Hybrid differential evolution algorithms for the optimal camera placement problem

Purpose – This paper investigates to what extent hybrid differential evolution (DE) algorithms can be successful in solving the optimal camera placement problem. Design/methodology/approach – 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, a greedy algorithm, and a row weighting local search (RWLS). Then, it is proposed to hybridize these algorithms with two 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 in order to find better solutions. Findings – 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. Originality/value – 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 in order to fully benefit from the DE mutation scheme

Initialization and Local Search Methods Applied to the Set Covering Problem: A Systematic Mapping

The set covering problem (SCP) is a classical combinatorial  optimization problem part of Karp's 21 NP-complete problems. Many real-world applications can be modeled as set covering problems (SCPs), such as locating emergency services, military planning, and decision-making in a COVID-19 pandemic context. Among the approaches that this type of problem has solved are heuristic (H) and metaheuristic (MH) algorithms, which integrate iterative methods and procedures to explore and exploit the search space intelligently. In the present research, we carry out a systematic mapping of the literature focused on the initialization and local search methods used in these algorithms that have been applied to the SCP in order to identify them and that they can be applied in other algorithms. This mapping was carried out in three main stages: research planning, implementation, and documentation of results. The results indicate that the most used initialization method is random with heuristic search, and the inclusion of local search methods in MH algorithms improves the results obtained in comparison to those without local search. Moreover, initialization and local search methods can be used to modify other algorithms and evaluate the impact they generate on the results obtained