Implementation of Multiobjective Memetic Algorithms for Combinatorial Optimization Problems: A Knapsack Problem Case Study

Abstract

In this chapter, we discuss various issues related to the implementation of multiobjective memetic algorithms (MOMAs) for combinatorial optimization problems. First we explain an outline of our MOMA, which is a hybrid algorithm of NSGA-II and local search. Our MOMA is a general framework where we can implement a number of variants. For example, we can use Pareto dominance as well as scalarizing functions such as a weighted sum in local search. Through computational experiments on multiobjective knapsack problems, we examine various issues in the implementation of our MOMA. More specifically, we examine the following issues: the frequency of local search, the choice of initial solutions for local search, the specification of an acceptance rule of local moves, the specification of a termination condition of local search, and the handling of infeasible solutions. We also examine the dynamic control of the balance between genetic operations (i.e., global search) and local search during the execution of our MOMA. Experimental results show that the hybridization with local search does not necessarily improve the performance of NSGA-II whereas local search with problem-specific knowledge leads to drastic performance improvement. Experimental results also show the importance of the balance between global search and local search. Finally we suggest some future research issues in the implementation of MOMAs.