A 2-level Metaheuristic for the Set Covering Problem

Claudio Valenzuela, Broderick Crawford, Ricardo Soto, Eric Monfroy, Fernando Paredes
2014 International Journal of Computers Communications & Control  
Metaheuristics are solution methods which combine local improvement procedures and higher level strategies for solving combinatorial and nonlinear optimization problems. In general, metaheuristics require an important amount of effort focused on parameter setting to improve its performance. In this work a 2-level metaheuristic approach is proposed so that Scatter Search and Ant Colony Optimization act as "low level" metaheuristics, whose parameters are set by a "higher level" Genetic Algorithm
more » ... uring execution, seeking to improve the performance and to reduce the maintenance. The Set Covering Problem is taken as reference since is one of the most important optimization problems, serving as basis for facility location problems, airline crew scheduling, nurse scheduling, and resource allocation. the task of parameters adjustment for a low level metaheuristic. This approach is considered as a multilevel metaheuristic since there are two metaheuristics covering tasks of parameter setting, for the former, and problem solving, for the latter [9] . The main design of the implementation proposed considers a Genetic Algorithm (GA) [10] at online (Control) and offline (Tuning) parameter setting for a low level metaheuristic (Ant Colony Optimization (ACO) or Scatter Search (SS)) using a Reactive Search approach and an Automatic Parameter Tuning approach. In Reactive Search, feedback mechanisms are able to modify the search parameters according to the efficiency of the search process, i.e. the balance between intensification and diversification can be automated by exploiting the recent past of the search process through dedicated learning techniques [13] . The Automatic Parameter Tuning is carried by an external algorithm which searches for the best parameters in the parameter space in order to tune the solver automatically. Ant Colony Optimization and Scatter Search techniques [11] have shown interesting results at solving SCP [6] and similar problems [5] . For the purpose of this work, the former is selected by its constructional approach for generating solutions, plus its stochastic-based operators. The latter is considered as an evolutionary (population-based) algorithm which uses, essentially, deterministic operators. Both of them provide good reference metaheuristics in terms of their foundations, their problem solving approaches, their design maturity, and in terms of how different one is from the other, making them highly suitable to the development of this work.
doi:10.15837/ijccc.2012.2.1417 fatcat:tojng75rifg4zcthw4eohv47my