Heterogeneous operator mechanism and stochastic configuration network-enhanced large-scale multi-objective evolutionary algorithm

The competitive swarm optimizer (CSO) classifies swarm particles into loser and winner particles and then uses the winner particles to efficiently guide the search of the loser particles. This approach has very promising performance in solving large-scale multiobjective optimization problems (LMOPs). However, most studies of CSOs ignore the evolution of the winner particles, although their quality is very important for the final optimization performance. Aiming to fill this research gap, this article proposes a new neural net-enhanced CSO for solving LMOPs, called NN-CSO, which not only guides the loser particles via the original CSO strategy, but also applies our trained neural network (NN) model to evolve winner particles. First, the swarm particles are classified into winner and loser particles by the pairwise competition. Then, the loser particles and winner particles are, respectively, treated as the input and desired output to train the NN model, which tries to learn promising evolutionary dynamics by driving the loser particles toward the winners. Finally, when model training is complete, the winner particles are evolved by the well-trained NN model, while the loser particles are still guided by the winner particles to maintain the search pattern of CSOs. To evaluate the performance of our designed NN-CSO, several LMOPs with up to ten objectives and 1000 decision variables are adopted, and the experimental results show that our designed NN model can significantly improve the performance of CSOs and shows some advantages over several state-of-the-art large-scale multiobjective evolutionary algorithms as well as over model-based evolutionary algorithms.

Recently, the large-scale optimization problems have become a common research topic in the field of evolutionary computation. It is hard to find optimal solutions when solving large-scale multi-objective optimization problems (LSMOPs), due to the ineffectiveness of existing operators. In the other word, the search ability of most existing MOEAs on solving LSMOPs is still weak. To address this issue, an efficient competitive swarm optimizer with a strong exploration ability, denoted as E-CSO, is presented in this paper, which designs a novel three-particle-based particle updating strategy to improve the search efficiency. The experimental results validate the high efficiency and effectiveness of our proposed approach when solving various LSMOPs.

Multi-objective optimization problems with large-scale decision variables, known as LSMOPs, are characterized by their large-scale search space and multiple conflicting objectives to be optimized. They have been involved in many emergent real-world applications, such as feature and instance selection, data clustering, adversarial attack, vehicle routing problem, and others. In this work, we propose a new teaching-learning-based optimization algorithm to effectively tackle large-scale multi-objective optimization problems. The proposed approach ensures both the diversity of solutions, requested for high dimensionality of LSMOPs, and the balance between the exploitation and exploration during the optimization process. The experimental studies conducted on 54 instances of a large-scale multi-objective optimization problems test suite and the comparisons against well-known and state-of-the-art algorithms have shown the superiority of the proposed algorithm in terms of Pareto front approximation and computation time by using limited evaluation budget.

A fast sampling based evolutionary algorithm for million-dimensional multiobjective optimization

Addressing the challenge of efficiently handling high-dimensional search spaces in solving large-scale multiobjective optimization problems (LMOPs) becomes an emerging research topic in evolutionary computation. In response, this paper proposes a new evolutionary optimizer with a tactic of autoencoder-based problem transformation (APT). The APT involves creating an autoencoder to learn the relative importance of each variable by competitively reconstructing the dominated and non-dominated solutions. Using the learned importance, all variables are divided into multiple groups without consuming any function evaluations. The number of groups dynamically increases according to the population's evolutionary status. Each variable group has an associated autoencoder, transforming the search space into an adaptable small-scale representation space. Thus, the search process occurs within these dynamic representation spaces, leading to effective production of offspring solutions. To assess the effectiveness of APT, extensive testing is performed on benchmark suites and real-world LMOPs, encompassing variable sizes ranging from 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> . The comparative results demonstrate the advantages of our proposed optimizer in solving these LMOPs with a limited budget of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> function evaluations.

Many engineering optimization problems are typically multi-objective in their natures and multidisciplinary with a large number of decision variables. Furthermore, Pareto dominance loses its effectiveness in such situations. Thus, developing a robust optimization algorithm undoubtedly becomes a true challenge. This paper proposes a multi-objective orthogonal opposition-based crow search algorithm (M2O-CSA) for solving large-scale multi-objective optimization problems (LSMOPs). In the M2O-CSA, a multi-orthogonal opposition strategy is employed to mitigate the conflicts among the convergence and distribution of solutions. First, two individuals are randomly chosen to undergo the crossover stage and then orthogonal array is presented to obtain nine individuals. Then individuals are used in the opposition stage to improve the diversity of solutions. The effectiveness of the proposed M2O-CSA is investigated by implementing it on different dimensions of multi-objective optimization problems (MOPs). The Pareto front solutions of these MOPs have various characteristics such as convex, non-convex and discrete. It is also applied to solve multi-objective design applications with distinctive features such as four bar truss (FBT) design, welded beam (WB) deign, disk brake (DB) design, and speed reduced (SR) design, where they involve different characteristics. In this context, a new decision making tool based on multi-objective optimization on the basis of ratio analysis (MOORA) technique is employed to help the designer for extracting the operating point as the best compromise or satisfactory solution to execute the candidate engineering design. Simulation results affirm that the proposed M2O-CSA works efficiently and effectively.

Although there are many studies on large-scale unconstrained optimization (e.g., with 100 to 1000 variables) and small-scale constrained optimization (e.g., with 10 to 30 variables) using nature-inspired algorithms (e.g., evolutionary algorithms and swarm intelligence algorithms), no publicly available nature-inspired algorithm is developed for large-scale constrained optimization. In this paper, we combine a cooperative coevolutionary particle swarm optimization (CCPSO) algorithm with the e constrained method to solve large-scale real-valued constrained optimization problems. The eCCPSO framework is proposed, and three different algorithms based on the framework, i.e., eCCPSOd, eCCPSOw and eCCPSOw2, are developed. The proposed algorithms compare favorably to the state-of-the-art constrained optimization algorithm eDEag on large-scale problems. The experimental results further suggest that eCCPSOw2 with adaptive improvement detection technique is highly competitive compared with the other algorithms considered in this work for solving large-scale real-valued constrained optimization problems.

Competitive swarm optimizer (CSO) based on multidirectional search plays a crucial role in addressing large-scale multiobjective optimization problems (LSMOPs). However, relying solely on uniform or cluster partitioning of the objective space for sampling, along with two search directions constructed with upper and lower boundaries of global variables, sometimes lacks consideration of regional information. This results in an inefficient search and hinders the global convergence of the algorithm. To solve these problems, this study proposes a large-scale multiobjective competitive swarm optimizer algorithm based on regional multidirectional search (AMSLMOEA). Firstly, an adaptive objective space partitioning method based on the evolutionary state of the population is designed to enhance the adaptability of partitioning. Secondly, an individual multidirectional search strategy is introduced. Considering the algorithm’s computational complexity, the strategy selects the optimal individual within each subregion and constructs four-directional search vectors based on the lower limit of the global decision variables and the upper limit of the individual decision variables within the subregion. To validate the effectiveness of AMSLMOEA, the performance is tested on four benchmark function sets. The results demonstrate that AMSLMOEA outperforms the vast majority of the compared algorithms in terms of the IGD and HV metrics.

Large-scale machine system optimization problems usually resist solution because large-scale machine systems often have a hierarchical general structure that produces numerous local optirna during hierarchical optimization. Genetic algorithms having hierarchical genotypes can be directly applied to the optimization of such problems, however the appearance of local optima during hierarchical optimization procedures often foils effective searching. To enable the global optimization of such problems, skillful analysis of the component relationships comprising the hierarchical problem allows the hierarchical structure to be divided into more tractable units. Divided optimization problems can then be optimized via multiple crenetic algorithm processes, and global large-scale optimization problems can be represented as hierarchical sets of genetic algorithm processes. The exchange of local searching information between these genetic algorithm processes enables global searching and parallel processing, both of which enhance the efficiency and quality of searching for optimum solutions to large-scale optimization problems.

We propose singular value decomposition (SVD) algorithms for very large-scale matrices based on a low-rank tensor decomposition technique called the tensor train (TT) format. By using the proposed algorithms, we can compute several dominant singular values and corresponding singular vectors of large-scale structured matrices given in a low-rank TT format. We propose a large-scale trace optimization problem, and in the proposed methods, the large-scale optimization problem is reduced to sequential small-scale optimization problems. We show that the computational complexity of the proposed algorithms scales logarithmically with the matrix size if the TT-ranks are bounded. Numerical simulations based on very large-scale Hilbert matrix demonstrate the effectiveness of the proposed methods.

A key part of CNC machine tools is the rolling bearing, and thus, it is vital to employ a data-driven approach for fault diagnosis. This paper proposes a two-stage fusion sparse learning algorithm for fault data processing that can identify and diagnose the fault types of rolling bearings based on sensor measurement data. During the feature extraction phase, temporal features of sequential data within the big data are extracted using a Long Short - Term Memory (LSTM) network. Moreover, the classification learning stage contains a new sparse learning algorithm, which applies regularization on stochastic configuration networks (SCN). The iterative learning formula combines the alternating direction method of multipliers (ADMM) with the analysis of the quadratic equations theory. Simultaneously, the model’s inequality supervision mechanism is updated based on convergence analysis. This developed algorithm incorporates the benefits of LSTM in extracting temporal data characteristics, along with the sparsity, ease of convergence, and lightweight nature of SCN. Consequently, it mitigates the shortcomings of deep models in end-to-end applications, particularly in terms of interpretability and structural redundancy, thus making it suitable for deployment on edge devices. Finally, a fusion sparse learning model (LSTM--SCN) is introduced based on the two-stage learning algorithm for rolling bearing fault diagnosis. In the experiments on the benchmark dataset, the optimal sparsity degree of this algorithm for the Sparse Coding Network (SCN) reached 76.66%, which was 30% higher than that of the Pooling-based Sparse Coding Network (PSCN). Moreover, in the experiments based on the dataset of Case Western Reserve University (CWRU), the optimal test classification accuracy achieved was 97.51%, and the optimal sparsity degree for SCN reached 29.39%. These results verify that the proposed algorithm exhibits sparsity, demonstrates effectiveness, and is capable of identifying faults in rolling bearings.

Meta-heuristic algorithms are widely viewed as feasible techniques to solve continuous large-scale numerical optimization problems. Grey wolf optimizer (GWO) is a relatively new stochastic algorithm with only a few parameters to adjust that can be easily used for global optimization. This paper presents an efficient and robust GWO (ERGWO) variant to solve large-scale numerical optimization problems. Inspired by particle swarm optimization, a nonlinearly adjustment strategy for parameter control is designed to balance exploration and exploitation. Additionally, a modified position-updating equation is presented to improve convergence speed. The performance of ERGWO is verified on 18 benchmark large-scale numerical optimization problems with dimensions ranging from 30 to 10,000, 30 benchmarks from CEC 2014, 30 functions in CEC 2017, respectively. Numerical experiments are performed to compare ERGWO to the basic GWO algorithm, other GWO variants, and other well-known meta-heuristic search techniques. Simulations demonstrate that the proposed ERGWO algorithm can find high quality solutions with low computational cost and very fast convergence.

This paper contributes to the development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed SC networks (SCNs). In contrast to the existing randomized learning algorithms for single layer feed-forward networks, we randomly assign the input weights and biases of the hidden nodes in the light of a supervisory mechanism, and the output weights are analytically evaluated in either a constructive or selective manner. As fundamentals of SCN-based data modeling techniques, we establish some theoretical results on the universal approximation property. Three versions of SC algorithms are presented for data regression and classification problems in this paper. Simulation results concerning both data regression and classification indicate some remarkable merits of our proposed SCNs in terms of less human intervention on the network size setting, the scope adaptation of random parameters, fast learning, and sound generalization.

A generic model-free approach for lithium-ion battery health management

Today, because of the exponential growth of the volume of data in big data applications, large-scale optimization problems (i.e., optimization problems with a large number of decision variables) have become ubiquitous in the real world [219, 220]. In this chapter, building on the algorithms and observations presented for solving both continuous and combinatorial optimization problems, we further present a novel multi-space evolutionary search framework based on EMT for solving large-scale single-objective optimization problem.