A Variable Importance-Based Differential Evolution for Large-Scale Multiobjective Optimization

Evolution algorithm with adaptive genetic operator and dynamic scoring mechanism for large-scale sparse many-objective optimization

Large-scale sparse multi-objective optimization problems are prevalent in numerous real-world scenarios, such as neural network training, sparse regression, pattern mining and critical node detection, where Pareto optimal solutions exhibit sparse characteristics. Ordinary large-scale multi-objective optimization algorithms implement undifferentiated update operations on all decision variables, which reduces search efficiency, so the Pareto solutions obtained by the algorithms fail to meet the sparsity requirements. SparseEA is capable of generating sparse solutions and calculating scores for each decision variable, which serves as a basis for crossover and mutation in subsequent evolutionary process. However, the scores remain unchanged in iterative process, which restricts the sparse optimization ability of the algorithm. To solve the problem, this paper proposes an evolution algorithm with the adaptive genetic operator and dynamic scoring mechanism for large-scale sparse many-objective optimization (SparseEA-AGDS). Within the evolutionary algorithm for large-scale Sparse (SparseEA) framework, the proposed adaptive genetic operator and dynamic scoring mechanism adaptively adjust the probability of cross-mutation operations based on the fluctuating non-dominated layer levels of individuals, concurrently updating the scores of decision variables to encourage superior individuals to gain additional genetic opportunities. Moreover, to augment the algorithm's capability to handle many-objective problems, a reference point-based environmental selection strategy is incorporated. Comparative experimental results demonstrate that the SparseEA-AGDS algorithm outperforms five other algorithms in terms of convergence and diversity on the SMOP benchmark problem set with many-objective and also yields superior sparse Pareto optimal solutions.

Two-Stage Cooperation Multiobjective Evolutionary Algorithm Guided by Constraint-Sensitive Variables

Constrained multiobjective optimization problems are widespread in practical engineering fields. Scholars have proposed various effective constrained multiobjective evolutionary algorithms (CMOEAs) for such problems. However, most existing algorithms overlook the differences between different decision variables in influencing the degree of constraint violation and still lack an effective handling mechanism for constraint-sensitive variables. To address this issue, a two-stage cooperation multiobjective evolutionary algorithm guided by constraint-sensitive variables (CV-TCMOEA) is proposed. In the first stage, a relatively simple auxiliary problem with only a few dominant constraints is constructed to approximate the original problem. After obtaining a set of approximate Pareto optimal solutions by dealing with the auxiliary problem, in the second stage, a constraint-sensitive variable-guided multistrategy cooperation search method is developed. In this method, decision variables are divided into two types: 1) constraint-sensitive and 2) constraint-insensitive variables, and a variable-type-guided cooperative individual update strategy is proposed to autonomously select appropriate search strategies for different types of variables. Experimental results on 28 benchmark functions and 10 engineering problems demonstrated the superiority of the CV-TCMOEA over seven state-of-the-art CMOEAs.

Neural Net-Enhanced Competitive Swarm Optimizer for Large-Scale Multiobjective Optimization

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.

Evolutionary multiobjective optimization via efficient sampling-based offspring generation

With the rising number of large-scale multiobjective optimization problems from academia and industries, some evolutionary algorithms (EAs) with different decision variable handling strategies have been proposed in recent years. They mainly emphasize the balance between convergence enhancement and diversity maintenance for multiobjective optimization but ignore the local search tailored for large-scale optimization. Consequently, most existing EAs can hardly obtain the global or local optima. To address this issue, we propose an efficient sampling-based offspring generation method for large-scale multiobjective optimization, where convergence enhancement and diversity maintenance, together with ad hoc local search, are considered. First, the decision variables are dynamically classified into two types for solving large-scale decision space in a divide-and-conquer manner. Then, a convergence-related sampling strategy is designed to handle those decision variables related to convergence enhancement. Two additional sampling strategies are proposed for diversity maintenance and local search, respectively. Experimental results on problems with up to 5000 decision variables have indicated the effectiveness of the algorithm in large-scale multiobjective optimization.

DBCC2: an improved difficulty-based cooperative co-evolution for many-modal optimization

Evolutionary multimodal optimization algorithms aim to provide multiple solutions simultaneously. Many studies have been conducted to design effective evolutionary algorithms for solving multimodal optimization problems. However, optimization problems with many global and acceptable local optima have not received much attention. This type of problem is undoubtedly challenging. In this study, we focus on problems with many optima, the so-called many-modal optimization problems, and this study is an extension of our previous conference work. First, a test suite including additively nonseparable many-modal optimization problems and partially additively separable many-modal optimization problems is designed. Second, an improved difficulty-based cooperative co-evolution algorithm (DBCC2) is proposed, which dynamically estimates the difficulties of subproblems and allocates the computational resources during the search. Experimental results show that DBCC2 has competitive performance.

Multi-objective multi-criteria evolutionary algorithm for multi-objective multi-task optimization

Evolutionary multi-objective multi-task optimization is an emerging paradigm for solving multi-objective multi-task optimization problem (MO-MTOP) using evolutionary computation. However, most existing methods tend to directly treat the multiple multi-objective tasks as different problems and optimize them by different populations, which face the difficulty in designing good knowledge transferring strategy among the tasks/populations. Different from existing methods that suffer from the difficult knowledge transfer, this paper proposes to treat the MO-MTOP as a multi-objective multi-criteria optimization problem (MO-MCOP), so that the knowledge of all the tasks can be inherited in a same population to be fully utilized for solving the MO-MTOP more efficiently. To be specific, the fitness evaluation function of each task in the MO-MTOP is treated as an evaluation criterion in the corresponding MO-MCOP, and therefore, the MO-MCOP has multiple relevant evaluation criteria to help the individual selection and evolution in different evolutionary stages. Furthermore, a probability-based criterion selection strategy and an adaptive parameter learning method are also proposed to better select the fitness evaluation function as the criterion. By doing so, the algorithm can use suitable evaluation criteria from different tasks at different evolutionary stages to guide the individual selection and population evolution, so as to find out the Pareto optimal solutions of all tasks. By integrating the above, this paper develops a multi-objective multi-criteria evolutionary algorithm framework for solving MO-MTOP. To investigate the proposed algorithm, extensive experiments are conducted on widely used MO-MTOPs to compare with some state-of-the-art and well-performing algorithms, which have verified the great effectiveness and efficiency of the proposed algorithm. Therefore, treating MO-MTOP as MO-MCOP is a potential and promising direction for solving MO-MTOP.