This study addresses the challenges faced by Multi- and Many-Objective Evolutionary Algorithms in converging to the optimal Pareto Front under limited budgets. It proposes integrating these algorithms with deterministic single-objective local search techniques tailored for scalarized multi-objective optimization problems to accelerate convergence. Two integrations of NSGA-III with local search techniques based on SQP and BFGS algorithms are proposed and evaluated through numerical experiments on DTLZ1-4 problems across various budget scenarios. Performance profiles constructed using IGD+ and epsilon-indicator performance indicators demonstrate that the hybrid algorithms outperform NSGA-III. Statistical analysis confirms the superiority of the hybrid approaches, making them more efficient and reliable for the addressed problems.

The most commonly used objective function in structural optimization is weight minimization. Nodal displacements, compliance, the first natural frequency of vibration, the critical load factor concerning global stability, and others can also be considered additional objective functions. This paper aims to propose seven innovative many-objective structural optimization problems (MOSOPs) applied to 25-, 56-, 72-, 120-, and 582-bar trusses, not yet presented in the literature, in which the main objectives, in addition to the structure’s weight, refer to the structures’ vibrational and stability aspects. These characteristics are essential in designing structural models, such as the natural frequencies of vibration and load factors concerning global stability. Such new MOSOPs have more than three objective functions and are called many-objective structural optimization problems. The chosen objective functions refer to the structure’s weight, the natural frequencies of vibration, the difference between some of the natural frequencies of vibration, the critical load factor concerning the structure’s global stability, and the difference between some of its load factors. The sizing design variables are the cross-sectional areas of the bars (continuous or discrete). The methodology involves the finite element method (FEM) to obtain the objective functions and constraints and multi-objective evolutionary algorithms (MOEAs) based on differential evolution to solve the MOSOPs analyzed in this study. In addition, multi-criteria decision-making (MCDM) is adopted to extract the solutions from the Pareto fronts according to the artificial decision-maker’s (DM) preference scenarios, and the complete data for each chosen solution are provided. For the MOSOP with seven objective functions, it is possible to observe variations in the final weights of the optimum designs, considering the hypothetic scenarios, of 21.09% (25-bar truss), 289.73% (56-bar truss), 70.46% (72-bar truss), 45.35% (120-bar truss), and 74.92% (582-bar truss).

Muitos problemas oriundos do mundo real podem ser modelados matematicamente como Problemas de Otimização Multiobjetivo (POMs), já que possuem diversas funções objetivo conflitantes entre si que devem ser minimizadas simultaneamente. POMs com mais de 3 funções objetivo recebem o nome de Problemas de Otimização com Muitos Objetivos (MaOPs, do inglês Many-objective Optimization Problems). Os POMs geralmente são resolvidos através de Algoritmos Evolutivos Multiobjetivos (MOEAs, do inglês Multiobjective Evolutionary Algorithms), os quais conseguem obter um conjunto de soluções ótimas não dominadas entre si, conhecidos como frente de Pareto, em uma única execução. O MOEA baseado em decomposição (MOEA/D) é um dos mais eficientes, o qual divide um POM em vários subproblemas monobjetivos otimizando-os ao mesmo tempo. Neste estudo foi realizada uma avaliação dos desempenhos do MOEA/D e quatro de suas variantes que representam o estado da arte da literatura (MOEA/DD, MOEA/D-DE, MOEA/D-DU e MOEA/D-AWA) em POMs e MaOPs. Foram conduzidos experimentos computacionais utilizando POMs e MaOPs benchmark do suite DTLZ considerando 3 e 5 funções objetivo. Além disso, foi realizada uma análise estatística que incluiu o teste de Wilcoxon para avaliar os resultados obtidos no indicador de desempenho IGD+. Também foi considerado o indicador de desempenho Hypervolume na frente de Pareto combinada, que é formada por todas as soluções obtidas por cada MOEA. Os experimentos revelaram que o MOEA/DD apresentou a melhor performance no IGD+ e o MOEA/D-AWA obteve o maior Hypervolume na frente de Pareto combinada, enquanto o MOEA/D-DE registrou o pior resultado nesse conjunto de problemas.

Several real-world problems can be modeled as optimization problems in which multiple conflicting objectives must be optimized simultaneously. Evolutionary algorithms (EA) are able to identify a set of non-dominated solutions (Pareto front) and are commonly used to solve these problems. Hybrid EAs that combine various optimization techniques can leverage the strengths of each method involved, enhancing their overall effectiveness. This study evaluates the performance of the well-known NSGA-III hybridized with Differential Evolution, Sine Cosine, and Arithmetic algorithms on optimization problems based on real-world applications with three, four and five objective functions, extracted from the CEC 2021 competition. Performance comparisons between the hybrid and original versions of NSGA-III were conducted using the IGD+ and HyperVolume indicators. Statistical analysis via the Wilcoxon test revealed significant improvements in NSGA-III performance when the hybrid version is considered.