Cooperative multiobjective optimization with bounds on objective functions

When solving large-scale multiobjective optimization problems, solvers can get stuck because of memory and/or time limitations. In such cases, one is left with no information on the distance to the best feasible solution, found before the optimization process has stopped, to the true Pareto optimal solution. In this work, we show how to provide such information. To this aim we make use of the concept of lower shells and upper shells, developed in our earlier works. No specific assumptions about the problems to be solved are made. We illustrate the proposed approach on biobjective multidimensional knapsack problems derived from single-objective multidimensional knapsack problems in the Beasley OR Library. We address cases when a top-class commercial mixed-integer linear solver fails to provide Pareto optimal solutions attempted to be derived by scalarization.

Automated summary

In this study, the concept of lower shells and upper shells is used to provide information on the distance from the best feasible solution found before the optimization process has stopped to the true Pareto optimal solution in large-scale multiobjective optimization problems. The proposed approach is illustrated on biobjective multidimensional knapsack problems derived from single-objective multidimensional knapsack problems, without specific assumptions about the problems to be solved.