In the realm of evolutionary multiobjective optimization, the hypervolume indicator serves as a crucial metric for assessing the quality of solution sets. Due to the high costs in hypervolume computation, hypervolume-based optimization algorithms always meet the challenge of finding a certain number of points in a given point set to maximize the hypervolume indicator, especially when there are many objectives. In response, the greedy decremental algorithm for hypervolume subset selection problem (gHSSD) has emerged as a noteworthy alternative. This paper introduces a general algorithm for gHSSD, applicable in any dimensionality above two. The proposed algorithm leverages a space partition tree and incorporates a once-build-multiple-use strategy, effectively reducing time complexity. We prove that the proposed algorithm has a time complexity of O((n-k+n)nd-12logn) where n is the number of points, k is the number of points to be reserved, and d the dimensionality. Theoretically, this complexity is competitive with the current best algorithms for d=3,4 and better than them for all 5≤d≤7. To validate our algorithm, we have conducted extensive tests on various random point sets and multiobjective optimization benchmarks. Experimental results suggest that our implementation is more efficient than or competitive with state-of-the-art algorithms on many instances as n increases for d=3,4.

This letter discusses the challenge when evaluating multi-objective optimisation algorithms under noise. It argues that it is important to take into account possible selection errors by a decision maker, due to inaccurate estimates of a solution’s true objective values. It demonstrates that commonly used performance metrics don’t properly account for such errors, and proposes two alternative performance metrics that do account for such errors by adapting the popular R2 and IGD+ metrics.

Both dual-population and two-phase strategies are effective for utilizing infeasible solution information and significantly enhancing the ability of algorithms to solve constrained multi-objective optimization problems. However, most existing algorithms tend to underperform when facing problems with complex constraints. To address these issues, a constrained multi-objective evolutionary algorithm named DPTPEA, which combines dual-population and two-phase strategies, is proposed in this paper. DPTPEA employs two collaborative populations (the exploitive population and the tractive population) and divides the evolutionary process of the tractive population into two phases (Phase 1 and Phase 2). In Phase 1, the tractive population ignores constraints and drags the exploitive population across the infeasible region by sharing offspring information. In Phase 2, the tractive population adopts the epsilon-constrained method to converge toward the constrained Pareto front and to guide the exploitive population exploiting different feasible regions. Moreover, a dynamic cooperation strategy, a boundary point direction sampling strategy, and a dynamic environmental selection are proposed to improve the exploration ability of tractive population for solving complex problems. Comprehensive experiments on three popular test suites demonstrate that DPTPEA outperforms seven state-of-the-art algorithms on most test problems.

Automatic design of intelligent robots plays a central role and has been a trending topic in embodied intelligence. A promising approach is the co-design framework, wherein evolutionary algorithms (EAs) are employed to optimize the robot’s morphology while reinforcement learning algorithms are utilized to refine its control strategies. However, the discrete morphology design space introduces significant challenges for EAs, to efficiently identify optimal morphologies. In this work, we propose a novel morphology optimization method driven by a classifier-guided diffusion model to enhance the search efficiency of EAs. Prior to the design process, a universal diffusion model is trained using a set of randomly sampled feasible morphologies, prompting that the generated structures satisfy physical constraints. In each iteration of the EA for morphology optimization, a classifier is trained using previously evaluated morphologies and is then used to condition the diffusion model to generate quality solutions. Subsequently, the generated morphology is further refined based on the voxel distribution to incorporate features from the current high-quality morphology. Extensive experiments on a large-scale benchmark for co-designing the morphology and control of voxel-based soft robots demonstrate that our method significantly improves search efficiency in the morphological design space, outperforming both traditional EAs and surrogate-assisted EAs.

Most of the current expensive multiobjective optimization (MOO) algorithms focus on identifying Pareto optimal solutions. However, in some applications such as multiobjective modular design, decision-makers often prefer a set of optimal solutions that share common components in the decision space, which may conflict with Pareto optimality. Existing expensive MOO algorithms are not specifically designed to address this preference. To bridge this gap, we propose modeling the component-sharing preference in MOO as a special bi-level multiobjective optimization problem. Specifically, the upper-level is a single-objective optimization problem that seeks the optimal shared variables, while the lower-level is a multiobjective optimization problem aimed at identifying trade-off solutions for given shared variable values. Moreover, the lower-level objective is expensive-to-evaluate and can only be evaluated for a limited number of times. To efficiently solve this problem, we introduce a data-efficient algorithm called Bayesian Bi-level Search (BBS). The effectiveness of BBS is validated through six new benchmark problems and a real-world application involving the planform shape design of Blended-Wing-Body underwater glider. The results show that our method effectively identifies solutions with shared components within limited computational budgets.

Defect recognition is an essential aspect of intelligent manufacturing, but it is a challenging task with noise and unpredictable uncertainties, where convolutional neural networks (CNNs) struggle to achieve good performance. The fuzzy neural network (FNN) emerges as a promising approach to handle uncertainties. However, conventional methods for designing FNNs are tedious and error-prone. A solution is to automatically search for efficient FNN, which can be achieved by neural architecture search (NAS). To achieve NAS for FNN, we propose an efficient classifier-assisted evolutionary multiobjective FNN framework for defect recognition. Considering the characteristics of FNN (e.g., difficult to train and prone to overfitting), we first construct the architecture search as a constrained multiobjective optimization problem, the network accuracy and the architecture size are two conflicting objectives, and the constraint is used to filter out low-quality architectures. Then, we design the search space to incorporate the fuzzy module and develop the corresponding architectural representation and evolutionary operators. Furthermore, the complex regression task of performance evaluation is transformed into a classification task, and a classifier is designed to simplify the performance evaluation process. Massive experiments on four defect recognition datasets (i.e., ELPV, CODEBRIM, MIXEDWM38, and WM-811K) show that the architectures can effectively handle inherent uncertainties from datasets. Our method achieves 94.77% accuracy on ELPV, 81.82% accuracy on CODEBRIM, 98.99% accuracy on MIXEDWM38, and 98.22% accuracy on WM-811K, respectively.

Multi-party multi-objective optimization, which aims to find a solution set that satisfies multiple decision makers (DMs) as much as possible, has attracted the attention of researchers recently. Although multi-party multi-objective optimization is of great significance in practical applications, most existing works focus on continuous problems while paying little attention to discrete problems. To this end, we propose a multi-party multi-objective evolutionary framework named MP-HCEA for discrete problems, where a multi-party population is used to optimize all objectives of multiple DMs, and multiple single-party populations are used to respectively optimize the objectives of each DM. In MP-HCEA, a dual-phase cooperation mechanism is firstly proposed to guide the population interaction, where the weak cooperation is performed in the early phase to share offspring individuals, while the strong cooperation is performed in the later phase to share parent individuals. This dual-phase cooperation mechanism not only ensures effective information sharing between multiple populations, but also helps them to obtain high-quality solutions. In addition, a novel dual-search mechanism is proposed to guide the evolution of the multi-party population, which further enhances the convergence ability of the algorithm. Finally, we apply MP-HCEA to a real application named multi-stakeholder recommendation as a case study. Experiments on real-world multi-stakeholder recommendation datasets show that the proposed MP-HCEA outperforms several representative baselines.

Evolutionary feature construction has seen notable advancements in recent years. A major limitation affecting the effectiveness of evolutionary feature construction is its failure to fully leverage the large number of building blocks evaluated during the evolutionary process. In this paper, to fully utilize historical building blocks, we propose a semantic local search algorithm that operates in the semantic space using a dynamically updated semantic library. This library collects up to 10,000 trees and subtrees during the evolutionary process, with a design that adapts linear scaling and considers tree complexity to enhance both accuracy and generalization performance. To manage a large semantic library, we employ a ball tree and an instance selection mechanism, optimizing computational and memory resources. Furthermore, a positive-negative search mechanism and a semantic library-guided mutation operator are introduced to further improve the effectiveness of the semantic library in feature construction. Experimental validation on 120 datasets demonstrates that our semantic library-based genetic programming approach significantly outperforms several symbolic regression and machine learning algorithms, highlighting its superior performance.