Memetic Algorithms for Multiobjective Optimization: Issues, Methods and Prospects

Abstract

Summary. The concept of optimization-finding the extrema of a function that maps candidate 'solutions' to scalar values of 'quality'-is an extremely general and useful idea that can be, and is, applied to innumerable problems in science, industry, and commerce. However, the vast majority of 'real' optimization problems, whatever their origins, comprise more than one objective; that is to say, 'quality' is actually a vector, which may be composed of such distinct attributes as cost, performance, profit, environmental impact, and so forth, which are often in mutual conflict. Until relatively recently this uncomfortable truth has been (wilfully?) overlooked in the sciences dealing with optimization, but now, increasingly, the idea of multiobjectiue optimization is taking over the centre ground. Multiobjective optimization takes seriously the fact that in most problems the different components that describe the quality of a candidate solution cannot be lumped together into one representative, overall measure, a t least not easily, and not before some understanding of the possible 'tradeoffs' available has been established. Hence a multiobjective optimization algorithm is one which deals directly with a vector objective function and seeks to find multiple solutions offering different, optimal tradeoffs of the multiple objectives. This approach raises several unique issues in optimization algorithm design, which we consider in this article, with a particular focus on memetic algorithms (MAS). We summarize much of the relevant literature, attempting to be inclusive of relatively unexplored ideas, highlight the most important considerations for the design of multiobjective MAS, and finally outline our visions for future research in this exciting area.

A Hybrid NSGA-II Algorithm for Multiobjective Quadratic Assignment Problems

“…While the constraints of QAP are 0-1 assignment constraints, the objective function is nonlinear, because of the quadratic structure. Based on these two reasons, QAP is classified as NP-Hard, and it is almost impossible to find optimal solutions if the number of instances is greater than 20 [2]. Thus, besides the exact solution methods to solve this kind of problems, metaheuristic algorithms like genetic algorithms, tabu search and neural networks [3,4] have been proposed.…”

“…Based on the multi objective structure of real life problems [5][6][7], multiobjective quadratic assignment problems (mQAP) were suggested by Knowles and Corne [2]. The difference of mQAP from the QAP is that it has multiple flow matrices (m > 2).…”

“…In addition, more than one nonlinear objective functions have to be considered. The objective of mQAP is [2]:…”

On the use of informed initialization and extreme solutions sub-population in multi-objective evolutionary algorithms

“…These combinations of evolutionary and local search are known by the names of Memetic Algorithms (MAs) [24], Hybrid Evolutionary Algorithms [10], [11], [17], and Genetic Local Search (GLS) [23]. These hybrids of evolutionary and local search algorithms have been shown to provide state-of-theart performance on a wide range of hard single objective combinatorial optimization problems [23], [21], [25] and also have shown to provide a good performance on multiobjective optimization problems [15], [16], [20], [17], [19], [22]. This paper proposes two modifications to improve the performance of multiobjective evolutionary algorithms through the use of a particular form of hybridization.…”

Local Search for Multiobjective Function Optimization: Pareto Descent Method

“…In order to avoid such a problem, GA can be hybridized with local search (LS), and the effectiveness of the hybridization has been demonstrated in the literature [6,7,9]. LS methods for multiobjective function optimization such as Evolution Strategies (ES) [8], Multiobjective Steepest Descent Method (MSDM) [4], Combined-Objectives Repeated Line-search (CORL) [1] have been proposed.…”