Multi-objective optimization problems (MOPs) require the simultaneous optimization of conflicting objectives. Real-world MOPs often exhibit complex characteristics, including high-dimensional decision spaces, many objectives, or computationally expensive evaluations. While population-based evolutionary computation has shown promise in addressing diverse MOPs through problem-specific adaptations, existing approaches frequently lack generalizability across distinct problem classes. Inspired by pre-training paradigms in machine learning, we propose a Population Pre-trained Model (PPM) that leverages historical optimization knowledge to solve complex MOPs within a unified framework efficiently. PPM models evolutionary patterns via population modeling, addressing two key challenges: (1) handling diverse decision spaces across problems and (2) capturing the interdependency between objective and decision spaces during evolution. To this end, we develop a population transformer architecture that embeds decision spaces of varying scales into a common latent space, enabling knowledge transfer across diverse problems. Furthermore, our architecture integrates objective-space features through objective fusion to enhance population prediction accuracy for complex MOPs. Our approach achieves robust generalization to downstream optimization tasks with up to 5,000 dimensions-five times the training scale and 200 times greater than prior work. Extensive evaluations on standardized benchmarks and out-of-training real-world applications demonstrate the consistent superiority of our method over state-of-the-art algorithms tailored to specific problem classes, improving the performance and generalization of evolutionary computation in solving MOPs.
Sequential perceptual aliasing is a cognitive challenge for learning agents when robots cannot differentiate states and their associations based on immediate observations, leading to poor decision-making. Existing systems struggle to abstract and distinguish observations effectively to achieve policy learning. This paper addresses this issue by introducing new aliasing types within the context of sequential aliasing and proposing an enhanced XCS classifier system that learns using a complete state-action map. The proposed system called hierarchical Frames-of-References-based XCS (Hi-FoRsXCS), can concatenate sequences of aliased states with the same observation into a chain. Hi- FoRsXCS then predicts associations between the observations and aliased states using the ends of the chain, enabling optimal policy learning with a complete action map. Experimental results demonstrate that Hi-FoRsXCS outperforms the existing systems in terms of accuracy. However, the limitations of Hi-FoRsXCS will be discussed in this paper.
The main challenge in handling dynamic multi-objective optimization problems lies in the need for algorithms to accurately track Pareto-optimal solutions in constantly changing environments. Most existing predictionbased dynamic multi-objective evolutionary algorithms (DMOEAs) conduct prediction either in the decision space or the objective space alone, or apply the same prediction model to both spaces. However, such approaches may fail to fully capture the distinct change patterns of each space, especially under nonlinear and complex environmental dynamics, thereby limiting the effectiveness of these algorithms. Furthermore, when sampling methods are used to help the algorithm generate populations in new environments, a large number of sampled individuals can impose a significant computational burden due to the increased number of function evaluations. To address these limitations, this paper proposes a dynamic multi-objective evolutionary algorithm, namely DS-DMOEA, which efficiently adapts to environmental changes through a dual-space prediction strategy and a surrogate-based sampling strategy. The dual-space prediction strategy captures dynamic changes by employing a weight vector-based method in the objective space and a geodesic flow kernel method in the decision space. Simultaneously, the surrogate-based sampling strategy generates a high-quality sampling population by training surrogate models with information from similar historical environments. The predicted and sampled populations are then combined to form an initial population well-suited for the new environment. DS-DMOEA has been tested against nine state-of-the-art DMOEAs on 19 benchmark problems with three types of environmental change patterns. The experimental results validate the effectiveness of the proposed algorithm.
Ill-conditioned problems are widely acknowledged as a major challenge in singleobjective optimization, yet they remain largely unexplored in evolutionary multiobjective optimization. In this paper, we introduce a decomposition-based multiobjective evolution strategy (MOES/D) for optimizing non-separable and ill-conditioned multiobjective problems. In contrast to most existing approaches that integrate evolution strategies while potentially compromising their essential features, we develop novel, tailored strategies to coordinate evolution strategies, maximizing their strengths. These strategies collectively contribute to the efficiency of MOES/D, which include an importance mixing algorithm that enhances sample efficiency in an unbiased manner, a collaborative ascent method that optimizes multiple subproblems simultaneously, and a principled resource allocation based on expectation-maximization that prioritizes the evolution strategy models. To bridge the gap in the field, we propose a novel benchmark suite in which all instances are non-separable and either moderate- or illconditioned. Extensive experiments on the suite demonstrate that MOES/D excels at solving moderate- or ill-conditioned multiobjective problems, outperforming most state-of-the-art algorithms by a significant margin.
