Conditional-Surrogate-Assisted Particle Swarm Optimization for Large-Scale Robust Optimization Over Time

In dynamic environments, optimization algorithms tend to track the changing optima. However, frequent changes to decision solutions often cause high switching costs and system instability. Decision solutions are expected to be robust to changes. Such problems bring new challenges to existing algorithms, i.e., solution evaluation in future environments and solution selection. Though multiple surrogate models are developed for fitness evaluation, they mainly focus on predicting absolute fitness in static environments. Thus, this paper proposes conditional-surrogate-assisted particle swarm optimization (CSPSO), which adopts a conditional surrogate model to predict the relative fitness of solutions in future for robust solution selection. In CSPSO, a problem is decomposed into multiple subproblems, which are optimized by multiple swarms. Searching data of swarms is collected to learn network models for predicting the future fitness of solutions. In order to coordinate with the multi-modal, decoupled, and dynamic property of the problem, networks are conditioned on some extra information, i.e., time, subproblems, and peaks. Particularly, neural networks are first trained to predict new optimal solutions and fitness conditioned on time and subproblems, and a surrogate model is then trained to predict the relative fitness of solutions conditioned on the closest peak, corresponding subproblem, and time. By combining the current fitness with future ones, solutions with the highest fitness are selected for decision making. Experimental results show that the proposed algorithm outperforms state-of-the-art algorithms on problem instances up to 1000-D in terms of solution optimality. The proposed conditional surrogate model can well predict future fitness to assist decision making.