal of this work is thus to provide a framework for multiobjective fitness landscape analysis that can be used to gain a greater understanding of the interaction between problem structure and search algorithm performance in multiobjective optimization. Under the umbrella of multiobjective fitness landscape analysis, a number of techniques are proposed that provide researchers with important information concerning particular types of problems and how to effectively solve them. The utility of the methods described within is demonstrated using a set of three benchmark classes of assignment problems, the Quadratic Assignment Problem, Generalized Assignment Problem, and a real-world example, the Sailor Assignment Problem. While unified under the label of assignment problems, each type of problem exhibits significant differences in structure. It is shown that the proposed landscape analysis techniques, when applied to these disparate types of assignment problems, yield insights that can be used to formulate more effective algorithms. The primary contributions of this work are a unified framework for multiobjective fitness landscape analysis and an improved understanding of when particular types of multiobjective algorithms perform well. In particular, multiobjective memetic algorithms, combinations of multiobjective evolutionary algorithms and local search operators, are examined using this framework. It is shown that the analysis presented here can help suggest better performing multiobjective memetic algorithms. In addition, a new benchmark multiobjective optimization problem, the Multiobjective Generalized Assignment Problem is proposed, and its relevant features explored.