Solution of a fuzzy resource allocation problem by various evolutionary approaches

In this paper we present a fuzzy resource allocation and assignment problem and propose two types of biologically inspired optimization methods to solve it. The resources in question are used for the maintenance of a network of nodes, each with its specific maintenance demands over time. Our goal is to assign sufficient capacities to storage locations and transport the appropriate amount of resources to the nodes at specific times during the simulation, so that the total cost of storage, transportation and malfunction is kept to a minimum. We use fuzzy numbers to describe the parameters of all the scenarios a solution has to fit, such as the maintenance demands of each node, the additional expenditure that malfunctions bring, and also the varying cost of transportation between nodes and storage locations. The optimization methods we used were the bacterial evolutionary algorithm and the particle swarm algorithm, both with a plain and a memetic variant complemented with gradient-based local search. All of them had a version where they only worked with crisp values, and one with fuzzy solutions. We tested the effectiveness of these four approaches on four examples with varying network sizes and durations.