A scalability analysis of a Multi-agent framework for solving combinatorial optimization via Metaheuristics

This paper addresses the scalability dimension of a multi-agent framework for solving combinatorial optimization problems using metaheuristics. The related literature discusses several properties of multi-agent systems. However, an important property that has received little attention is scalability, which refers to the ability of a system to perform useful work uniformly as the dimension of the system itself increases. This article introduces a methodology for assessing the scalability of multi-agent frameworks using scenarios with one, two, four, eight, ten, fifty, thirty, forty, fifty, and sixty agents. The framework Multi-Agent Architecture for Metaheuristics (AMAM) is the adopted architecture for performing the computational tests, using instances of the Vehicle Routing Problem with Time Windows (VRPTW) and the Unrelated Parallel Machine Scheduling Problem with Sequence-Dependent Setup Times (UPMSP-ST). The proposed methodology uses the obtained values concerning the objective function and the associated runtimes of the instanced problems to perform statistical measurements and tests that revealed an improvement in the framework's performance concerning the quality of solutions despite the slight increase in runtime for the VRPTW case. The results of a linear regression approach concerning the objective function data showed an adequate representation of agent inclusion but, regarding the runtime values, did not demonstrate such precise adjustments. The final results suggest that the adopted framework is scalable and demonstrates a robust response to the increase in the number of agents in its structure.