Fixed set search applied to the traveling salesman problem

In this paper we present a new population based metaheuristic called the fixed set search (FSS). The proposed approach represents a method of adding a learning mechanism to the greedy randomized adaptive search procedure (GRASP). The basic concept of FSS is to avoid focusing on specific high quality solutions but on parts or elements that such solutions have. This is done through fixing a set of elements that exist in such solutions and dedicating computational effort to finding near optimal solutions for the underlying subproblem. The simplicity of implementing the proposed method is illustrated on the traveling salesman problem. Our computational experiments show that the FSS manages to find significantly better solutions than the GRASP it is based on and also the dynamic convexized method.

An Ant Colony Optimization Algorithm for Partitioning Graphs with Supply and Demand

In this paper we focus on finding high quality solutions for the problem of maximum partitioning of graphs with supply and demand (MPGSD). There is a growing interest for the MPGSD due to its close connection to problems appearing in the field of electrical distribution systems, especially for the optimization of self-adequacy of interconnected microgrids. We propose an ant colony optimization algorithm for the problem. With the goal of further improving the algorithm we combine it with a previously developed correction procedure. In our computational experiments we evaluate the performance of the proposed algorithm on both trees and general graphs. The tests show that the method manages to find optimal solutions in more than 50% of the problem instances, and has an average relative error of less than 0.5% when compared to known optimal solutions.

A Multi-Heuristic Approach for Solving the Pre-Marshalling Problem

Minimizing the number of reshuffling operations at maritime container terminals incorporates the Pre-Marshalling Problem (PMP) as an important problem. Based on an analysis of existing solution approaches we develop new heuristics utilizing specific properties of problem instances of the PMP. We show that the heuristic performance is highly dependent on these properties. We introduce a new method that exploits a greedy heuristic of four stages, where for each of these stages several different heuristics may be applied. Instead of using randomization to improve the performance of the heuristic, we repetitively generate a number of solutions by using a combination of different heuristics for each stage. In doing so, only a small number of solutions is generated for which we intend that they do not have undesirable properties, contrary to the case when simple randomization is used. Our experiments show that such a deterministic algorithm significantly outperforms the original nondeterministic method when the quality of found solutions is observed, with a much lower number of generated solutions.