There exist many multiobjective optimization problems (MOPs) containing a large number of decision variables in real-world applications, which are known as large-scale MOPs. Due to the ...ineffectiveness of existing operators in finding optimal solutions in a huge decision space, some decision variable division-based algorithms have been tailored for improving the search efficiency in solving large-scale MOPs. However, these algorithms will encounter difficulties when solving problems with complicated landscapes, as the decision variable division is likely to be inaccurate and time consuming. In this paper, we propose a competitive swarm optimizer (CSO)-based efficient search for solving large-scale MOPs. The proposed algorithm adopts a new particle updating strategy that suggests a two-stage strategy to update position, which can highly improve the search efficiency. The experimental results on large-scale benchmark MOPs and an application example demonstrate the superiority of the proposed algorithm over several state-of-the-art multiobjective evolutionary algorithms, including problem transformation-based algorithm, decision variable clustering-based algorithm, particle swarm optimization algorithm, and estimation of distribution algorithm.
This article presents a novel evolution strategy-based evolutionary algorithm, named DMOES, which can efficiently and effectively solve multiobjective optimization problems in dynamic environments. ...First, an efficient self-adaptive precision controllable mutation operator is designed for individuals to explore and exploit the decision space. Second, the simulated isotropic magnetic particles niching can guide the individuals to keep uniform distance and extent to approximate the entire Pareto front automatically. Third, the nondominated solutions (NDS) guided immigration can facilitate the population convergence with two different strategies for the NDSs and the dominated solutions, respectively. As a result, our algorithm can track the new approximate Pareto set and approximate Pareto front as quickly as possible when the environment changes. In addition, DMOES can obtain a well-converged and well-diversified Pareto front with much less population size and far lower computational cost. The larger the number of individuals, the sharper the contour of the resulted approximate Pareto front will be. Finally, the proposed algorithm is evaluated by the FDA, dMOP, UDF, and ZJZ test suites. The experimental results have been demonstrated to provide a competitive and oftentimes better performance when compared against some chosen state-of-the-art dynamic multiobjective evolutionary algorithms.
This paper suggests a preference-based methodology, which is embedded in an evolutionary multiobjective optimization algorithm to lead a decision maker (DM) to the most preferred solution of her or ...his choice. The progress toward the most preferred solution is made by accepting preference based information progressively from the DM after every few generations of an evolutionary multiobjective optimization algorithm. This preference information is used to model a strictly monotone value function, which is used for the subsequent iterations of the evolutionary multiobjective optimization (EMO) algorithm. In addition to the development of the value function which satisfies DM's preference information, the proposed progressively interactive EMO-approach utilizes the constructed value function in directing EMO algorithm's search to more preferred solutions. This is accomplished using a preference-based domination principle and utilizing a preference-based termination criterion. Results on two- to five-objective optimization problems using the progressively interactive NSGA-II approach show the simplicity of the proposed approach and its future promise. A parametric study involving the algorithm's parameters reveals interesting insights of parameter interactions and indicates useful parameter values. A number of extensions to this paper are also suggested.
Sparse large scale multiobjective optimization problems (sparse LSMOPs) contain numerous decision variables, and their Pareto optimal solutions' decision variables are very sparse (i.e., the majority ...of these solutions' decision variables are zero-valued). This poses grand challenges to an algorithm in converging to the Pareto set. Numerous evolutionary algorithms (EAs) tailored for sparse LSMOPs have been proposed in recent years. However, the final population generated by these EAs is not sparse enough because the location of the nonzero decision variables is difficult to locate accurately and there is insufficient interaction between the nonzero decision variables' locating process and the nonzero decision variables' optimizing process. To address this issue, we propose a dynamic sparse grouping evolutionary algorithm (DSGEA) that dynamically groups decision variables in the population that have a comparable amount of nonzero decision variables. Improved evolutionary operators are introduced to optimize the decision variables in groups. As a result, the population obtained by DSGEA can stably evolve towards the sparser Pareto optimal that has a precise location of nonzero decision variables. The proposed algorithm outperforms existing up-to-date EAs for sparse LSMOPs in experiments on three real-world problems and eight benchmark problems.
Multimodal multiobjective evolutionary algorithms are expected to search for not only Pareto optimal front but also the corresponding multiple equivalent Pareto optimal sets. To this end, this paper ...designs a framework to ameliorate the performance of the existing multiobjective evolutionary algorithms (MOEAs) for solving multimodal multiobjective optimization problems (MMOPs). In this framework, an MMOP is transformed into a bi-objective optimization problem. The first objective is built by either decomposition-based method or indicator-based method in MOEAs to ensure the population convergence. A diversity indicator is another objective used to preserve the population diversity. Based on these two objectives, two diversity selection strategies are developed, which are responsible for balancing the diversity and the convergence in the decision and objective spaces, respectively, at the same time. According to the feedback information in the evolution, our framework adaptively selects one of them to pick out the promising individuals. Four variants based on our framework are built and are evaluated on 22 MMOPs benchmark functions. Six feature selection problems are also employed to test the performance of our framework. The experimental results confirm that our proposed framework performs well in all criteria.
Optimizing the convergence and diversity of solutions simultaneously under constraints is a challenge in solving constrained multiobjective optimization problems. In existing multiobjective ...optimization algorithms, general diversity maintenance mechanisms have difficulty determining all optimal solutions in discrete feasible regions. This paper proposes a staged constrained multiobjective optimization algorithm with a diversity enhancement method (SDEM), which can explore potential discrete feasible regions by retaining well-distributed offspring. Specifically, after solutions have converged to optimal feasible regions by niching-based constraint dominance in the early stage, the SDEM improves the diversity of solutions through a proposed diversity enhancement dominance principle in the mid-term. Finally, the optimize objective functions and constraints of all solutions are optimized under constraint dominance to balance convergence, diversity, and feasibility during the three stages. Experiments on four well-known test suites and six real-world case studies demonstrate that the SDEM is competitive with or comparable to seven state-of-the-art constrained multiobjective evolutionary algorithms.
•Develop a finite element (FE) models for the aluminum/CFRP hybrid structures.•Reveal the interactive effect and energy absorption mechanisms of hybrid structures.•Investigate the effects of wall ...thickness, sectional dimension and sectional shape on the energy absorption capacity and performance-cost of the hybrid structures.•Design the hybrid structure adopting single/multi-objective discrete optimization method.
As a class of promising cost-effective lightweight structures, metal-composite hybrid structures has rapidly emerged in automotive industry largely attributable to their outstanding multifunctional and crashworthy characteristics. Recently, continuous efforts have been devoted to the studies on the crashworthiness of various hybrid tubes, which commonly present two typical configurational schemes, namely metal-composite (i.e. a metal outer tube internally filled with an inner carbon fiber reinforced plastic (CFRP) tube) and composite-metal (i.e. an outer composite tube internally filled with an inner metal tube). Nevertheless, rather limited studies have focused on revealing energy absorption mechanisms of hybrid structures; and how to optimize the performance to cost characteristics of hybrid structures still remains an open question in literature to date. This study aimed to maximize the energy absorption of different configurational aluminum/CFRP hybrid tubes. First, the finite element (FE) models were developed and validated by comparing the damage modes and crashworthiness indictors with the dedicated experimental study. Second, the interactive effects of the hybrid tubes were investigated by analyzing the discrepancies in the deformation pattern and internal energy absorption of each material through the validated FE models. For the AL-CF configuration (i.e. CFRP inner tube with aluminum outer tube), changes of deformation mode increased the internal energies of aluminum and CFRP tubes by 43.6% and 17.8% compared to the net aluminum tube and net CFRP tube, respectively; and increased the frictional dissipation energy by 45.6% compared to the sum of that of net aluminum and net CFRP tubes, largely enhancing energy absorption of AL-CF. For the CF-AL configuration (i.e. aluminum inner tube with CFRP outer tube), the internal energy increased by 27.6% for the aluminum tube but decreased 31.9% for the CFRP tube compared to the net aluminum tube and net CFRP tube, respectively; whereas the frictional dissipation energy decreased by 47.6% compared to the sum of that of net aluminum and CFRP tubes, indicating the vital importance of hybrid configuration to energy absorption. Third, the effects of wall thickness, sectional dimension and sectional shape on the energy absorption capacity as well as the performance-cost characteristics of the hybrid tubes were further studied. It was found that from a performance perspective, the hybrid tube with a thicker CFRP tube had higher capacity of energy absorption; whilst from a performance to cost perspective, the hybrid tube with a thinner aluminum tube offered better cost-effective energy absorption characteristics. Moreover, with the same weight, the hybrid tube with a circular sectional shape and a smaller sectional size exhibit a better performance. Finally, a multiobjective discrete optimization was conducted to optimize the AL-CF hybrid tube with various sectional shapes, sizes and wall thicknesses. As a result, the weight, peak crush force (PCF) and cost were finally reduced by 41.3%, 18.0% and 11.2% respectively, while the energy absorption (EA) was enhanced by 48.0% in comparison with the baseline design.
Multimodal multiobjective optimization problems (MMOPs) possess multiple Pareto optimal sets (PSs) corresponding to the identical Pareto optimal front (PF). To handle MMOPs, we propose a bi-objective ...evolutionary algorithm (BOEA), which transforms an MMOP into a bi-objective optimization problem. This problem is constructed by the penalty boundary intersection technique and a diversity indicator to obtain multiple PSs. The first objective reflects the population convergence and factors in the population diversity in the objective space, while the other objective concentrates more on the population diversity in the decision space. Furthermore, an environmental selection strategy is designed to choose the offspring solutions, which consists of nondominated sorting based on the transformed optimization problem and hierarchical clustering for selecting promising solutions. Experiments on 34 MMOPs demonstrate that BOEA performs better than selected state-of-the-art representatives, including 22 MMOPs from CEC2019 and 12 imbalanced MMOPs. In addition, the effectiveness of BOEA is further validated by six feature selection problems in real-world applications.
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