Evolutionary feature selection methods face the challenge of “curse of dimensionality" when dealing with high-dimensional data. Focusing on this challenge, this paper studies a variable-size cooperative coevolutionary particle swarm optimization algorithm (VS-CCPSO) for feature selection. The proposed algorithm employs the idea of “divide and conquer" in cooperative coevolutionary approach, but several new developed problem-guided operators/strategies make it more suitable for feature selection problems. Firstly, a space division strategy based on the feature importance is presented, which can classify relevant features into the same subspace with a low computational cost. Following that, an adaptive adjustment mechanism of sub-swarm size is developed to maintain an appropriate size for each sub-swarm, with the purpose of saving computational cost on evaluating particles. Moreover, a particle deletion strategy based on fitness-guided binary clustering, and a particle generation strategy based on feature importance and crossover both are designed to ensure the quality of particles in the sub-swarms. We apply VS-CCPSO to 12 typical datasets, and compare it with six state-of-the-art methods. Experimental results show that VS-CCPSO has the capability of obtaining good feature subsets, suggesting its competitiveness for tackling feature selection problems with high dimensionality.

The performance of decomposition-based algorithms is sensitive to the Pareto front shapes since their reference vectors preset in advance are not always adaptable to various problem characteristics with no a priori knowledge. For this issue, this article proposes an adaptive reference vector reinforcement learning (RVRL) approach to decomposition-based algorithms for industrial copper burdening optimization. The proposed approach involves two main operations, that is: 1) a reinforcement learning (RL) operation and 2) a reference point sampling operation. Given the fact that the states of reference vectors interact with the landscape environment (quite often), the RL operation treats the reference vector adaption process as an RL task, where each reference vector learns from the environmental feedback and selects optimal actions for gradually fitting the problem characteristics. Accordingly, the reference point sampling operation uses estimation-of-distribution learning models to sample new reference points. Finally, the resultant algorithm is applied to handle the proposed industrial copper burdening problem. For this problem, an adaptive penalty function and a soft constraint-based relaxing approach are used to handle complex constraints. Experimental results on both benchmark problems and real-world instances verify the competitiveness and effectiveness of the proposed algorithm.

Dynamic interval multi-objective optimization problems (DI-MOPs) are very common in real-world applications. However, there are few evolutionary algorithms that are suitable for tackling DI-MOPs up to date. A framework of dynamic interval multi-objective cooperative co-evolutionary optimization based on the interval similarity is presented in this paper to handle DI-MOPs. In the framework, a strategy for decomposing decision variables is first proposed, through which all the decision variables are divided into two groups according to the interval similarity between each decision variable and interval parameters. Following that, two sub-populations are utilized to cooperatively optimize decision variables in the two groups. Furthermore, two response strategies, rgb0.00,0.00,0.00i.e., a strategy based on the change intensity and a random mutation strategy, are employed to rapidly track the changing Pareto front of the optimization problem. The proposed algorithm is applied to eight benchmark optimization instances rgb0.00,0.00,0.00as well as a multi-period portfolio selection problem and compared with five state-of-the-art evolutionary algorithms. The experimental results reveal that the proposed algorithm is very competitive on most optimization instances.

For dynamic multi-objective vehicle routing problems, the waiting time of vehicle, the number of serving vehicles, and the total distance of routes were normally considered as the optimization objectives. Except for the above objectives, fuel consumption that leads to the environmental pollution and energy consumption was focused on in this paper. Considering the vehicles' load and the driving distance, a corresponding carbon emission model was built and set as an optimization objective. Dynamic multi-objective vehicle routing problems with hard time windows and randomly appeared dynamic customers, subsequently, were modeled. In existing planning methods, when the new service demand came up, global vehicle routing optimization method was triggered to find the optimal routes for non-served customers, which was time-consuming. Therefore, a robust dynamic multi-objective vehicle routing method with two-phase is proposed . Three highlights of the novel method are: (i) After finding optimal robust virtual routes for all customers by adopting multi-objective particle swarm optimization in the first phase, static vehicle routes for static customers are formed by removing all dynamic customers from robust virtual routes in next phase. (ii) The dynamically appeared customers append to be served according to their service time and the vehicles' statues. Global vehicle routing optimization is triggered only when no suitable locations can be found for dynamic customers. (iii) A metric measuring the algorithms robustness is given. The statistical results indicated that the routes obtained by the proposed method have better stability and robustness, but may be sub-optimum. Moreover, time-consuming global vehicle routing optimization is avoided as dynamic customers appear.

Constrained multi-objective optimization problems (CMOPs) are difficult to solve since they involve the optimization of multiple objectives and the satisfaction of various constraints. Most constrained multi-objective evolutionary algorithms (CMOEAs) are prone to fall into the local optima due to the imbalance between objectives and constraints as well as the poor search ability of the population. To better solve CMOPs, this paper proposes a double-balanced evolutionary multi-task optimization (DBEMTO) algorithm, which evolves two populations to respectively solve the main task (CMOP) and the auxiliary task (MOP extracted from the CMOP). In DBEMTO, three evolutionary strategies are assigned to each population for offspring generation. The three evolutionary strategies include an individual transfer-based inter-task strategy and two intra-task strategies, not only utilizing the information of inter-task but also providing diverse search abilities of intra-task. Moreover, a self-adaptive scheme is developed to self-adaptively employ three strategies, so that the population can balance the information utilization of both intra-task and inter-task. Then, in the environmental selection, the performance of the three strategies is adopted to guide the sharing of the two offspring populations. Compared with several other state-of-the-art CMOEAs, DBEMTO has performed more competitively according to the final results.