A Dual-Purpose Memory Approach for Dynamic Particle Swarm Optimization of Recurrent Problems

In a dynamic optimization problem (DOP) the optima can change either in a sequential or in a recurrent manner. In sequential DOPs, the optima change gradually over time while in recurrent DOPs, previous optima reappear over time. The common strategy to tackle recurrent DOPs is to employ an archive of solutions along with information allowing to associate them with their respective problem instances. In this paper, a memory-based Dynamic Particle Swarm Optimization (DPSO) approach which relies on a dual-purpose memory for fast optimization of streams of recurrent problems is proposed. The dual-purpose memory is based on a Gaussian Mixture Model (GMM) of candidate solutions estimated in the optimization space which provides a compact representation of previously-found PSO solutions. This GMM is estimated over time during the optimization phase. Such memory operates in two modes: generative and regression. When operating in generative mode, the memory produces solutions that in many cases allow avoiding costly re-optimizations over time. When operating in regression mode, the memory replaces costly fitness evaluations with Gaussian Mixture Regression (GMR). For proof of concept simulation, the proposed hybrid GMM-DPSO technique is employed to optimize embedding parameters of a bi-tonal watermarking system on a heterogeneous database of document images. Results indicate that the computational burden of this watermarking problem is reduced by up to 90.4 % with negligible impact on accuracy. Results involving the use of the memory of GMMs in regression mode as a mean of replacing fitness evaluations (surrogate-based optimization) indicate that such learned memory also provides means of decreasing computational burden in situations where re-optimization cannot be avoided.