Differential evolution for discrete optimization: An experimental study on Combinatorial Auction problems

Differential evolution (DE) mutates solution vectors by the weighted difference of other vectors using arithmetic operations. As these operations cannot be directly extended to discrete combinatorial space, DE algorithms have been traditionally applied to optimization problems where the search space is continuous. In this paper, we use JADE, a self-adaptive DE algorithm, for winner determination in combinatorial auctions (CAs) where users place bids on combinations of items. To adapt JADE to discrete optimization, we use a rank-based representation schema that produces only feasible solutions and a regeneration operation that constricts the problem search space. It is shown that JADE compares favorably to a local stochastic search algorithm, Casanova, and a genetic algorithm based approach, SGA.