Local search heuristics for the multidimensional assignment problem

The Multidimensional Assignment Problem (MAP) (abbreviated s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s also have a large number of applications. We consider several known neighborhoods, generalize them and propose some new ones. The heuristics are evaluated both theoretically and experimentally and dominating algorithms are selected. We also demonstrate that a combination of two neighborhoods may yield a heuristics which is superior to both of its components

An Efficient Hybrid Ant Colony System for the Generalized Traveling Salesman Problem

The Generalized Traveling Salesman Problem (GTSP) is an extension of the well-known Traveling Salesman Problem (TSP), where the node set is partitioned into clusters, and the objective is to find the shortest cycle visiting each cluster exactly once. In this paper, we present a new hybrid Ant Colony System (ACS) algorithm for the symmetric GTSP. The proposed algorithm is a modification of a simple ACS for the TSP improved by an efficient GTSP-specific local search procedure. Our extensive computational experiments show that the use of the local search procedure dramatically improves the performance of the ACS algorithm, making it one of the most successful GTSP metaheuristics to date.Comment: 7 page

A Memetic Algorithm for the Multidimensional Assignment Problem

The Multidimensional Assignment Problem (MAP or s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s have also a number of applications. In this paper we propose a memetic algorithm for MAP that is a combination of a genetic algorithm with a local search procedure. The main contribution of the paper is an idea of dynamically adjusted generation size, that yields an outstanding flexibility of the algorithm to perform well for both small and large fixed running times. The results of computational experiments for several instance families show that the proposed algorithm produces solutions of very high quality in a reasonable time and outperforms the state-of-the art 3-AP memetic algorithm.Comment: 14 page

Proposição de um modelo de alocação baseado em competências : um estudo sobre o problema da designação generalizada aplicado a equipes de prestação de serviços

Essa dissertação aborda o desenvolvimento e a aplicação de um modelo para a solução do problema de alocação de equipes baseado em competências. Fundamentado no tradicional problema da alocação generalizada, inicialmente introduzido por Ross e Soland (1975), este trabalho propõe um método heurístico considerando três dimensões (trabalhador, região e competência). Considerando-se uma prestadora de serviços cuja demanda é variável segundo a sua região de origem, a quantidade de atendimentos necessários e o perfil de competências exigido para cada atendimento. Supondo ser inerente ao serviço que os trabalhadores possam realizar tanto atendimentos locais quanto em outras regiões e que é desejável priorizar atendimentos com profissionais locais. O objetivo do modelo é determinar a melhor região para a alocação individual de um grupo de profissionais, com base em seu perfil de competências e no comportamento da demanda por essas competências. O modelo desenvolvido é aplicado em uma empresa prestadora de serviços de segurança e saúde no trabalho. Quatro cenários são avaliados comparativamente, sendo um desses o ambiente original e os demais resultantes de três simulações com o método realizadas sob considerações distintas. Os resultados indicam que o modelo proposto possui significativa convergência com a solução ótima, assim como uma potencial contribuição a estratégia de atendimento da empresa.This dissertation addresses the development and the implementation of a method for solving the competency-based team allocation problem. Based on the traditional generalized assignment problem, initially introduced by Ross and Soland (1975), this paper proposes a heuristic method considering three dimensions (worker, region and competence). Considering a service provider whose demand varies according to its location (region), the amount of needed assistance and the expertise profile required for each service demanded. Assuming it is inherent to the service that workers can provide assistance both locally and remotely, and that it is desirable to prioritize local professionals for service assignment. The method’s main objective is to determine the best region for the individual assignment of a group of professionals, based on their competency profile and the demand behavior for those competencies. The developed method is applied in a company that provides occupational health and safety services. Four scenarios are comparatively evaluated, one of them being the original environment and the others resulting from three simulations with the method performed under different considerations. The outcomes indicate that the proposed method has significant convergence to the optimal solution, as well as a potential contribution to the company's service strategy