Alexandre Xavier Martins

GENVNS-TS-CL-PR: a heuristic approach for solving the vehicle routing problem with simultaneous pickup and delivery.

This work addresses the Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD). Due to its complexity, we propose a heuristic algorithm for solving it, so-called GENVNS-TS-CL-PR. This algorithm combines the heuristic procedures Cheapest Insertion, Cheapest Insertion with multiple routes, GENIUS, Variable Neighborhood Search (VNS), Variable Neighborhood Descent (VND), Tabu Search (TS) and Path Relinking (PR). The first three procedures aim to obtain an good initial solution, and the VND and TS are used as local search methods for VNS. TS is called after some iterations without any improvement through of the VND. The PR procedure is called after each VNS iteration and it connects a local optimum with an elite solution generated during the search. The algorithm uses an strategy based on Candidate List to reduce the number of solutions evaluated in the solution space. The algorithm was tested on benchmark instances taken from the literature and it was able to generate high quality solutions.

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.

Branch-and-cut and hybrid local search for the multi-level capacitated minimum spanning tree problem

We propose algorithms to compute tight lower bounds and high quality upper bounds (UBs) for the multilevel capacitated minimum spanning tree problem. We first develop a branch-and-cut algorithm, introducing some new features: (i) the exact separation of cuts corresponding to some master equality polyhedra found in the formulation; (ii) the separation of Fenchel cuts, solving LPs considering all the possible solutions restricted to small portions of the graph. We then use that branch-and-cut within a GRASP that performs moves by solving to optimality subproblems corresponding to partial solutions. The computational experiments were conducted on 450 benchmark instances from the literature. Numerical results show improved best known (UBs) for almost all instances that could not be solved to optimality.

Model-hierarchical column generation and heuristic for the routing and wavelength assignment problem

The routing and wavelength assignment (RWA) problem typically occurs in wavelength division multiplexing optical networks. Given a number of available wavelengths, we consider here the problem of maximising the number of accepted connections with respect to the clash and continuity constraints. We first propose a new strategy which combines two existing models. This leads to an improved column generation scheme. We also present two heuristics to compute feasible solutions: a hybrid heuristic and the integer solution at the root node of the column generation. Our approaches are compared with the best existing results on a set of classic RWA instances.

GARP: A New Genetic Algorithm for the Unrelated Parallel Machine Scheduling Problem with Setup Times

This work addresses the Unrelated Parallel Machine Scheduling Problem where setup times are sequence-dependent and machine-dependent, the UPMSPST. The maximum completion time of the schedule, known as makespan, is considered as the objective to minimize. The UPMSPST is often found in industries and belongs to the NP-hard class. Aiming to its resolution, is proposed an algorithm named GARP. This algorithm is based on Genetic Algorithm (GA) combined with Variable Neighborhood Descent (VND) and Path Relinking (PR). In addition, is used a local search method based on a Mixed-Integer Programming (MIP) model to solve the Asymmetric Traveling Salesman Problem (ATSP). The developed algorithm explores the solution space using multiple insertions and swaps movements. GARP was tested using benchmark instances and the computational results showed that it is able to produce better solutions than the algorithms found in literature, with lower variability and setting new upper bounds for the majority of the test problems.

An Efficient Genetic Algorithm for the Design of Hub-and-Spoke Networks

We propose an efficient genetic algorithm (GA) for the design of hub-and-spoke networks with single allocation. The creation of the initial population is based on the greedy randomized search procedure, which provides high quality individuals. Furthermore, new crossover and mutation operators were implemented in order to improve the solution over the evolutionary process. Additionally, a local search procedure is applied in the best individuals. The adapted GA is tested in the Australian Post (AP) and Civil Aeronautics Board (CAB) data sets and clearly outperforms four other evolutionary algorithms of the literature, both in solution quality and CPU time.

Um modelo de programação matemática para otimizar a composição de lotes de minério de ferro da mina Cauê da CVRD

This work focuses on the problem of blending iron ore products, at the Caue mine stockyard, of Companhia Vale do Rio Doce, in the state of Minas Gerais, for the formation of lots. It consists in elaborating a linear goal programming model that seeks to determine the areas to recapture the stored ore in such a way that the blending of products be in conformity with the quality specification required by the customer. This work is a case study of an applied nature. The mathematical programming model was developed with the support of the optimization software LINGO 9.0 in conjunction with EXCEL 2000 spreadsheets, making it possible to handle and export data in formats used by the mining company. With the purpose of validating the implemented system, the results obtained by the system were compared with real data. These results proved that is possible to improve the composition of the product lots applying the proposed model.

Proposed Solutions to the Tripper Car Positioning Problem.

The trippers are equipments often found in mineral processing plants. Their role is to distribute ore coming from past stages of process in a silo with several hoppers. Positioning trippers is a scheduling problem defined by position determination of the equipment through the bins and along time. The system silo-tripper was modeled as a combinatorial linear optimization program aiming to get the optimal tripper positioning. Two paradigms were used to find out an exact solution: mixed integer linear programming and dynamic programming.

HMS: A hybrid multi-start algorithm for solving binary linear programs

Abstract This work presents a hybrid multi-start algorithm for solving generic binary linear programs. This algorithm, called HMS, is based on a Multi-Start Metaheuristic and combines exact and heuristic strategies to address the problem. The initial solutions are generated by a strategy that applies linear programming and constraint propagation for defining an optimized set of fixed variables. In order to refine them, a local search, guided by a Variable Neighborhood Descent heuristic, is called, which, in turn, uses Local Branching cuts. The algorithm was tested in a set of binary LPs from the MIPLIB 2010 library and the results pointed out its competitive performance, resulting in a promising matheuristic.

A hybrid VNS algorithm for solving the multi-level capacitated minimum spanning tree problem

Abstract This work addresses the multi-level capacitated minimum spanning tree (MLCMST) problem. It consists of finding a minimal cost spanning tree such that the flow to be transferred from a central node (root) to the other nodes is bounded by the edge capacities. In this paper, a hybrid algorithm, combining the Variable Neighborhood Search (VNS) metaheuristic and one mathematical programming formulation of the literature, is used for solving it. The formulation is used to give an initial solution to VNS. Five neighborhoods are used for exploring the solution space. Results show that the VNS is able to improve the initial solutions and to obtain small gap solutions for all instance sets.