Set Of Elite Solutions Research Articles

A GRASP/Path‐Relinking algorithm for the traveling purchaser problem

AbstractThe Traveling Purchaser Problem (TPP) is a generalization of the TSP that consists in choosing which nodes (markets) to visit to create a tour that allows to buy a set of products at minimum transportation and purchasing cost. The TPP has gained attention due to the computational challenges it poses and the potential applications it can support in today's technology‐driven industry. This paper presents a GRASP‐based methodology for the TPP based on three constructive procedures (route‐first, purchase‐first, and purchase‐and‐route) and two local search operators (insert and remove). The methodology is strengthened with a Path Relinking strategy to improve the GRASP performance by re‐combining a set of elite solutions and with a Filtering strategy to improve the algorithm's efficiency by avoiding local search operations on the least promising solutions. The algorithm is tested with 855 instances of the asymmetric TPP and 190 instances of the symmetric TPP. Computational results prove the benefit of including the Path Relinking and Filtering strategies and suggest that the purchase‐first constructive procedure is the most competitive in terms of objective function value with little extra effort in execution time with respect to the other constructive procedures. Our results outperform published results for the asymmetric TPP in a statistically significant way and show competitive performance for the symmetric TPP.

GRASP with path relinking for the manufacturing cell formation problem considering part processing sequence

In this study, a hybrid heuristic is proposed for the Manufacturing Cell Formation Problem considering part processing sequence. The hybrid heuristic is based on a GRASP heuristic and then it uses a path relinking strategy on a set of elite solutions obtained by GRASP. The proposed GRASP heuristic constructs feasible solutions using a two-stage randomised greedy procedure, that are improved with a local search procedure. This procedure explores two neighbourhoods: machine reassignments and machine interchanges. The path relinking is used as an intensification strategy to improve the GRASP solutions. The performance of the proposed heuristic is evaluated with data-sets from the literature and a set of larger size instances randomly generated. The obtained results show that the GRASP heuristic provides optimal or near optimal solutions with very small computational burden. These results are further improved with a Path Relinking strategy. The most remarkable features of the proposed heuristic are its simplicity and its ease of implementation.

GRASP duplamente reativa com path-relinking para o problema de p-medianas aplicado à formação de clusters em logística de localização

Este trabalho relata a experiência de formular, construir e testar um procedimento duplamente reativo para a meta-heurística GRASP com path-relinking destinado à solução do problema generalizado de p-medianas aplicado à logística de localização. São usados dois parâmetros de reação para controlar a busca de soluções na fase de construção da GRASP. O uso simultâneo dos dois parâmetros reativos permitiu criar uma disciplina para alocação dos clientes aos agrupamentos das medianas: clientes mais próximos são alocados primeiro. Para implementação do path-relinking, um conjunto elite de soluções foi criado através de um conceito denominado “índice vocação mediana” que estabelece o quanto cada cidade está próxima das demais cidades do grupo. Para testar a qualidade das soluções, foi utilizado um problema envolvendo as cidades brasileiras de médio e grande porte.

Iterated local search heuristics for the Vehicle Routing Problem with Cross-Docking

This work addresses the Vehicle Routing Problem with Cross-Docking (VRPCD). The problem consists in defining a minimum cost set of routes for a fleet of vehicles that meets the demands of products for a set of suppliers and customers. The vehicles leave a single Cross-Dock (CD) towards the suppliers, pick up products and return to the CD, where products can be exchanged before being delivered to their customers. The vehicle routes must respect the vehicle capacity constraints, as well as the time window constraints. We adapted a constructive heuristic and six local search procedures from the literature of VRP, and made them efficient in the presence of the synchronization constraints of VRPCD. Besides, we propose three Iterated Local Search (Lourenço et al., 2010) heuristics for VRPCD. The first heuristic is a standard implementation of ILS, while the second extends the classic ILS framework by keeping a set of elite solutions, instead of a single current solution. The latter set is used in a restart procedure. As far as we can tell, this is the first ILS heuristic in the literature that keeps a population of current elite solutions. The third heuristic is an extension of the second that relies on an intensification procedure based on an Integer Programming formulation for the Set Partitioning problem. The latter allows a neighborhood with an exponential number of neighbors to be efficiently evaluated. We report computational results and comparisons with the best heuristics in the literature. Besides, we also present a new set with the largest instances in the literature of VRPCD, in order to demonstrate that the improvements we propose for the ILS metaheuristic are efficient even for large size instances. Results show that the best of our heuristics is competitive with the best heuristics in the literature of VRPCD. Besides, it improved the best solution known for half of the benchmark instances in the literature.

Two-Phase Genetic Local Search Algorithm for the Multimode Resource-Constrained Project Scheduling Problem

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, the resource-constrained project scheduling problem with multiple execution modes for each activity is explored. This paper aims to find a schedule of activities such that the makespan of the schedule is minimized subject to the precedence and resource constraints. We present a two-phase genetic local search algorithm that combines the genetic algorithm and the local search method to solve this problem. The first phase aims to search globally for promising areas, and the second phase aims to search more thoroughly in these promising areas. A set of elite solutions is collected during the first phase, and this set, which acts as the indication of promising areas, is utilized to construct the initial population of the second phase. By suitable applications of the mutation with a large mutation rate, the restart of the genetic local search algorithm, and the collection of good solutions in the elite set, the strength of intensification and diversification can be properly adapted and the search ability retained in a long term. Computational experiments were conducted on the standard sets of project instances, and the experimental results revealed that the proposed algorithm was effective for both the short-term (with 5000 schedules being evaluated) and the long-term (with 50000 schedules being evaluated) search in solving this problem. </para>

WBMOAIS: A novel artificial immune system for multiobjective optimization

This study presents a novel weight-based multiobjective artificial immune system (WBMOAIS) based on opt-aiNET, the artificial immune system algorithm for multi-modal optimization. The proposed algorithm follows the elementary structure of opt-aiNET, but has the following distinct characteristics: (1) a randomly weighted sum of multiple objectives is used as a fitness function. The fitness assignment has a much lower computational complexity than that based on Pareto ranking, (2) the individuals of the population are chosen from the memory, which is a set of elite solutions, and a local search procedure is utilized to facilitate the exploitation of the search space, and (3) in addition to the clonal suppression algorithm similar to that used in opt-aiNET, a new truncation algorithm with similar individuals (TASI) is presented in order to eliminate similar individuals in memory and obtain a well-distributed spread of non-dominated solutions. The proposed algorithm, WBMOAIS, is compared with the vector immune algorithm (VIS) and the elitist non-dominated sorting genetic system (NSGA-II) that are representative of the state-of-the-art in multiobjective optimization metaheuristics. Simulation results on seven standard problems (ZDT6, SCH2, DEB, KUR, POL, FON, and VNT) show WBMOAIS outperforms VIS and NSGA-II and can become a valid alternative to standard algorithms for solving multiobjective optimization problems.

Reactive tabu adaptive memory programming search for the vehicle routing problem with backhauls

A heuristic approach based on a hybrid operation of reactive tabu search (RTS) and adaptive memory programming (AMP) is proposed to solve the vehicle routing problem with backhauls (VRPB). The RTS is used with an escape mechanism which manipulates different neighbourhood schemes in a sophisticated way in order to get a continuously balanced intensification and diversification during the search process. The adaptive memory strategy takes the search back to the unexplored regions of the search space by maintaining a set of elite solutions and using them strategically with the RTS. The AMP feature brings an extra robustness to the search process that resulted in early convergence when tested on most of the VRPB instances. We compare our algorithm against the best methods in the literature and report new best solutions for several benchmark problems.