Surrogate-Assisted Hybrid Metaheuristic for Mixed-Variable 3-D Deployment Optimization of Directional Sensor Networks

A major concern in designing sensor networks is the deployment problem. However, establishing an efficient algorithm for the real-world deployment problem is challenging due to three issues, which are 1) the realistic mixed-integer nonlinear programming problem (MINLP) with mixed-variable; 2) the combinatorial subset selection problem; and 3) the expensive computational cost for fitness evaluation in the 3-D coverage problem. Therefore, this paper addresses these challenges and proposes a surrogate-assisted hybrid metaheuristic for mixed-variable 3-D deployment optimization of directional sensor networks (DSNs). First, an MINLP with flexible coordinate transformation technique and an efficient mixed-variable encoding scheme are introduced to model and represent the problem. We propose hybrid metaheuristic which applies two reproduction methods respectively for discrete and continuous variables. Second, we design sparse population-based incremental learning (s-PBIL) to handle inherent subset selection problem. s-PBIL could accurately learn the required information, and automatically learn a sparse distribution. Third, a mixed-variable surrogate with unifying space under Bayesian model management is incorporated to reduce the expensive computational cost. Experiment results on real-world deployment scenarios scaling from small-size to large-size show the effectiveness of the proposed algorithm.