Selection hyper-heuristics for the multi and many-objective quadratic assignment problem

Abstract

Hyper-heuristics (HH) emerged as more generalized and robust solutions for combinatorial optimization, being successfully addressed to solve several real-world problems. Implemented within an association of MOEA/DD and Differential Evolution, four selection hyper-heuristics (high-level heuristics) are studied in this work: Thompson Sampling, Probability Matching, Adaptive Pursuit and Self-Adaptive Differential Evolution. In the proposal, low-level heuristics rely on crossover performed by operators taken from a candidate pool. The HH selection is based on operators’ previous performance during the evolutionary process, using a warm-up phase necessary to provide proper information regarding the most efficient operators. A discard mechanism is also considered to eliminate from the pool operators with similar performance. To evaluate the proposed approach, Quadratic Assignment Problem (QAP) instances are considered with 2, 3, 5, 7 and 10 objectives, totaling 148 instances with different dimensions and correlations between the flow matrices. Statistical tests indicate that the best version of the proposed approach, named HHMOEA/DD, outperforms those with fixed crossover operator and different literature approaches. In addition, the experiments indicate results’ improvement by the joined inclusion of the warm-up and operator discard mechanisms.