A modified NBI and NC method for the solution of N-multiobjective optimization problems

Abstract

Multiobjective optimization (MO) techniques allow a designer to model a specific problem considering a more realistic behavior, which commonly involves the satisfaction of several targets simultaneously. A fundamental concept, which is adopted in the multicriteria optimization task, is that of Pareto optimality. In this paper we test several well-known procedures to deal with multiobjective optimization problems (MOP) and propose a novel modified procedure that when applied to the existing Normal Boundary Intersection (NBI) method and Normal Constraint (NC) method for more than two objectives overcomes some of their deficiencies. For the three and four objective applications analyzed here, the proposed scheme presents the best performance both in terms of quality and efficiency to obtain a set of proper Pareto points, when compared to the analyzed existing approaches.

A Novel Hybrid Fuzzy Multi-objective Linear Programming Method of Aggregate Production Planning

“…Mathematical programming and Evolutionary algorithms have been used, as well as the evolutionary multi-objective optimization (EMO) algorithms for solving the MOLP associated. Thus Normal Boundary Intersection (NBI) [12], Modified Normal Boundary Intersection (NBIm) [13], Normal Constraint (NC), [14,15] Successive Pareto Optimization (SPO) [16] and for the seconds Non-dominated Sorting Genetic Algorithm-II (NSGA-II) [17] and Strength Pareto Evolutionary Algorithm 2 (SPEA-2) [18]. Also a hybrid approach incorporating Multi-Criteria Decision Making (MCDM) approaches into EMO algorithms as a local search operator and to lead a DM to the most preferred solution(s).…”

Optimal design of frequency dependent three-layered rectangular composite beams for low mass and high damping

“…As long as the objectives are contradictory, the solution of this multi-objective optimization problem is a set of compromise points, commonly called Pareto front or Pareto surface, that enables to minimize at best one objective without degrading the others. To generate the Pareto surface many methods are available [33][34][35][36][37]. Evolutionary algorithms employ principles of natural selection (mutation, crossover, etc.)…”

Artificial Development by Reinforcement Learning Can Benefit From Multiple Motivations

“…More complex methods consider the so-called pareto-front, wellknown from classical multi-objective optimization. In fact, much of the discussion on optimal decision making for multiple objectives and methods for finding the pareto-optimal solutions (Das and Dennis, 1998;Miettinen, 1999;Mueller-Gritschneder et al, 2009;Motta et al, 2012) can be useful for MORL (see Van Moffaert and Nowé, 2014;Pirotta et al, 2015;Vamplew et al, 2017).…”