EmoDM: A Diffusion Model for Evolutionary Multi-objective Optimization

TL;DR

This work tackles the high evaluation cost of solving multi-objective optimization problems by introducing EmoDM, a diffusion-model that learns the dynamics of evolutionary search from historical generations. By treating the reversed evolutionary process as forward diffusion and employing a mutual entropy-based attention mechanism, EmoDM can generate approximate Pareto fronts for new MOPs with drastically fewer objective evaluations. The method demonstrates competitive performance on WFG and large-scale LSMOP benchmarks, including up to 5000 decision variables, and shows strong generalization to unseen problems. These results suggest diffusion-based pre-training as a promising direction for efficient, scalable multi-objective optimization with potential extensions to reinforcement learning and combinatorial problems.

Abstract

Evolutionary algorithms have been successful in solving multi-objective optimization problems (MOPs). However, as a class of population-based search methodology, evolutionary algorithms require a large number of evaluations of the objective functions, preventing them from being applied to a wide range of expensive MOPs. To tackle the above challenge, this work proposes for the first time a diffusion model that can learn to perform evolutionary multi-objective search, called EmoDM. This is achieved by treating the reversed convergence process of evolutionary search as the forward diffusion and learn the noise distributions from previously solved evolutionary optimization tasks. The pre-trained EmoDM can then generate a set of non-dominated solutions for a new MOP by means of its reverse diffusion without further evolutionary search, thereby significantly reducing the required function evaluations. To enhance the scalability of EmoDM, a mutual entropy-based attention mechanism is introduced to capture the decision variables that are most important for the objectives. Experimental results demonstrate the competitiveness of EmoDM in terms of both the search performance and computational efficiency compared with state-of-the-art evolutionary algorithms in solving MOPs having up to 5000 decision variables. The pre-trained EmoDM is shown to generalize well to unseen problems, revealing its strong potential as a general and efficient MOP solver.

Figures (4)

• Figure 1: An example of the forward and reverse diffusion processes of a DM for evolutionary multi-objective optimization.
• Figure 2: A framework of the proposed EmoDM, where the reversed evolutionary search process (from the final generation to the first generation) is used as the training data (evolutionary prompts) to learn a sequence of Gaussian noise models. An mutual entropy-based attention mechanism is introduced for focusing on the most important decision variables. After training, EmoDM can approximate a set Pareto solutions for a new MOP by gradually reducing the noise based on the learned noise distributions.
• Figure 3: Approximated PFs on the 2-objective WFG3 instance and 3-objective LSMOP8 instance.
• Figure 4: IGD profiles of EmoDM for Pareto set generation on LSMOP6 and LSMOP7 with 500, 1000, 3000, and 5000 decision variables.