MAXIMIZING THE ACCEPTED BIDS OVER THE ε-NON-DOMINATED NONCONVEX SET FOR A MULTIOBJECTIVE WINNER DETERMINATION PROBLEM USING AN EVOLUTIONARY APPROACH

Abstract

ABSTRACT This paper addresses the Winner Determination Problem (WDP) within a multiobjective framework, extending the traditional approach that focuses solely on revenue maximization. We develop a mathematical model that simultaneously integrates four strategic objectives: maximizing the number of accepted bids, total revenue, the value of items (including unsold ones), and sales diversification. To solve this complex problem, we propose a novel approach that consists of optimizing a function over the set of ε-non-dominated solutions. We implement an Estimation of Distribution Algorithm (EDA), an evolutionary metaheuristic that models the probability distribution of promising solutions to efficiently guide the search. The performance and robustness of our approach are validated through numerical experiments, which demonstrate the algorithm’s ability to converge to high-quality solutions in a stable manner, thereby offering a practical and powerful decision-support tool for auction organizers.