AS-PSO, Ant Supervised by PSO Meta-heuristic with Application to TSP. Nizar Rokbani *1 , Arsene L. Momasso *2 , Adel.M Alimi *3 # REGIM-Lab, Research Groups on Intelligent Machine University of Sfax, Tunisia 1 Nizar.rokbani@ieee.org 3 adel.alimi@ieee.org Abstract— Optimization problems occupy a prominent place in engineering, management, process control, it consist in finding a fair solution of a problem in accordance with specific environment, and respecting a given list of constraints. Whether it is to determine the best chemical balance of a product, or to predict future market trends, we need optimization methods. Bio-inspired techniques and swarm intelligence as well as various numerical techniques, are used to solve problems increasingly difficult. This paper investigates a new Meta-heuristic, called AS- PSO, Ant Supervised by Particle Swarm Optimization, based on the famous ant colony, ACO, and particle swarm optimization. AS-PSO is an adaptive heuristic, since the user is not in need to fit any parameter of the search strategy. In AS-PSO, the ACO algorithm is in charge with the problem solving, while the PSO is managing the optimality of the ACO parameters. The paper includes also an application of AS-PSO to the travelling Salesman Problem (TSP). Keywords— PSO, ACO, AS-PSO, Optimization, Heuristics, TSP I. INTRODUCTION The importance of optimization in economics, industry, science and engineering is well established today. Indeed, we live in a world more and more optimized. The main challenges is to find a quality result and/or a reliable prediction for a specific problem what ever its nature, Optimization process should be adapted in order to fit the problem requirements’ and specific attributes [1], That depends essentially on the main topic of application example robotics, mechanical design, soft computing …etc. To find an optimal solution, several approaches could be investigated, including exact algorithms that work in order to have an optimal solution, with the disadvantage of reaching slowly to the solution, and heuristics that provide a feasible solution quickly, but not necessarily optimal, it is in this context that ant colony and particle swarm optimization are involved. Searching for an optimum, is a challenging task starting by defining what makes a solutions optimal, optimality is quantified using mathematical and numerical criteria that should be fitted with respect to constraints, These criteria are expressed as a set of mathematical functions, also called objective functions. Form this point of view, a problem could be solved by different techniques including heuristics and several analyses are needed to consider the best solution among them. Even within a specific class of heuristics, the optimality of a solution depends on the heuristic parameters; adaptive methods are a sub-class of optimizer’s able to self tune their parameters. Within optimization methods we distinguish deterministic and probabilistic algorithms; PSO, particle swarm optimization [2], and ACO, Ant Colony Optimization [3], are probabilistic methods; they belong also evolutionary techniques. The hybrid methods can be classified into two groups: the hybrid metaheuristics that combine several heuristics [4], and the group combining exact methods and heuristic ones. It is possible to classify the hybrid methods, following the taxonomy of Talbi [ref] that provides qualitative comparison of hybrid methods. The hierarchical heuristics are seen as :  Low-level hybridization, in witch a function of an heuristic is replaced by another heuristic.  High_level hybridation, where two heuristics are hybridized without their internal functioning is related. Within these classes, two additional mechanisms could be involved:  The Hierarchical mechanism, when heuristics are executed sequentially, one using the output of the previous as an input, there is hybridization with relay.  Co-evolutionary mechanism, qualify an evolution in witch agents cooperate in parallel to explore the space of solutions. [5]. In this paper and according to the previous classification, AS-PSO, is observed as High-level Hierarchical, HLH, meta- heuristic. Initially the AS-PSO were proposed by Elloumi et al, 2009 in [6], in this paper, we investigate an aspect of AS-PSO, focusing only on the self adaptation of (α,β) of the ACO, with a constrain weight PSO. The remaining of this paper is organized as follows : Paragraph II, review the PSO and ACO algorithms. Paragraph III, is dedicated to the presentation of AS-PSO, then the application of AS-PSO to the travelling salesman problem, around Tunisian cities, is presented. The paper is ended by results discussions and further works openings.