Enhancing Hyperheuristics for the Knapsack Problem through Fuzzy Logic

Abstract

Hyperheuristics rise as powerful techniques that get good results in less computational time than exact methods like dynamic programming or branch and bound. These exact methods promise the global best solution, but with a high computational time. In this matter, hyperheuristics do not promise the global best solution, but they promise a good solution in a lot less computational time. On the contrary, fuzzy logic provides the tools to model complex problems in a more natural way. With this in mind, this paper proposes a fuzzy hyperheuristic approach, which is a combination of a fuzzy inference system with a selection hyperheuristic. The fuzzy system needs the optimization of its fuzzy rules due to the lack of expert knowledge; indeed, traditional hyperheuristics also need an optimization of their rules. The fuzzy rules are optimized by genetic algorithms, and for the rules of the traditional methods, we use particle swarm optimization. The genetic algorithm will also reduce the number of fuzzy rules, in order to find the best minimal fuzzy rules, whereas traditional methods already use very few rules. Experimental results show the advantage of using our approach instead of a traditional selection hyperheuristic in 3200 instances of the 0/1 knapsack problem.