Complex constrained multi-objective optimization problems are often characterized by narrow and disconnected feasible regions, making it challenging to obtain the optimal constrained Pareto front. To ...improve feasibility, diversity, and convergence in the optimization process, this paper introduces an adaptive dynamic migration-based constrained multi-objective state transition algorithm. The approach starts with an individual-based state transition algorithm, which searches for candidate solutions across the entire search space. Subsequently, these candidate solutions are evaluated using an adaptive dynamic migration constraint handling technique, which enhances the convergence of candidate solutions in the early stages of optimization and ensures their feasibility in the later stages. The migration process is adaptively adjusted based on the diversity and convergence of the population to maintain a balance among feasibility, diversity, and convergence. Experiments conducted on 14 benchmark problems reveal that the proposed method demonstrates superior or, at the very least, competitive performance when compared to other well-established methods.
A new optimization technique, multiobjective optimization immune algorithm for constrained nonlinear multiobjective optimization problems is designed based on immune metaphors of humoral immune and ...Pareto optimality, especially, some interactive metaphors between antigen population and antibody population. It includes four main mechanisms:
(1)
constraint-handling operation that provides an alternative feasible solution set for rapidly finding Pareto optimal solutions;
(2)
antibody evolution associated with clonal selection principle and ideas of immune regulation; competition and update of antigens that induces evolution of antibody populations;
(3)
memory pool used for collecting the best solutions of evolving antibody populations. Convergence is proven through Markov theory as well as demonstrated by the experiment results. Comparative analysis and applications illustrate that it is effective and valuable.
We develop an extended version of the extremal principle in variational analysis that can be treated as a variational counterpart to the classical separation results in the case of nonconvex sets and ...which plays an important role in the generalized differentiation theory and its applications to optimization-related problems. The main difference between the conventional extremal principle and the extended version developed below is that, instead of the translation of sets involved in the extremal systems, we allow deformations. The new version seems to be more flexible in various applications and covers, in particular, multiobjective optimization problemswith general preference relations. In this way we obtain new necessary optimality conditions for constrained problems of multiobjective optimization with nonsmooth data and also for multiplayer multiobjective games.
The magnetron injection gun (MIG) of the gyrotron is a complex particle dynamics system. It is a tedious and difficult task to design the MIG, especially under a pulsed high magnetic field. In this ...paper, the design process of the MIG for the gyrotron with a pulsed magnet is proposed based on the idea of optimization. The pulsed magnet is optimized by considering the efficient factor, field homogeneity, electrical parameters, thermal and mechanical strength. With the obtained magnetic field distribution, the electrode of the MIG is automatically designed by using constrained multiobjective optimization. Based on this process, a case study of the MIG with a 15 T pulsed magnet for a 400 GHz gyrotron is given.
When tackling constrained multi-objective optimization problems (CMOPs), especially problems with complex feasible areas, it is challenging for handling both objective optimization and constraint ...satisfaction. To remedy this problem, this paper introduces a novel two-stage constrained multi-objective evolutionary algorithm, NTEA, with different emphases on the objectives and constraints. In the first stage of NTEA, a dynamic balance method is used to dynamically adjust the selection preference from Pareto dominance to constrained dominance. The purpose of this stage is to obtain a certain feasible solutions and solutions with good objective values, thereby preventing the population from becoming trapped in local optima. In the second stage, an efficient search method based on competitive swarm optimizer is used to accelerate the convergence to the constrained Pareto front while maintaining the diversity of the whole population. To test the effectiveness of the proposed NTEA, experiments are carried out on two popular benchmark suites LIR-CMOP and DAS-CMOP. The outcomes demonstrate that the suggested algorithm competes effectively with state-of-the-art constrained multi-objective optimization evolutionary algorithms (CMOEAs).
Dynamic constrained multi-objective optimization problems (DCMOPs) are characterized by time-varying objectives and constraints, requiring optimization algorithms that can rapidly track the changing ...Pareto-Optimal Set (POS).A new dynamic constrained multi-objective evolutionary algorithm with adaptive two-stage archiving and autoencoder prediction is proposed in this paper, called ATAP to effectively solve DCMOPs. Specifically, ATAP designs a differential denoising autoencoder (DDA) prediction strategy, which applies a denoising autoencoder to thoroughly analyze change trends of historical population and predict some initial solutions in the new environment. Subsequently, to promote greater diversity within the initial population, a differential rule is implemented, effectively addressing the potential scarcity of diversity caused by constraints. Moreover, ATAP introduces an adaptive two-stage archiving (ATA) constraint handling technique, which can dynamically adjust evolutionary stages based on the state of the population. This approach can adaptively determine preferences between objectives and constraints, achieving a better balance. In this way, ATA and DDA are well cooperated to efficiently solve DCMOPs with time-varying constraints and objectives. The experimental results demonstrate that the proposed ATAP is effective and has some advantages over three competitive algorithms when solving the CEC2023 DCMOP benchmark.
The constrained multiobjective optimization problem (CMOP) is common in the real-world applications that need to simultaneously optimize conflicting objectives under certain constraints. In the past ...two decades, considerable efforts have been devoted to designing constrained multiobjective evolutionary algorithms (CMOEAs) for solving the CMOP. However, as the constraints become more complex, CMOEAs encounter a significant challenge of finding a set of well-distributed Pareto optimal solutions. The infeasible regions caused by the constraints become a major challenge in solving the CMOP since they hinder the population from moving toward the constrained Pareto front. The landscape of infeasible regions plays a significant role in the CMOP but is not well-studied. The present study aims to explore the influences of different landscapes of infeasible regions on the difficulty in solving a CMOP. To this end, we propose an approach to adjusting the landscapes through weights and present the MOEA/D-WSCV that enables the adjustment accordingly. The experimental results show that the inverted generation distance (IGD) and hypervolume (HV) obtained from MOEA/D-WSCV vary with weights, indicating the influences of infeasible regions upon the difficulty in solving CMOPs.
A differential evolution algorithm is proposed here to solve constrained multiobjective optimization problems (CMOPs). In this paper, an Adaptive Penalty Method (APM), which was successfully applied ...to solve single objective optimization problems, is used to handle the constraints. That constraint handling technique is incorporated to a multiobjective DE which combines the non-dominated ranking and crowding distance schemes when the candidate solutions are replaced. Previously, several variants of the APM were proposed and, here, those variants are tested in order to asses their performance when solving CMOPs. The results obtained in the computational experiments are used to compare the proposal with another well known constraint handling scheme in the literature.
The existence solution for a class of economic equilibrium type problems in reflexive Banach space is considered. New results concerning the variational inequality approach to Arrow–Debreu model of ...economic equilibrium introduced in Naniewicz (Math Oper Res 32:436–466,
2007
) are found and applied to ensure the existence of Pareto optimal solutions for a class of multiobjective optimization problems with so-called budget-like constraints. To achieve this goal, the theory of pseudo-monotone multivalued mappings combined with some fixed point technique for multivalued mappings with nonconvex values is used.
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