A Case Study of Controlling Crossover in a Selection Hyper-heuristic Framework with MKP

In evolutionary algorithms, crossover operators are used to recombine multiple candidate solutions to yield a new solution that hopefully inherits good genetic material. Hyper-heuristics are high-level methodologies which operate on a search space of heuristics for solving complex problems. In a selection hyper-heuristic framework, a heuristic is chosen from an existing set of low-level heuristics and applied to the current solution to produce a new solution at each point in the search. Crossover is increasingly being included in general purpose hyper-heuristic tools such as HyFlex and Hyperion, however little work has been done to assess how best to utilise it. Since a single-point search hyper-heuristic operates on a single candidate solution and two candidate solutions are required for crossover, a mechanism is required to control the choice of the other solution. The frameworks we propose maintain a list of potential solutions for use in crossover. We investigate the use of such lists at two conceptual levels. Firstly, crossover is controlled at the hyper-heuristic level where no problemspecific information is required. Secondly, it is controlled at the problem domain level where problem-specific information is used to produce good quality solutions to use for crossover. A number of selection hyper-heuristics are compared using these frameworks over three benchmark libraries with varying properties for an NP-hard optimisation problem; the multidimensional 0-1 knapsack problem. It is shown that allowing crossover to be managed at the domain level outperforms managing crossover at the hyper-heuristic level in this problem domain.