An Efficient Application of Goal Programming to Tackle Multiobjective Problems with Recurring Fitness Landscapes

TL;DR

This paper introduces a hybrid approach combining multiobjective algorithms and goal programming to efficiently solve multiple related instances of complex decision problems with similar fitness landscapes, demonstrated on vehicle routing benchmarks.

Contribution

It proposes a novel methodology that exploits recurring fitness landscape features to reduce computation time while maintaining solution quality in multiobjective problems.

Findings

Effective in producing good solutions quickly on benchmark instances.

Combines strengths of multiobjective algorithms and goal programming.

Applicable to scenarios with recurring fitness landscape features.

Abstract

Many real-world applications require decision-makers to assess the quality of solutions while considering multiple conflicting objectives. Obtaining good approximation sets for highly constrained many-objective problems is often a difficult task even for modern multiobjective algorithms. In some cases, multiple instances of the problem scenario present similarities in their fitness landscapes. That is, there are recurring features in the fitness landscapes when searching for solutions to different problem instances. We propose a methodology to exploit this characteristic by solving one instance of a given problem scenario using computationally expensive multiobjective algorithms to obtain a good approximation set and then using Goal Programming with efficient single-objective algorithms to solve other instances of the same problem scenario. We use three goal-based objective functions and show that on benchmark instances of the multiobjective vehicle routing problem with time windows, the methodology is able to produce good results in short computation time. The methodology allows to combine the effectiveness of state-of-the-art multiobjective algorithms with the efficiency of goal programming to find good compromise solutions in problem scenarios where instances have similar fitness landscapes.