Abstract
Abstract Routing problems are classical combinatorial optimization tasks that find much 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 restocking 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 a 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 companyβs 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, hyper- mutation, 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 neighborhood. 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.
Highlights
Artificial Immune systems (AIS) represent a branch of Computational Intelligence (CI), and have been successfully applied to a wide variety of application areas, such as for instance in combinatorial and global optimization [1,2,3], as well as in systems and synthetic biology [4,5,6]
To evaluate the goodness of the performance of hybrid clonal selection algorithm (HCSA) and its search ability into the solutions space, we have used two different evaluation measures: (1) if HCSA is able to obtain good approximate solutions using the capacity of the vehicles as small as possible, and (2) the homogeneity in the assignment of the vehicles to the vertices; i.e., to avoid that a vehicle has to supply two vertices placed in opposite sites from a topological point of view
If we give a look to the results obtained using the same capacity for all vehicles, one can see that, the best solution is obtained with high values of dup, in the overall the better performances are instead obtained using smaller values; this is proved by the mean values
Summary
Artificial Immune systems (AIS) represent a branch of Computational Intelligence (CI), and have been successfully applied to a wide variety of application areas, such as for instance in combinatorial and global optimization [1,2,3], as well as in systems and synthetic biology [4,5,6]. An Ag is the problem to tackle, whilst the B cell represents a solution for the Ag. In particular, in our study, the Ag is an undirected graph, whose vertices are the customers1 and edges are i.e. fuel stations that have a contract with the distribution company, included the ones that havenβt made demands the road connections between customers
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