An infeasible interior-point technique to generate the nondominated set for multiobjective optimization problems. (July 2023) - Jauny,; Ghosh, Debdas; Ansari, Qamrul Hasan; Ehrgott, Matthias; Upadhayay, Ashutosh
Abstract: In this paper, an infeasible interior-point technique is proposed to generate the nondominated set of nonlinear multi-objective optimization problems with the help of the direction-based cone method. We derive the proposed method for both convex and nonconvex problems. In order to solve the parametric optimization problems of the cone method, the infeasible interior-point method starts with an initial iterate outside the feasible region, and then gradually reduces the primal and dual infeasibility measures and the objective function value across the iterations with the help of a merit function. Estimates of the reduction of primal and dual infeasibility parameters per iteration are given. The convergence analysis of the method and an estimate of the number of iterations to reach an ϵ -precise solution are also provided. We provide the performance of the proposed methods on a variety of convex and nonconvex multi-objective test problems. Performance comparison between the proposed method and popular existing solvers is provided with respect to two performance measures and the corresponding relative efficiency measures. The reduction of a combined infeasibility measure, as the iterations progress, on the test problems is also shown graphically. Highlights: An interior point method to solve convex and nonconvex multiobjective optimization. Proposed method solves sub-problems of the cone method (Ghosh and Chakraborty, 2014 ). The interior-point method can start from any point irrespective of its feasibility. The number of steps to reach ɛ -optimal solutions to the sub-problems is estimated. Numerical tests on 12 problems demonstrate the effectiveness of the algorithms.