Evolutionary and heuristic algorithms for multiobjective 0-1 knapsack problem

Abstract

We consider a formulation of multiobjective 0-1 knapsack problem which involves a single knapsack. We solve this problem using multiobjective evolutionary algorithms (MOEAs), and quantify the solution-fronts obtained; we observe that they show good diversity and (local) convergence. Then, we consider two heuristic algorithms and observe that the quality of solutions obtained by MOEAs is much inferior. Interestingly, none of the MOEAs could yield the entire coverage of the Pareto-front. Therefore, we incorporate problem-specific knowledge in the initial population, and get good quality solutions using MOEAs too. The main point we stress with this work is that, for real world applications of unknown nature, it is indeed difficult to realize how good/bad is the quality of the solutions obtained. Conversely, if we know the solution space, it is trivial to get the desired solution space using MOEAs, which is a paradox in itself.