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This paper proposes an evolutionary algorithm with clustering-based selection strategies to deal with multi-objective optimization problems. In the proposed algorithm, two clustering based selection strategies, named local indicator selection and local crowding selection, have been devised to appropriately search the space. The local indicator selection is developed to select diverse and well-converged individuals for mating while the local crowding selection strategy is designed to maintain a set of evenly distributed individuals on the Pareto front for next generation of evolution. The proposed method is further enhanced by a clustering based crowding degree strategy, which is introduced to extract a uniformly distributed and convergent solutions as the final output. The performance of proposed algorithm has been evaluated on 31 benchmark problems and compared with related methods. The results clearly show the merits of proposed strategies and the proposed method could significantly outperform related methods to be compared. [ABSTRACT FROM AUTHOR]

Surrogate-assisted evolutionary algorithms (SAEAs) are promising methods for addressing computationally expensive problems. This paper proposes a multiple surrogates and offspring-assisted differential evolution (MSODE) algorithm for high-dimensional expensive problems. Ensemble models consisting of multiple base models are built based on bagging. The ensemble models contribute toward reducing the variations of predictions and the uncertainty of base models. The algorithm proposes a multiple-offspring evolution strategy in which it generates multiple offspring for each parent individual to enhance the search ability of the population. The appropriate number of offspring was investigated, considering the tradeoff between optimization results and efficiency. MSODE consists of a global prescreening search, local search, and uncertainty prescreening search. The global prescreening search adopts a global ensemble to prescreen promising offspring. The local search accelerates the convergence by searching for the optimum of a local ensemble. The uncertainty prescreening search requires a number of fitness evaluations that slightly deteriorate the results. A comprehensive analysis was conducted to determine the optimal parameter settings. MSODE was compared with meta -heuristic algorithms and SAEAs on a series of benchmark problems. The results show that MSODE behaves better than most algorithms and is competitive against the best ones. [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]

Due to the fixed and monotonous search direction, the performance of decomposition-based multiobjective evolutionary algorithms (MOEAs) highly depends on the Pareto front (PF) shape. Recent studies have highlighted the complementary effect of the ideal and nadir points. They roughly employed both as the reference points to diversify the search direction. However, few works investigate whether two points are equally important. This paper thereby proposes a novel decomposition-based MOEA, where the ideal point is consistently considered as the global reference point while the nadir point is conditionally employed as the local one. We show that the nadir point may aid the ideal point in some cases and be recognized as a redundant one in others. More specifically, an assignment strategy is suggested to determine the necessity of using a local reference point for each subproblem, by considering whether the solution found by the nadir point and corresponding weight vector can improve the quality of the population. Experimental results finally verify the effectiveness of the proposed algorithm on 57 benchmark test problems with various PF shapes. In comparison with the state-of-the-art decomposition-based MOEAs, the proposed algorithm is promising to bring a more refined search and prevent redundant search behaviors. [ABSTRACT FROM AUTHOR]

• A surrogate model based on IRL is suggested, which applies the max-margin method to approximate the reward function. • Under different dynamic environments, IRL learns the reward function and helps accelerate the convergence of the algorithm. • On the basis of learned reward function, IRL-DMOEA generates promising non-dominated solutions during the evolutionary process. Due to the widespread interest in dynamic multiobjective optimization in real-world applications, more and more approaches exploiting machine learning are deployed to tackle this type of problems. Unfortunately, recent works do not make full use of the data obtained during the optimization process, which could be benefit for model training thereby mining the dynamic characteristics of the underlying problem. To address this issue, this paper proposes a dynamic multiobjective evolutionary algorithm driven by inverse reinforcement learning to solve the dynamic multiobjective optimization problems. IRL is widely used to recover the unknown reward function, making it possible to perform at an expert level. The notable features of the proposed algorithm mainly consist of data-driven evolutionary technique, which uses inverse reinforcement learning as a surrogate-assisted model for model training. This design makes full use of the surrogate management strategy based on inverse reinforcement learning to optimize the reward function within a reinforcement learning framework. At the same time, the algorithm can generate a promising policy based on limited training data during the optimization process to achieve better algorithm evolution and guide the search. The experimental results on the benchmark problems validate that the proposed algorithm is effective in dealing with dynamic multiobjective optimization. [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]

• Propose to divide the whole population into heterogeneous CL subpopulation and DMS subpopulation respectively mainly responsible for exploitation and exploration. • Propose to classify the DMS subpopulation sub-swarms search level and construct a new adaptive nonlinear decrease inertia weight formula. • Propose to introduce the non-uniform mutation operator in the DMS subpopulation and introduce a Gaussian mutation operator in the global optimal experiences of the whole population. • The performance of the proposed HCLDMS-PSO algorithm is compared with other 8 state-of-the-art PSO variants and 11 evolutionary algorithms on two classical benchmark optimization problems (CEC2005 and CEC2017) and a real-world engineering problem. In this paper, a heterogeneous comprehensive learning and dynamic multi-swarm particle swarm optimizer with two mutation operators (HCLDMS-PSO) is presented. In addition, a comprehensive learning (CL) strategy with the global optimal experience of the whole population is conducted to generate an exploitation subpopulation exemplar. However, a modified dynamic multi-swarm (DMS) strategy is specially designed to construct the exploration subpopulation exemplar. In the canonical DMS strategy, it is unfavorable for different sub-swarms to use the same linear decreasing inertia weight parameter. We first propose classifying the DMS sub-swarms at the search level and then constructing a novel nonlinear adaptive decreasing inertia weight for different sub-swarms, introducing a non-uniform mutation operator to enhance its exploration capability. Finally, the gbest of the whole population also adopts a Gaussian mutation operator to avoid falling into the local optimum. The particles of the two subpopulations will update their velocity independently without crippling one another to prevent a loss of diversity. The performance of HCLDMS-PSO is compared with those of 8 other PSO variants and 11 evolutionary algorithms on two classical benchmark optimization problems and a real-world engineering problem. Experimental results demonstrate that the HCLDMS-PSO improves the convergence speed, accuracy, and reliability on most optimization problems. [ABSTRACT FROM AUTHOR]

• Propose a mechanism combining key features of Linkage Tree Genetic Algorithm (LTGA) and Multifactorial Optimization (MFO). • Propose a method for building the linkage tree based on unified search space to exploit both information between problem variables and transfer knowledge of independent tasks. • Propose an assortative mating mechanism to enhance the compatibility between the main features of MFO and LTGA. • Introduce a crossover operator to keep the key advantages of MFO and LTGA as well as maintain population diversity. • Demonstrate the effectiveness of the proposed algorithm on two benchmark problems. Linkage Tree Genetic Algorithm (LTGA) is an effective Evolutionary Algorithm (EA) to solve complex problems using the linkage information between problem variables. LTGA performs well in various kinds of single-task optimization and yields promising results in comparison with the canonical genetic algorithm. However, LTGA is an unsuitable method for dealing with multi-task optimization problems. On the other hand, Multifactorial Optimization (MFO) can simultaneously solve independent optimization problems, which are encoded in a unified representation to take advantage of the process of knowledge transfer. In this paper, we introduce Genetic Algorithm (MF-LTGA) by combining the main features of both LTGA and MFO. MF-LTGA is able to tackle multiple optimization tasks at the same time, each task learns the dependency between problem variables from the shared representation. This knowledge serves to determine the high-quality partial solutions for supporting other tasks in exploring the search space. Moreover, MF-LTGA speeds up convergence because of knowledge transfer of relevant problems. We demonstrate the effectiveness of the proposed algorithm on two benchmark problems: Clustered Shortest-Path Tree Problem and Deceptive Trap Function. In comparison to LTGA and existing methods, MF-LTGA outperforms in quality of the solution or in computation time. [ABSTRACT FROM AUTHOR]

Multi-objective optimization problems with interval parameter (IMOPs) are among the most critical optimization problems in practical applications. However, in contrast to deterministic multi-objective optimization, few studies have addressed IMOPs. Moreover, the uncertainty in such problems makes the convergence and diversity of the algorithm more challenging. Therefore, this paper proposes an interval multi-objective optimization algorithm based on elite genetic strategy (EG-IMOEA). First, existing interval dominance relations cannot comprehensively determine which of the two intervals is better when their midpoints are equal but their upper and lower limits are unequal. Therefore, a conditional-based interval confidence dominance relation is proposed that considers both the average level of convergence and value of the minimum lower limit of intervals. The interval crowding distance (ICD) applied to multiple objectives is then defined to evaluate the solutions more completely. Furthermore, an elite genetic strategy for crossover and mutation is proposed to generate better offspring. The proposed algorithm was evaluated on nine benchmark test problems and compared with the typical algorithm as well as state-of-the-art algorithms. The results showed that this algorithm outperformed the comparison algorithms in terms of convergence, diversity, imprecision, and uniform distribution. [ABSTRACT FROM AUTHOR]