Investigation of Archiving Techniques for Evolutionary Multi-objective Optimizers

Abstract: The optimization of multi-objective problems from the Pareto dominance viewpoint can lead to huge sets of incomparable solutions. Many heuristic techniques proposed to these problems have to deal with approximation sets that can be limited or not. Usually, a new solution generated by a heuristic is compared with other archived non-dominated solutions generated previously. Many techniques deal with limited size archives, since comparisons within unlimited archives may require significant computational effort. To maintain limited archives, solutions need to be discarded. Several techniques were proposed to deal with the problem of deciding which solutions remain in the archive and which are discarded. Previous investigations showed that those techniques might not prevent deterioration of the archives. In this study, we propose to store discarded solutions in a secondary archive and, periodically, recycle them, bringing them back to the optimization process. Three recycling techniques were investigated for three known methods. The datasets for the experiments consisted of 91 instances of discrete and continuous problems with 2, 3 and 4 objectives. The results showed that the recycling method can benefit the tested optimizers on many problem classes

Prize Collecting Traveling Salesman Problem with Ridesharing

The Prize Collecting Traveling Salesman Problem with Ridesharing is a model that joins elements from the Prize Collecting Traveling Salesman and the collaborative transport. The salesman is the driver of a capacitated vehicle and uses a ridesharing system to minimize travel costs. There are a penalty and a bonus associated with each vertex of a graph, G, that represents the problem. There is also a cost associated with each edge of G. The salesman must choose a subset of vertices to be visited so that the total bonus collection is at least a given a parameter. The length of the tour plus the sum of penalties of all vertices not visited is as small as possible. There is a set of persons demanding rides. The ride request consists of a pickup and a drop off location, a maximum travel duration, and the maximum amount the person agrees to pay. The driver shares the cost associated with each arc in the tour with the passengers in the vehicle. Constraints from ride requests, as well as the capacity of the car, must be satisfied. We present a mathematical formulation for the problem investigated in this study and solve it in an optimization tool. We also present three heuristics that hybridize exact and heuristic methods. These algorithms use a decomposition strategy that other enriched vehicle routing problems can utilize

O problema do caixeiro viajante com vários passageiros, cota de bônus opcional e tempo / The Traveling Salesman Problem with Multiple Passengers Optional Bonus Quota and Time

Este artigo apresenta o Problema do Caixeiro Viajante com Múltiplos Passageiros Bônus Optativos Quota e Tempo. O problema consiste em maximizar o lucro de um caixeiro viajante que realiza serviço de transporte de mercadorias, considerando a possibilidade de rateio das despesas da rota com eventuais passageiros embarcados em seu veículo. As mercadorias devem ser transportadas obrigatoriamente das suas origens até os seus destinos e devem contabilizar uma quota mínima definida a priori. Nesta variante, ao passar em uma cidade, o caixeiro decide se coleta ou não a mercadoria a ser transportada. A coleta da mercadoria requer tempo de carregamento e de descarregamento. É proposto um modelo de programação matemática que é resolvido por um solver. São propostas, também, três heurísticas, sendo duas desenvolvidas segundo as meta-heurísticas Colônia de Formigas e GRASP. Os resultados e análises de um experimento computacional são apresentados

Problema de Roteamento de Veículo Suficientemente Próximo Assimétrico: Formulação e Heurística / Close-Enough Vehicle Routing Problem Asymmetric: Formulation and Heuristics

Este trabalho propõe a versão assimétrica do Problema de Roteamento de Veículo Suficientemente Próximo, utilizado para planejamento de rotas de reconhecimento aéreo. O problema foi formulado com um modelo de programação cônica de segunda ordem e para solucioná-lo foram aplicadas técnicas de otimização heurística baseadas em uma propriedade geométrica. Também são descritos os resultados de experimentos computacionais extensivos de 240 instâncias adaptadas da literatura com até 20 pontos de observação. Destas, é possível encontrar resultados ótimos para 101 instâncias e os primeiros limites superiores para outras. Além disso, elaborou-se uma heurística baseada em clusterização, que utiliza propriedades geométricas em conjunto com o VNS. Os testes mostraram que o método proposto produz soluções de alta qualidade

O problema de roteamento e escalonamento de profissionais de saúde: The home healthcare routing and scheduling problem

Problema de Roteamento e Escalonamento de Profissionais de Saúde consiste em determinar a melhor rota para profissionais de saúde para atendimento domiciliar. Existem diversas variantes deste problema que diferem nas restrições e funções objetivo. Este artigo apresenta uma revisão da literatura, com o objetivo de identificar os problemas de roteamento utilizados pelos autores, os diferentes tipos de função objetivo, e as técnicas de solução utilizadas

Traveling Salesman Problem with Optional Bonus Collection, Pickup Time and Passengers

This study introduces a variant of the Traveling Salesman Problem, named Traveling Salesman Problem with Optional Bonus Collection, Pickup Time and Passengers (PCVP-BoTc). It is a variant that incorporates elements of the Prize Collecting Traveling Salesman Problem and Ridesharing into the PCV. The objective is to optimize the revenue of the driver, which selectively defines which delivery or collection tasks to perform along the route. The economic effect of the collection is modeled by a bonus. The model can be applied to the solution of hybrid routing systems with route tasks and solidary transport. The driver, while performing the selected tasks, can give rides to persons who share route costs with him. Passengers are protected by restrictions concerning the maximum value they agree to pay for a ride and maximum travel duration. The activity of collecting the bonus in each locality demands a specific amount of time, affects the route duration, and is interconnected with the embarkment of passengers. Two mathematical formulations are presented for the problem and validated by a computational experiment using a solver. We propose four heuristic algorithms; three of them are hybrid metaheuristics. We tested the mathematical formulation implementations for 24 instances and the heuristic algorithms for 48

A Hybrid Transgenetic Algorithm for the Prize Collecting Steiner Tree Problem

Evolutionary algorithms are effective search tools for tackling difficult optimization problems. In this paper an algorithm based on living processes where cooperation is the main evolutionary strategy is applied to the Prize Collecting Steiner Tree Problem, an NP-hard combinatorial optimization problem. The Transgenetic Algorithm presented here is hybridized with path-relinking. Computational results of an experiment performed with benchmark instances are reported. The results obtained for the Prize Collecting Steiner Tree Problem with the application of the hybrid Transgenetic Algorithm are compared with the results of three effective approaches presented previously. The computational experiment shows that the proposed approach is very competitive concerning both quality of solution and processing time

A Multi-objective Version of the Lin-Kernighan Heuristic for the Traveling Salesman Problem

The Lin and Kernighan’s algorithm for the single objective Traveling Salesman Problem (TSP) is one of the most efficient heuristics for the symmetric case. Although many algorithms for the TSP were extended to the multi-objective version of the problem (MTSP), the Lin and Kernighan’s algorithm was still not fully explored. Works that applied the Lin and Kernighan’s algorithm for the MTSP were driven to weighted sum versions of the problem. We investigate the LK from a Pareto dominance perspective. The multi-objective LK was implemented within two local search schemes and applied to 2 to 4-objective instances. The results  showed that the proposed algorithmic variants obtained better results than a state-of-the-art algorithm

A TABU SEARCH ALGORITHM WITH PROBABILISTIC MEMORY FOR THE PIPE SIZING PROBLEM OF NATURAL GAS DISTRIBUTION NETWORKS

Natural gas distribution networks are becoming a very important part of the infrastructure of Brazilian cities, serving residential, commercial, industrial and utility markets. An important problem that a decision maker must deal is to determine the kind and diameter of each pipe to be laid such that a minimum required pressure is available at each demand point. Pipes are produced and commercialized only in a certain number of materials and in certain fixed diameters. Their costs per unit of length usually vary with the kind of material and diameter. Pressure drops along pipes in a decreasing rate with diameter for a constant flow. In this work a Tabu Search algorithm with a new permanence criterion of a given element on the tabu list is applied to the pipe sizing problem. A comparison with two approaches proposed previously in the literature is reported