Evolution of hyperheuristics for the biobjective 0/1 knapsack problem by multiobjective genetic programming

Abstract

The 0/1 knapsack problem is one of the most exhaustively studied NP-hard combinatorial optimization problems. Many different approaches have been taken to obtain an approximate solution to the problem in polynomial time. Here we consider the biobjective 0/1 knapsack problem. The contribution of this paper is to show that a genetic programming system can evolve a set of heuristics that can give solutions on the Pareto front for multiobjective combinatorial problems. The genetic programming (GP) system outlined here evolves a heuristic which decides whether or not to add an item to the knapsack in such a way that the final solution is one of the Pareto optimal solutions. Moreover, the Pareto front obtained from the GP system is comparable to the front obtained from other human-designed heuristics. We discuss the issue of the diversity of the obtained Pareto front and the application of strongly-typed GP as a means of obtaining better diversity.