Spike-driven Sparse Binary Representation Learning for Large-scale Multi-objective Optimization

Many real-world multi-objective optimization problems contain binary-encoding and large-scale decision variables but sparse Pareto solutions, posing stiff challenges to evolutionary algorithms. With the rapid developments and broad applications of deep neural networks (DNNs), DNN-based decision space reduction has attracted increasing attention in this area. Nevertheless, the computational overhead of DNNs is a lasting challenge, and existing methods struggle to learn sparse binary representations as their continuous activations and gradient-based updates may inherently mismatch. Differently, as the third generation of artificial neural networks, spiking neural networks (SNNs) offer a more natural and efficient framework for representing sparse binary data owing to their spike-triggered event-driven working mechanism. This paper presents a first attempt to introduce spike-driven sparse binary representation learning into sparse large-scale multi-objective optimization problems (SLMOPs). Specifically, a lightweight SNN with leaky integrate-and-fire neurons is developed for evolutionary online solution modeling in solving SLMOPs. In the training process, we integrate Hebbian learning to learn the patterns of non-zero variables as local plasticity, and Kullback-Leibler divergence loss to learn the distribution of obtained Pareto solutions as global plasticity. Moreover, an adaptive firing threshold mechanism is proposed to improve the versatility across problems with different sparsities and avoid parameter tuning. Experimental results demonstrate the advantage of our methods over algorithms tailored for SLMOPs on benchmark and 20 real-world problems from different areas in terms of both effectiveness and efficiency, especially on real-world problems with unknown characteristics and sparsities.