An Efficient Application of Goal Programming to Tackle Multiobjective Problems with Recurring Fitness Landscapes
This work addresses the problem of efficiently handling similar multiobjective instances for decision-makers, but it is incremental as it builds on existing goal programming and multiobjective techniques.
The paper tackles the challenge of solving multiobjective problems with recurring fitness landscapes by proposing a method that combines expensive multiobjective algorithms for one instance with efficient goal programming for others, achieving good results on benchmark vehicle routing problems with time windows in short computation time.
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.