Comparison of Evolutionary Algorithms on the Minimax Sensor Location Problem

The Minimax Sensor Location Problem (SELP) is a nonlinear, nonconvex programming problem which aims to locate sensors to monitor a planar region. The objective is to determine the locations that will minimize the maximum probability of “missing” an event in the region. Two evolutionary algorithms, differential evolution (DE) and the co-variance matrix adaptation evolutionary strategy (CMA-ES), are used to solve the SELP when 2 to 10 sensors are to be located in the unit square. Several variants of each algorithm were tested and results show that the DE/best/2/bin variant of DE and the weighted recombination variant of CMA-ES yield the best performance. A comparison of DE and CMA-ES, in terms of the objective value obtained, reveals that the algorithms obtain comparable solutions. However, CMA-ES requires approximately half as many function evaluations as DE.