Túlio A. M. Toffolo

GRASP with hybrid heuristic-subproblem optimization for the multi-level capacitated minimum spanning tree problem

We propose a GRASP using an hybrid heuristic-subproblem optimization approach for the Multi-Level Capacitated Minimum Spanning Tree (MLCMST) problem. The motivation behind such approach is that to evaluate moves rearranging the configuration of a subset of nodes may require to solve a smaller-sized MLCMST instance. We thus use heuristic rules to define, in both the construction and the local search phases, subproblems which are in turn solved exactly by employing an integer programming model. We report numerical results obtained on benchmark instances from the literature, showing the approach to be competitive in terms of solution quality. The proposed GRASP have in fact improved the best known upper bounds for almost all of the considered instances.

A two-dimensional heuristic decomposition approach to a three-dimensional multiple container loading problem

Efficient container loading has the potential to considerably reduce logistics and transportation costs. The container loading problem is computationally complex and, despite extensive academic effort, there remains room for algorithm improvement. Real-world problems are not always addressed satisfactorily primarily due to the large number of complex constraints and objectives. The problem addressed by this work is an unsolved multiple container loading problem introduced by Renault on the occasion of the 2014/2015 ESICUP challenge, organized by the EURO Special Interest Group on Cutting and Packing (ESICUP). Renault’s problem requires a large number of different items to be packed into containers of different types and sizes. Items must be grouped into stacks and respect the ‘this side up’ constraint. The primary objective is to minimize the volume of shipped containers. The smallest volume container may be left behind for the next shipment and is excluded from the main objective. Nevertheless, only a limited percentage of each product may be packed into this container. Additionally, a set of secondary objectives is considered. This work presents a decomposition approach embedded in a multi-phase heuristic for the problem. Feasible solutions are generated quickly, and subsequently improved by local search and post-processing procedures. Experiments revealed that the approach generates optimal solutions for two instances, in addition to good quality solutions for those remaining from the Renault set. The algorithmic contribution is, however, not restricted to the Renault instances. Experiments on less constrained container loading instances from the literature demonstrate the approach’s general applicability and competitiveness.

Multi-machine energy-aware scheduling

The traditional set of manufacturing scheduling problems concern general and easy-to-measure economic objectives such as makespan and tardiness. The variable nature of energy costs over the course of the day remains mostly ignored by most previous research. This variability should not be considered an added complexity, but rather an opportunity for businesses to minimise their energy bill. More effectively scheduling jobs across multiple machines may result in reduced costs despite fixed consumption levels. To this end, this paper proposes a scheduling approach capable of optimising this largely undefined and, consequently, currently unaddressed situation. The proposed multi-machine energy optimisation approach consists of constructive heuristics responsible for generating an initial solution and a late acceptance hill climbing algorithm responsible for improving this initial solution. The combined approach was applied to the scheduling instances of the ICON challenge on Forecasting and Scheduling [The challenge is organized as part of the EU FET-Open: Inductive Constraint Programming (ICON) project (O’Sullivan et al., ICON challenge on forecasting and scheduling. UCC, University College Cork, ICON, Cork. http://iconchallenge.insight-centre.org/challenge-energy, 2014)] whereupon it was proven superior to all other competing algorithms. This achievement highlights the potential of the proposed algorithm insofar as solving the multi-machine energy-aware optimisation problem (MEOP). The new benchmarks are available for further research.

Variable neighborhood search accelerated column generation for the nurse rostering problem

Abstract The Nurse Rostering Problem (NRP) is an optimization problem where nurses with specific skills must be assigned shifts in a schedule. The objective is to obtain a feasible solution while minimizing the number of soft constraint violations. This work presents a Variable Neighborhood Search accelerated Column Generation procedure for the NRP in addition to a Relax-and-fix Heuristic for obtaining feasible solutions. The algorithm improved the best known solutions by at least 10% for all 29 hidden instances from the Second International Nurse Rostering Competition (2014) with 4 weeks. The improved solutions have an optimality gap of at most 8%.

Analysis of a constructive matheuristic for the traveling umpire problem

Abstract The Traveling Umpire Problem (TUP) is a combinatorial optimization problem concerning the assignment of umpires to the games of a fixed double round-robin tournament. The TUP draws inspiration from the real world multi-objective Major League Baseball (MLB) umpire scheduling problem, but is, however, restricted to the single objective of minimizing total travel distance of the umpires. Several hard constraints are employed to enforce fairness when assigning umpires, making it a challenging optimization problem. The present work concerns a constructive matheuristic approach which focuses primarily on large benchmark instances. A decomposition-based approach is employed which sequentially solves Integer Programming (IP) formulations of the subproblems to arrive at a feasible solution for the entire problem. This constructive matheuristic efficiently generates feasible solutions and improves the best known solutions of large benchmark instances of 26, 28, 30 and 32 teams well within the benchmark time limit. In addition, the algorithm is capable of producing feasible solutions for various small and medium benchmark instances competitive with those produced by other heuristic algorithms. The paper also details experiments conducted to evaluate various algorithmic design parameters such as subproblem size, overlap and objective functions.

Stochastic local search with learning automaton for the swap-body vehicle routing problem

Abstract This work presents the stochastic local search method for the Swap-Body Vehicle Routing Problem (SB-VRP) that won the First VeRoLog Solver Challenge. The SB-VRP, proposed on the occasion of the challenge, is a generalization of the classical Vehicle Routing Problem (VRP) in which customers are served by vehicles whose sizes may be enlarged via the addition of a swap body (trailer). The inclusion of a swap body doubles vehicle capacity while also increasing its operational cost. However, not all customers may be served by vehicles consisting of two bodies. Therefore swap locations are present where one of the bodies may be temporarily parked, enabling double body vehicles to serve customers requiring a single body. Both total travel time and distance incur costs that should be minimized, while the number of customers visited by a single vehicle is limited both by its capacity and by a maximum travel time. State of the art VRP approaches do not accommodate SB-VRP generalizations well. Thus, dedicated approaches taking advantage of the swap body characteristic are desired. The present paper proposes a stochastic local search algorithm with both general and dedicated heuristic components, a subproblem optimization scheme and a learning automaton. The algorithm improves the best known solution for the majority of the instances proposed during the challenge. Results are also presented for a new set of instances with the aim of stimulating further research concerning the SB-VRP.

The sport teams grouping problem

The sport teams grouping problem (STGP) concerns the assignment of sport teams to round-robin tournaments. The objective is to minimize the total travel distance of the participating teams while simultaneously respecting fairness constraints. The STGP is an NP-Hard combinatorial optimization problem highly relevant in practice. This paper investigates the performance of some complimentary optimization approaches to the STGP. Three integer programming formulations are presented and thoroughly analyzed: two compact formulations and another with an exponential number of variables, for which a branch-and-price algorithm is proposed. Additionally, a meta-heuristic method is applied to quickly generate feasible high-quality solutions for a set of real-world instances. By combining the different approaches’ results, solutions within 1.7% of the optimum values were produced for all feasible instances. Additionally, to support further research, the considered STGP instances and corresponding solutions files were shared online.

Neighborhood Composition Strategies in Stochastic Local Search

Methods based on Stochastic Local Search (SLS) have been ranked as the best heuristics available for many hard combinatorial optimization problems. The design of SLS methods which use many neighborhoods poses difficult questions regarding the exploration of these neighborhoods: how much computational effort should be invested in each neighborhood? Should this effort remain fixed during the entire search or should it be dynamically updated as the search progresses? Additionally, is it possible to learn the best configurations during runtime without sacrificing too much the computational efficiency of the search method? In this paper we explore different tuning strategies to configure a state-of-the-art algorithm employing fourteen neighborhoods for the Multi-Mode Resource Constrained Multi-Project Scheduling Problem. An extensive set of computational experiments provide interesting insights for neighborhood selection and improved upper bounds for many hard instances from the literature.