In this paper, we deal with the problem of handling solutions in an external archive with the use of a relaxed form of Pareto dominance called ǫ-dominance and a variation of it called paǫ-dominance. These two relaxed forms of Pareto dominance have been used as archiving strategies in some multi-objective evolutionary algorithms (MOEAs). The main objective of this work is to improve the ǫ-domina...

The geometric duality theory of Heyde and Löhne (2006) defines a dual to a multiple objective linear programme (MOLP). In objective space, the primal problem can be solved by Benson’s outer approximation method (Benson, 1998a,b) while the dual problem can be solved by a dual variant of Benson’s algorithm (Ehrgott et al., 2007). Duality theory then assures that it is possible to find the nondomi...

Let C and D be two distinct coteries under the vertex set V of a graph G = (V, E) that models a distributed system. Coterie C is said to G-dominate D (with respect to G) if the following condition holds: For any connected subgraph H of G that contains a quorum in D (as a subset of its vertex set), there exists a connected subgraph H ¢ of H that contains a quorum in C. A coterie C on a graph G i...

This paper presents a new procedure for the nondominated sorting with constraint handling to be used in a multiobjective evolutionary algorithm. The strategy uses a sorting algorithm and binary search to classify the solutions in the correct level of the Pareto front. In a problem with m objective functions, using n solutions in the population, the original nondominated sorting algorithm, used ...

Abstract Nondominated Neighbor Immune Algorithm (NNIA) is proposed for multiobjective optimization by using a novel nondominated neighbor-based selection technique, an immune inspired operator, two heuristic search operators, and elitism. The unique selection technique of NNIA only selects minority isolated nondominated individuals in the population. The selected individuals are then cloned pro...

Nondominated Neighbor Immune Algorithm (NNIA) is proposed for multiobjective optimization by using a novel nondominated neighbor-based selection technique, an immune inspired operator, two heuristic search operators, and elitism. The unique selection technique of NNIA only selects minority isolated nondominated individuals in the population. The selected individuals are then cloned proportional...

This paper presents a newmultiobjective genetic algorithm based on the Tchebycheff scalarizing function, which aims to generate a good approximation of the nondominated solution set of the multiobjective problem. The algorithm performs several stages, each one intended for searching potentially nondominated solutions in a different part of the Pareto front. Pre-defined weight vectors act as piv...

Nondominated sorting, also called Pareto Depth Analysis (PDA), is widely used in multi-objective optimization and has recently found important applications in multicriteria anomaly detection. Recently, a partial differential equation (PDE) continuum limit was discovered for nondominated sorting leading to a very fast approximate sorting algorithm called PDE -based ranking. We propose in this pa...

The augmented weighted Tchebycheff norm was introduced in the context of multicriteria optimization by Steuer and Choo (1983) in order to avoid the generation of weakly nondominated points. It augments a weighted l∞-norm with an l1-term, multiplied by a “small” parameter ρ > 0. However, the appropriate selection of the parameter ρ remained an open question: A too small value of ρ may cause nume...