An Immunological Algorithm for Combinatorial Optimization: the Fuel Distribution Problem as Case Study

Routing problems are classical combinatorial optimization tasks that find many applicability in numerous industrial and real-world scenarios. One challenging variant of the routing problem is the "Fuel Distribution Problem" (FDP) that a transportation company must face in its everyday operations. The main activity of a transportation fuel company is restock all its stores, i.e. petrol stations, along a geographical map, with the goal to minimizing its overall costs.In this research work we present an hybrid heuristic based on the metaphor of the immune system for solving the FDP, which basically asks to find a set of routes as shorter as possible for a fixed number of company's vehicles in order to satisfy the several received demands of customers.In particular, the presented immunological algorithm takes inspiration by the clonal selection principle, whose key features are cloning, hypermutation, and aging operators. Such algorithm is also characterized, in having a (i) deterministic approach based on the "Depth First Search" (DFS) algorithm - used in the scheme of assigning a vertex to a vehicle - and (ii) a local search operator, based on the exploration of the neighbourhood.The algorithm has been tested on one real data instance, with 82 vertices, and 25 others artificial different instances, taken from DIMACS graph coloring benchmark. The experimental results presented in this work, not only prove the robustness and efficiency of the developed algorithm, but show also the goodness of the local search, and the approach based on the DFS algorithm. Both methodologies help the algorithm to better explore the complex search space.