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Distributed optimization algorithms have the advantages of privacy protection and parallel computing. However, the distributed nature of these algorithms makes the system vulnerable to external attacks. This paper presents two penalty function based resilient algorithms for constrained distributed optimization under static and dynamic attacks. The objective function of the optimization problem is extended to nonsmooth ones and the convergence of the proposed algorithms in this case are proved under some mild conditions. Simulation experiments are performed and compared with some existing resilient primal-dual optimization algorithms using median-based mean estimator. For static attack, the proposed algorithm has better performance and faster convergence rate in the simulation experiments. For dynamic attack, the proposed algorithm has better performance and robustness in the simulation experiments, which illustrate that the proposed algorithms are more effective. [ABSTRACT FROM AUTHOR]

Constrained multi-objective optimization problems (CMOPs) require a delicate balance between satisfying constraints and optimizing objectives. Existing constrained multi-objective evolutionary algorithms (CMOEAs) often struggle to balance convergence, diversity, and feasibility, especially when dealing with CMOPs that have complex feasible regions. This paper proposes a multi-task-based self-organizing mapping evolutionary algorithm (MTSOM) to tackle this challenge, which includes a main and auxiliary task. Two populations independently optimize two tasks without considering constraints in the early stage. Subsequently, in the middle stage, both tasks explore the distribution structure of the population in parallel by employing a novel constraint-to-constraint self-organizing mapping (SOM) approach. In the late stage, the main task fully considers feasibility, while the auxiliary task focuses solely on the highest priority constraints. This approach enables rapid convergence toward feasible regions. To evaluate MTSOM's effectiveness, we conducted a series of experiments on five benchmark suites. Results indicate that MTSOM is competitive when compared to other state-of-the-art CMOEAs. Additionally, our proposed constraint-to-constraint SOM is superior in handling complex CMOPs. [ABSTRACT FROM AUTHOR]

Many domination-based multi-objective evolutionary algorithms (MOEAs) are designed for constrained multi-objective optimization problems (CMOPs). However, they still face the challenge of balancing the feasibility, convergence and distribution. This paper tackles this issue by proposing a multi-objective differential evolution algorithm based on domination and a mechanism of constraint-handling switching (MODE-CHS). In constraint-handling switching, if there are no feasible solutions in the population, the population evolves by constraint-handling; otherwise, the population evolves without handling constraints. This mechanism enhances the rate of population convergence to the maximum while obtaining the feasible solutions. Furthermore, in MODE-CHS, the feasible solutions are saved to an external archive and evolve together with the population to explore the feasible region. Meanwhile, to enhance the distribution, the offspring of the external archive also participates in the individual-update procedure of the population. 27 bench-mark test problems and two real-world problems are used for the performance comparison of the proposed algorithm with other five state-of-the-art algorithms. In the experiment, the proposed algorithm, MODE-CHS, is shown to produce satisfactory solutions for most of the tested functions, where other five MOEAs perform relatively worse. The experiment results demonstrate MODE-CHS is very competitive for solving CMOPs. [ABSTRACT FROM AUTHOR]

A key issue in evolutionary constrained optimization is how to achieve a balance between feasible and infeasible solutions. The quality of generated solutions in decomposition-based multi-objective evolutionary algorithms (MOEAs) depends strongly on the weights' setting. To fully utilize both the promising feasible and infeasible solutions, this paper proposes two-type weight adjustments based on MOEA/D for solving highly constrained many-objective optimization problems (CMaOPs). During the course of the search, the number of infeasible weights is dynamically reduced, to guide infeasible solutions with better convergence to cross the infeasible barrier, and also to lead infeasible solutions with better diversity to locate multiple feasible subregions. Feasible weights are evenly distributed and keep unchanged throughout the evolution process, which aims to guide the population to search Pareto optimal solutions. The effectiveness of the proposed algorithm is verified by comparing it against six state-of-the-art CMaOEAs on three sets of benchmark problems. Experimental results show that the proposed algorithm outperforms compared algorithms on majority problems, especially on highly constrained optimization problems. Besides, the effectiveness of the proposed algorithm has also been verified on an antenna array synthesis problem. [ABSTRACT FROM AUTHOR]

Hybridization in context to Evolutionary Computation (EC) strives to combine operators, components, and the best merits of different EC paradigms, to form a new evolutionary algorithm that enjoys a statistically superior performance, compared to its ancestors, over a wide range of application-specific optimization problems. In this paper, we propose a simple yet powerful amalgam composed of a modified Cultural Algorithm (CA) that is supported with an Enhanced Levy Flight Search (ELFS) to guide the search and further promote the harmony between the explorative and exploitative capacities of the conventional techniques. The novel amalgam, denoted by q-a CA + m IS, utilizes a balanced search scheme where it employs an adapted Influence Function (IF) with a novel quality function that establishes a harmony between the Knowledge Sources (KSs) in the Belief Space (BS), and between the BS and other components in the hybrid to produce the most suitable knowledge needed for a certain search mode. The CA framework is reinforced with an updated Selection Function (SF) that employs a successful selection strategy that uses the extended situational knowledge for the future selection of individuals. The proposed algorithm is tested using more than 50 benchmark functions that are taken from the IEEE CEC'06, and the IEEE CEC'19 competitions on constrained real-parameter optimization. Moreover, three well-known engineering design problems are used to test the validity of the algorithm for the solution of complex real-life problems. The comparative study indicates that the q-a CA + m IS algorithm was able to obtain a statistically superior performance and scalability behavior over most of the considered functions in comparison with other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

• The niche-based density estimation and angle-based selection strategy are devised. • Individuals with poor diversity are identified by niche-based density estimation. • Individuals with worse convergence are removed via angle-based selection. • NAEA can be easily extended to constrained many-objective optimization problems. It is well known that balancing population diversity and convergence plays a crucial role in evolutionary many-objective optimization. However, most existing multiobjective evolutionary algorithms encounter difficulties in solving many-objective optimization problems. Thus, this paper suggests niche-based and angle-based selection strategies for many-objective evolutionary optimization. In the proposed algorithm, two strategies are included: niche-based density estimation strategy and angle-based selection strategy. Both strategies are employed in the environmental selection to eliminate the worst individual from the population in an iterative way. To be specific, the former estimates the diversity of each individual and finds the most crowded area in the population. The latter removes individuals with weak convergence in the same niche. Experimental studies on several well-known benchmark problems show that the proposed algorithm is competitive compared with six state-of-the-art many-objective algorithms. Moreover, the proposed algorithm has also been verified to be scalable to deal with constrained many-objective optimization problems. [ABSTRACT FROM AUTHOR]

Balancing multiple objectives and various constraints is crucial for effectively solving constrained multi-objective optimization problems (CMOPs). Excessive focus on either convergence or feasibility may not result in favorable outcomes of the algorithm. To confront this challenge, this paper proposes a cooperative evolutionary algorithm named SaE-CMO, which aims to achieve a harmonious balance between convergence and feasibility by extracting valuable information from both feasible and infeasible regions. To achieve this, SaE-CMO employs a dual-population approach to enhance search progress, consisting of a main population, Population1, and an auxiliary population, Population2. These two populations complement each other to achieve optimal results. A newly proposed self-adaptive epsilon method is employed in both Population1 and Population2, using different comparison criteria to select next population from mating pools, respectively. Population2 can retain some solutions that are well-constrained but poorly converged, thereby preserving information about both the constrained and the unconstrained Pareto front. This property enables Population2 to assist Population1 in maintaining diversity in certain complex CMOPs. To verify the effectiveness of SaE-CMO, we conduct experiments on three benchmark test instances and four real-world CMOPs with some related state-of-the-art constrained multi-objective optimization algorithms, experimental results prove that the proposed algorithm outperforms the compared algorithms. [ABSTRACT FROM AUTHOR]

It is of necessity to select appropriate optimization algorithms from an algorithm library due to the universality of constrained multi-objective optimization problems and the suitability of intelligent optimization algorithms, which requires a rich optimization algorithm library. This paper proposes a migration-based method of enriching the algorithm library for constrained multi-objective optimization problems. After calculating the similarity between problems based on their landscape features, the proposed method calculates the migration probabilities of intelligent optimization algorithms solving similar problems based on the performance of each algorithm and the similarity between problems. According to the redundancy and compatibility of components, the algorithms with large migration probabilities enrich the algorithm library for solving the current problem. Based on the enhanced algorithm library, a Softmax regression model is trained to generate an optimal intelligent algorithm to solve the current problem. The proposed method is applied to solve a series of constrained multi-objective optimization benchmark problems and the operation optimization problems of an integrated coal mine energy system, and the experimental results verify its effectiveness and feasibility. • A method based on landscape features is proposed to determine similar problems. • A method is given to select migrated algorithms based on similarity and performance. • A method based on redundancy and compatibility is presented to enrich an IOAL. [ABSTRACT FROM AUTHOR]

• A novel CHT is proposed based on Pareto dominance-based ranking and CDP-based ranking. • A search algorithm based on four mutation operators is proposed. • A new constrained multiobjective differential evolution algorithm is proposed. The tradeoff between objective functions and constraints is a key issue that needs to be addressed by constrained multiobjective optimization algorithms, and constraint handling techniques (CHTs) are an important technique for balancing objective functions and constraints. In this paper, a novel CHT that fuses two rankings is proposed. Specifically, each individual is assigned two rankings: one ranking calculated based on Pareto dominance (regardless of constraints) and another calculated based on the constrained dominance principle (CDP). The fitness value of an individual is the weighted sum of these two rankings, and the weight is related to the generation number and the proportion of feasible solutions in the current generation. Based on the proposed CHT, a constrained multiobjective differential evolution algorithm is proposed. To generate high-quality offspring, the proposed constrained multiobjective differential evolution algorithm combines four mutation operations as core components of the search algorithm. The proposed algorithm is compared with eight state-of-the-art algorithms in experiments with five test suites, and the experimental results show that the proposed algorithm performs significantly better than the eight state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]