Filtering Algorithms for Biobjective Mixed Binary Linear Optimization Problems with a Multiple-Choice Constraint

This paper deals with a class of biobjective mixed binary linear programs having a multiple-choice constraint, which are found in applications such as Pareto set–reduction problems, single-supplier selection, and investment decisions, among others. Two objective space–search algorithms are presented. The first algorithm, termed line search and linear programming filtering, is a two-phase procedure. Phase 1 searches for supported Pareto outcomes using the parametric weighted sum method, and Phase 2 searches for unsupported Pareto outcomes by solving a sequence of auxiliary mixed binary linear programs. An effective linear programming filtering procedure excludes any previous outcomes found to be dominated. The second algorithm, termed linear programming decomposition and filtering, decomposes the mixed binary problem by iteratively fixing binary variables and uses the linear programming filtering procedure to prune out any dominated outcomes. Computational experiments show the effectiveness of the linear programming filtering and suggest that both algorithms run faster than existing general-purpose objective space–search procedures.