A Fuzzy Hyper-Heuristic Approach for the 0-1 Knapsack Problem

Hyper-heuristics are potent techniques that represent the synergy of low-level heuristics when solving optimization problems. This synergy usually leads to better solutions. Similarly, fuzzy logic has been successfully applied to several domains, thanks to the expert knowledge it encompasses. Thus, combining the benefits of both approaches should lead to a more reliable and effective method. Hence, in this work, we propose a fuzzy-based selection hyper-heuristic model. We considered seven features and four low-level heuristics, which represent the inputs and output of the fuzzy inference system, respectively. Each input was defined with two membership functions. Since there is no expert knowledge available, we lay out all the rules (128) and use a genetic algorithm to find optimum values for the consequents of these rules. In other words, the genetic algorithm will evolve the rules of the fuzzy inference system until it become an expert, and will then save such knowledge as the set of fuzzy rules. The main concern of this paper is to find out if a fuzzy inference system can help to get better results in the inner working of a hyperheuristic. To prove this, we make a comparison between a fuzzy hyper-heuristic model optimized by a genetic algorithm against three traditional selection hyper-heuristic models (with a different number of rules) optimized by a particle swarm optimization method. We applied all these methods using the same set of low-level heuristics to solve an 800 instance set of the 0-1 Knapsack problem as a testbed.