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.

Dynamic multi-objective optimization problems (DMOPs) not only involve multiple conflicting objectives, but these objectives may also vary with time, raising a challenge for researchers to solve them. This paper presents a cooperative co-evolutionary strategy based on environment sensitivities for solving DMOPs. In this strategy, a new method that groups decision variables is first proposed, in which all the decision variables are partitioned into two subcomponents according to their interrelation with environment. Adopting two populations to cooperatively optimize the two subcomponents, two prediction methods, i.e., differential prediction and Cauchy mutation, are then employed respectively to speed up their responses on the change of the environment. Furthermore, two improved dynamic multi-objective optimization algorithms, i.e., DNSGAII-CO and DMOPSO-CO, are proposed by incorporating the above strategy into NSGA-II and multi-objective particle swarm optimization, respectively. The proposed algorithms are compared with three state-of-the-art algorithms by applying to seven benchmark DMOPs. Experimental results reveal that the proposed algorithms significantly outperform the compared algorithms in terms of convergence and distribution on most DMOPs.

To balance the unexpected power disturbances, an independent system operator (ISO) should assign the dynamic power regulation commands to all the regulation resources via an automatic generation control (AGC) dispatch. It can be described as a bi-objective Pareto optimization by considering the minimizations of total power deviation and total regulation mileage payment. In this work, a novel dropout deep neural network assisted transfer learning (DDNN-TL) is proposed to rapidly approximate the high-quality Pareto optimal solutions for AGC dispatch. Firstly, the training data is generated from the Pareto optimal solutions and fronts obtained by various multi-objective optimization algorithms according to the anticipated total power regulation commands. Secondly, the network parameters of DDNN will be updated via an off-line training with these data at each frequency regulation service period. Finally, based on an efficient transfer learning with a correction of infeasible solutions, DDNN-TL can directly approximate the high-quality Pareto optimal solutions for on-line decision of AGC dispatch. Case studies of DDNN-TL for bi-objective Pareto AGC dispatch are carried out on a two-area load frequency control model and Hainan power grid of China Southern Power Grid (CSG), which demonstrates its superior performance on optimization speed and stability compared with other multi-objective optimization algorithms.

Real-world production scenarios often involve multiobjective optimization problems with intricate constraints. Although there has been a growing interest in multiobjective problems with complex constraints, such as the vehicle routing problem with time windows, existing multiobjective evolutionary optimization techniques still face significant challenges, particularly when addressing the fragmented and narrow feasible regions that arise from these constraints. Our research introduces a refined framework tailored for complex constrained multiobjective evolutionary optimization. The methodology conducts an initial strong-weak analysis to categorize constraints and merges each strong constraint with all weak constraints to form subsets. Each subset, combined with the original objective functions, defines a subproblem. Independent optimization of the original problem and subproblems is carried out by utilizing multiple populations. Information acquired from the subproblems’ populations is transferred into the population of the original issue, thereby expediting the detection of the feasible region and simplifying the resolution of the original problem. The efficacy of our innovative algorithm, when benchmarked against traditional constrained multiobjective evolutionary algorithms across 72 test functions, has demonstrated superior convergence, diversity, and competitiveness.

As the length of electrocardiogram (ECG) sequences increases, most current transformer models demand substantial computational resources for ECG arrhythmia detection. Additionally, conventional single-scale tokens encounter difficulties in accommodating various patterns of arrhythmia. Thus, in this study, a refined-attention transformer model for arrhythmia detection was proposed. Our model introduces two refined attention mechanisms, namely, refined diag- and gated linear (GAL) attentions, effectively alleviating computational burdens associated with unnecessary correlations between heartbeats. To address rhythmic and beat-pattern arrhythmias, we used two refined transformer models with a collaborative block, leveraging coarse- and fine-grained tokens to capture inter and intraheartbeat correlations. The collaborative block between two models facilitates the exchange of rhythm information, thereby improving the accuracy of beat detection. On the MIT-BIH dataset, our refined attentions yield over a 65% reduction in computational efforts compared with conventional self-attention. Notably, our refined transformer models achieve 96% accuracy for rhythmic detection and rank within the top two performers for all types of heartbeat detection. Moreover, the collaborative block enhances the recall by 8.8% and precision by 3.4% for atrial premature detection.