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Comparison of pareto efficiency and weighted objectives method to solve the multi-criteria vehicle routing problem using the artificial immune system

Mrówczyńska B.

Applied Computer Science

2016

Vol. 12, no 4

78--87

The solutions to the multi-criteria vehicle routing problem, dependent on route length and travelling time of delivery van, are presented in the paper. This type of problem is known as a traveling salesman problem. The artificial immune system is used to solve it in this article. Since there are two variables – route length and travelling time – two methods are employed. They are: Weighted Objectives Method and Pareto Efficiency Method. The results of calculation are compared.

Multi-Criteria 3-Dimension Bin Packing Problem

Kacprzak Ł., Rudy J., Żelazny D.

Research in Logistics & Production

2015

Vol. 5, No. 1

85--94

In this paper a multi-criteria approach to the 3-dimensions bin packing problem is considered. The chosen maximization criteria are the number and the total volume of the boxes loaded into the container. Existing solution representation and decoding method are applied to the problem. Next, two metaheuristic algorithms, namely simulated annealing and genetic algorithm are developed using the TOPSIS method for solution evaluation. Both algorithms are then used to obtain approximations of the Pareto front for a set of benchmarks from the literature. Despite the fact that both criteria work in favor of each other, we managed to obtain multiple solutions in many cases, proving that lesser number of boxes can lead to better utilization of the container volume and vice versa. We also observed, that the genetic algorithms performs slightly better in our test both in the terms of hyper-volume indicator and number of non-dominated solutions.

A survey on Pareto efficiency in infinite dimensional vector spaces

Postolica V.

Foundations of Computing and Decision Sciences

2008

Vol. 33, No. 3

271-284

This research work was exhibited at MCDA'65, 12-14 April 2007, Poznań, Poland and it represents a survey on some recent studies concerning Pareto type efficiency in infinite dimensional ordered vector spaces. We present the main directions of research on the efficiency: the existence of the efficient points, the immediate properties and applications, our recent extension for the concept of the efficiency in infinite dimensional ordered vector spaces, emphasized by the approximate efficiency - a natural generalization of the efficiency and some important connections with other significant fields of research in Mathematics. New links between the approximate efficiency and the strong optimization by the full nuclear cones and our recent coincidence result between the approximate efficient points sets and the corresponding Choquet boundaries are specified. Several pertinent references conclude the study.