There have been few researches on solving multi-modal multi-objective optimization problems, whereas they are commonly seen in real-world applications but difficult for the existing evolutionary optimizers. In this study, we propose a novel multi-modal multi-objective evolutionary algorithm using two-archive and recombination strategies. In the proposed algorithm, the properties of decision variables and the relationships among them are analyzed at first to guide the evolutionary search. Then, a general framework using two archives, i.e., the convergence and the diversity archives, is adopted to cooperatively solve these problems. Moreover, the diversity archive simultaneously employs a clustering strategy to guarantee diversity in the objective space and a niche-based clearing strategy to promote the same in the decision space. At the end of evolution process, solutions in the convergence and the diversity archives are recombined to obtain a large number of multiple Pareto optimal solutions. In addition, a set of benchmark test functions and a performance metric are designed for multi-modal multi-objective optimization. The proposed algorithm is empirically compared with two state-of-the-art evolutionary algorithms on these test functions. The comparative results demonstrate that the overall performance of the proposed algorithm is significantly superior to the competing algorithms.

With the global energy shortage, climate anomalies, environmental pollution becoming increasingly prominent, energy saving scheduling has attracted more and more concern than before. This paper studies the energy-efficient distributed hybrid flow-shop scheduling problem (DHFSP) with blocking constraints. Our aim is to find the job sequence with low energy consumption as much as possible in a limited time. In this paper, we formulate a mathematical model of the DHFSP with blocking constraints and propose an improved iterative greedy (IG) algorithm to optimize the energy consumption of job sequence. In the proposed algorithm, first, a problem-specific strategy is presented, namely, the global search strategy, which can assign appropriate jobs to the factory and minimize the energy consumption of each processing factory. Next, a new selection mechanism inspired by Q-learning is proposed to provide strategic guidance for factory scheduling. This selection mechanism provides historical experience for different factories. Finally, five types of local search strategies are designed for blocking constraints of machines and sequence to be scheduled. These proposed strategies can further improve the local search ability of the QIG algorithm and reduce the energy consumption caused by blocking. Simulation results and statistical analysis on 90 test problems show that the proposed algorithm is superior to several high-performance algorithms on convergence rate and quality of solution.

Multimodal multiobjective optimization problems (MMOPs) are commonly seen in real-world applications. Many evolutionary algorithms have been proposed to solve continuous MMOPs. However, little effort has been made to solve combinatorial (or discrete) MMOPs. Searching for equivalent Pareto optimal solutions in the discrete decision space is challenging. Moreover, the true Pareto optimal solutions of a combinatorial MMOP are usually difficult to know, which has limited the development of its optimizer. In this paper, we first propose a test problem generator for multimodal multiobjective traveling salesman problems (MMTSPs). It can readily generate MMTSPs with known Pareto optimal solutions. Then we propose a novel evolutionary algorithm to solve MMTSPs. In our proposed algorithm, we develop two new edge assembly crossover operators, which are specialized in searching for superior solutions to MMTSPs. Moreover, the proposed algorithm uses a new environmental selection operator to maintain a good balance between the objective space diversity and decision space diversity. We compare our algorithm with five state-of-the-art designs. Experimental results convincingly show that our algorithm is powerful in solving MMTSPs.

Molecular interaction prediction plays a crucial role in forecasting unknown interactions between molecules, such as drug-target interaction (DTI) and drug-drug interaction (DDI), which are essential in the field of drug discovery and therapeutics. Although previous prediction methods have yielded promising results by leveraging the rich semantics and topological structure of biomedical knowledge graphs (KGs), they have primarily focused on enhancing predictive performance without addressing the presence of inevitable noise and inconsistent semantics. This limitation has hindered the advancement of KGbased prediction methods. To address this limitation, we propose BioKDN (Biomedical Knowledge Graph Denoising Network) for robust molecular interaction prediction. BioKDN refines the reliable structure of local subgraphs by denoising noisy links in a learnable manner, providing a general module for extracting task-relevant interactions. To enhance the reliability of the refined structure, BioKDN maintains consistent and robust semantics by smoothing relations around the target interaction. By maximizing the mutual information between reliable structure and smoothed relations, BioKDN emphasizes informative semantics to enable precise predictions. Experimental results on real-world datasets show that BioKDN surpasses state-of-theart models in DTI and DDI prediction tasks, confirming the effectiveness and robustness of BioKDN in denoising unreliable interactions within contaminated KGs