Hybrid differential evolution algorithms for the optimal camera placement problem

This paper aims to investigate to what extent hybrid differential evolution (DE) algorithms can be successful in solving the optimal camera placement problem.

This problem is stated as a unicost set covering problem (USCP) and 18 problem instances are defined according to practical operational needs. Three methods are selected from the literature to solve these instances: a CPLEX solver, greedy algorithm and row weighting local search (RWLS). Then, it is proposed to hybridize these algorithms with two hybrid DE approaches designed for combinatorial optimization problems. The first one is a set-based approach (DEset) from the literature. The second one is a new similarity-based approach (DEsim) that takes advantage of the geometric characteristics of a camera to find better solutions.

The experimental study highlights that RWLS and DEsim-CPLEX are the best proposed algorithms. Both easily outperform CPLEX, and it turns out that RWLS performs better on one class of problem instances, whereas DEsim-CPLEX performs better on another class, depending on the minimal resolution needed in practice.

Up to now, the efficiency of RWLS and the DEset approach has been investigated only for a few problems. Thus, the first contribution is to apply these methods for the first time in the context of camera placement. Moreover, new hybrid DE algorithms are proposed to solve the optimal camera placement problem when stated as a USCP. The second main contribution is the design of the DEsim approach that uses the distance between camera locations to fully benefit from the DE mutation scheme.