Application to Winner Determination Problems in Combinatorial Auctions

Abstract

The crucial idea behind DE is the scheme of generating mutant vectors using the weighted difference of other vectors randomly chosen from the population. This mutation operation relies on arithmetic operations (add, subtract, multiply, etc.) rather than general data manipulation operations (sort, swap, permute, etc.). It cannot be directly extended to the discrete combinatorial space.

In this chapter, we apply parameter adaptive differential evolution to a seminal combinatorial optimization problem of winner determination in Combinatorial Auctions (CAs). To adapt JADE to this problem, we use a rank-based representation scheme that produces only feasible solutions and a regeneration operation that constricts the search space. It is shown that JADE compares favorably to the classic DE algorithm, a local stochastic search algorithm Casanova, and a genetic algorithm based approach SGA.