The search-and-remove algorithm for biobjective mixed-integer linear programming problems

In this study, biobjective mixed-integer linear programming problems are considered and a search-andremove (SR) algorithm is presented. At each stage of the algorithm, Pareto outcomes are searched with the dichotomic search algorithm and these outcomes are excluded from the objective space with the help of Tabu constraints. The algorithm is also enhanced with lower and upper bounds, which are updated at each stage of the algorithm. The SR algorithm continues until proved that all Pareto slices of the biobjective mixedinteger linear programming problem are found. The algorithm finally returns a set of outcome slices including all Pareto slices of the problem. Then, the profile of the Pareto frontier is constructed from outcome slices with the help of an upper envelope finding algorithm. A computational analysis is performed on several benchmark problems and the results are reported.