Evolutionary multi objective optimisation EMO now boasts a proliferation of algorithms and bench mark problems We need principled ways to compare the performance of di erent EMO algorithms but this is com plicated by the fact that the result of an EMO run is not a single scalar value but a collection of vectors forming a non dominated set Various metrics for non dominated sets have been suggest...

While most of the published exact methods for solving multiobjective integer linear programming (MOILP) problems are based on solving many integer linear programs (ILP), we propose a branch and bound multi-objective method to find the whole non-dominated set. Two types of nodes are created in the tree. The first type corresponds to not integer optimal solution of solved (LP) problems . In this ...

distribution centers (dcs) play important role in maintaining the uninterrupted flow of goods and materials between the manufacturers and their customers.this paper proposes a mathematical model as the bi-objective capacitated multi-vehicle allocation of customers to distribution centers. an evolutionary algorithm named non-dominated sorting ant colony optimization (nsaco) is used as the optimi...

numerous problems encountered in real life cannot be actually formulated as a single objective problem; hence the requirement of multi-objective optimization (moo) had arisen several years ago. due to the complexities in such type of problems powerful heuristic techniques were needed, which has been strongly satisfied by swarm intelligence (si) techniques. particle swarm optimization (pso) has ...

in this study, a two-objective mixed-integer linear programming model (milp) for multi-product re-entrant flow shop scheduling problem has been designed. as a result, two objectives are considered. one of them is maximization of the production rate and the other is the minimization of processing time. the system has m stations and can process several products in a moment. the re-entrant flow sho...

This paper uses the weighted L$_1-$norm to propose an algorithm for finding a well-dispersed subset of non-dominated solutions of multiple objective mixed integer linear programming problem. When all variables are integer it finds the whole set of efficient solutions. In each iteration of the proposed method only a mixed integer linear programming problem is solved and its optimal solutions gen...

During the last decades, research in multi-objective optimisation has seen considerable growth. However, this activity been focused on linear, non-linear, and combinatorial with multiple objectives. Multi-objective mixed integer (linear or non-linear) programming received considerably less attention. In paper we propose an algorithm to compute a finite set of non-dominated points/efficient solu...

8 Abstract 9 The goal of this paper is to explore solution concepts for set-valued TU-games. Several stability conditions can be 10 defined since one can have various interpretations of an improvement within the multicriteria framework. We present 11 two different core solution concepts and explore the relationships among them. These concepts generalize the classic 12 core solution for scalar g...

This paper proposes a Trust-Region Based Augmented Method (TRALM) to solve a combined Environmental and Economic Power Dispatch (EEPD) problem. The EEPD problem is a multi-objective problem with competing and non-commensurable objectives. The TRALM produces a set of non-dominated Pareto optimal solutions for the problem. Fuzzy set theory is employed to extract a compromise non-dominated sol...