A criterion space decomposition approach to generalized tri-objective tactical resource allocation

We present a tri-objective mixed-integer linear programming model of the tactical resource allocation problem with inventories, called the\ua0generalized tactical resource allocation problem\ua0(GTRAP). We propose a specialized criterion space decomposition strategy, in which the projected two-dimensional criterion space is partitioned and the corresponding sub-problems are solved in parallel by application of the\ua0quadrant shrinking method\ua0(QSM) (Boland in Eur J Oper Res 260(3):873–885, 2017) for identifying non-dominated points. To obtain an efficient implementation of the parallel variant of the QSM we suggest some modifications to reduce redundancies. Our approach is tailored for the GTRAP and is shown to have superior computational performance as compared to using the QSM without parallelization when applied to industrial instances

Effective anytime algorithm for multiobjective combinatorial optimization problems

In multiobjective optimization, the result of an optimization algorithm is a set of efficient solutions from which the decision maker selects one. It is common that not all the efficient solutions can be computed in a short time and the search algorithm has to be stopped prematurely to analyze the solutions found so far. A set of efficient solutions that are well-spread in the objective space is preferred to provide the decision maker with a great variety of solutions. However, just a few exact algorithms in the literature exist with the ability to provide such a well-spread set of solutions at any moment: we call them anytime algorithms. We propose a new exact anytime algorithm for multiobjective combinatorial optimization combining three novel ideas to enhance the anytime behavior. We compare the proposed algorithm with those in the state-of-the-art for anytime multiobjective combinatorial optimization using a set of 480 instances from different well-known benchmarks and four different performance measures: the overall non-dominated vector generation ratio, the hypervolume, the general spread and the additive epsilon indicator. A comprehensive experimental study reveals that our proposal outperforms the previous algorithms in most of the instances.This research has been partially funded by the Spanish Ministry of Economy and Competitiveness (MINECO) and the European Regional Development Fund (FEDER) under contract TIN2017-88213-R (6city project), the European Research Council under contract H2020-ICT-2019-3 (TAILOR project), the University of Málaga, Consejería de Economía y Conocimiento de la Junta de Andalucía and FEDER under contract UMA18-FEDERJA-003 (PRECOG project), the Ministry of Science, Innovation and Universities and FEDER under contract RTC-2017-6714-5, and the University of Málaga under contract PPIT.UMA.B1.2017/07 (EXHAURO Project)

Finding a representative nondominated set for multi-objective mixed integer programs

In this paper, we develop algorithms to find small representative sets of nondominated points that are well spread over the nondominated frontiers for multi-objective mixed integer programs. We evaluate the quality of representations of the sets by a Tchebycheff distance-based coverage gap measure. The first algorithm aims to substantially improve the computational efficiency of an existing algorithm that is designed to continue generating new points until the decision maker (DM) finds the generated set satisfactory. The algorithm improves the coverage gap value in each iteration by including the worst represented point into the set. The second algorithm, on the other hand, guarantees to achieve a desired coverage gap value imposed by the DM at the outset. In generating a new point, the algorithm constructs territories around the previously generated points that are inadmissible for the new point based on the desired coverage gap value. The third algorithm brings a holistic approach considering the solution space and the number of representative points that will be generated together. The algorithm first approximates the nondominated set by a hypersurface and uses it to plan the locations of the representative points. We conduct computational experiments on randomly generated instances of multi-objective knapsack, assignment, and mixed integer knapsack problems and show that the algorithms work well