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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.