A sensitivity analysis indicator to adapt the shift length in a metaheuristic Peio Loubière CY Cergy Paris University Pau, France plo@eisti.eu Astrid Jourdan CY Cergy Paris University Pau, France aj@eisti.eu Patrick Siarry LISSI UPEC Vitry-sur-Seine, France siarry@u-pec.fr Rachid Chelouah CY Cergy Paris University Cergy, France rc@eisti.eu Abstract— Population based metaheuristics (e.g. Genetic Algorithm, Particle Swarm Optimization, …) deal with a dichotomy between exploration (discover unexplored areas) and exploitation (dig around a good solution). The consequence is a wide exploration of the search space. A lot of information about the link between the objective function and the input variables is collected during the algorithm. Sensitivity analysis methods allow to transform this information in order to characterize the effect of an input variable on the objective function: linear impact, nonlinear impact, negligible impact. We propose to integrate a sensitivity analysis method in the optimization process in order to increase or decrease the shift length when offsetting a variable according to its behavior. The offset of a variable with a nonlinear impact has to be small in order to catch possible local optima of the objective function. On the contrary, the offset of a variable with a linear impact has to be high in order to move faster the variable toward its best position. A toy example is used to illustrate the interest of the method. Keywords—optimization, metaheuristics, sensitivity analysis, convergence speed I. INTRODUCTION Metaheuristics are strategies that guide a global optimization process of nonlinear objective functions. The goal is to efficiently explore the search space in order to find near–optimal solutions. Metaheuristics deal with a dichotomy between exploration, to discover unexplored areas, and exploitation, to dig around a good solution. Population based metaheuristics (e.g. genetic algorithm, particle swarm optimization, …) ensure a wide exploration of the search space. Starting from a set of initial points, the metaheuristic iterations randomly explore the neighborhood of each point. A neighbor is generated by offsetting a set of variables of the current point. The variables and the offset are randomly chosen. We propose to use the information gathered during the iterations for guiding the algorithm toward cleverer choices. The idea is to use the points evaluations to characterize the variables behavior (relevance and shape) thanks to a sensitivity analysis (SA) method [2][13]. Sensitivity analysis is the study of how the input variables affect an output variable. In optimization, SA methods are often used to eliminate non influential variables before the process, thereby reducing the dimension. In this paper, we present an another way to use the information given by a SA method for improving the convergence of the metaheuristic. We assume that proceeding in two steps may not be suitable. Removing variables definitively can be damaging to the optimization process. Irrelevant variables at the beginning of the algorithm may become relevant further in the search process and could discriminate the points (during the exploitation process). Moreover, sensitivity analysis requires a lot of evaluations of the objective function, as the metaheuristic. Directly integrating a sensitivity analysis method in a metaheuristic saves evaluations and allows to focus on relevant variables. The goal is not the computation of accurate sensibility analysis indices, but to obtain enough information on the variable behavior in order to guide the optimization process. According to their search process, metaheuristics can be split into three families: those which search along one direction (variable), those which select a subset of variables and those which search along all directions. For the two first families, SA would help to focus on the most influential variables. In all cases the information about variable behavior (monotony, non-linearity, ...) would help adapting the offset when generating a new neighbor. In a previous work [9], Morris’ sensitivity method [4], has been integrated in Artificial Bee Colony (ABC) algorithm [4][5]. ABC algorithm integrates fairly well Morris’ method, because of its one-direction neighborhood search process. They both offset a point according to a single variable at time and analyze the impact on the objective function output. Among all search processes implemented in metaheuristics, ABC neighborhood search is a particular case. Many metaheuristics algorithms search a neighbor in a hyper-sphere, offsetting various variables at a time (tabu search [1], differential evolution DE [11], swarm intelligence based metaheuristics such particular swarm optimization PSO [6][12]). In a second work [10], we generalized this approach. We defined a new sensitivity analysis method adapted to a multidimensional neighborhood context. This method was successfully integrated in a second family algorithm (DE). The SA performed during the algorithm allows to compute for each variable a weight proportional to the impact of this variable on the objective function. The uniform random selection of the variables to offset is then replaced a random selection based on the weights. The most influential variables have more chance of being selected. 978-1-7281-6929-3/20/$31.00 ©2020 IEEE