Combining basic heuristics for solving multi-objective scheduling problems

Abstract

We present an agent-based approach to multiobjective combinatorial optimization. It allows to flexibly combine elementary heuristics that may be optimal for the corresponding single objective problem. In the multi-objective case a smart combination of such heuristics is supposed to efficiently approximate the whole Pareto-front of trade-off solutions. Exemplarily, we optimize an instance of the bi-objective single-machine scheduling problem and show that the modular building block architecture of our optimization model and the distribution of acting entities enable the integration of problem specific knowledge. We present a universal mutation operator for combinatorial problem encodings that allows to construct certain solution strategies, such as advantageous sorting or known optimal sequencing procedures. In this way, it becomes possible to derive more complex heuristics from atomic local heuristics that are known to tackle fractions of the complete problem. We unveil that it is possible to cover different areas of the Pareto-front with special operators and make evident that the whole front can be covered if those operators are applied simultaneously. Further, we apply this concept also to two more challenging multi-objective scheduling problems, that involve the objectives makespan, total completion time, and number of tardy jobs.