Controlling Crossover in a Selection Hyper-heuristic Framework

In evolutionary algorithms, crossover is used to recombine two candidate solutions to yield a new solution which hopefully inherits good material from both. Hyper-heuristics are high-level search methodologies which operate on a search space of heuristics. Hyper-heuristics can be broadly split into two categories; heuristic selection and generation methodologies. Here we will investigate hyper-heuristics from the former category. Selection hyper-heuristics select a heuristic to apply from an existing set of low-level heuristics at a given point in the search. Crossover is increasingly being included in general purpose hyper-heuristic frameworks 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 needed for crossover, a mechanism is required to control the choice of the other solution. We propose a framework which maintains a list of potential solutions for use in crossover. We investigate the control of such lists at two levels. Firstly, crossover is controlled at the hyper-heuristic level where no problem speci c information is required. Secondly, it is controlled at the problem domain level where problem speci c information is used to produce good quality solutions to use for crossover. A number of selection hyper-heuristics are tested over three well-known benchmark libraries for an NP-hard optimisation problem; the multidimensional 0-1 knapsack problem (MKP). Exact solvers such as CPLEX also use heuristics and have improved signi cantly since the last published application to some of the benchmark data. New results are presented using CPLEX 12.2 over the benchmark instances. *Corresponding author