Solving uncapacitated multiple allocation p-hub center problem by Dijkstra’s algorithm-based genetic algorithm and simulated annealing

Abstract

In the existing literature, there are a huge number of studies focused on p-hub median problems and inventing heuristic or metaheuristic algorithms for solving them. But such analogous body of literature does not exist for its counterpart problem; p-hub center problem. In fact, since p-hub center has been lately introduced and has a particular objective function, minimizing the maximum cost between origin-destination nodes, there are few studies investigating the problem and the challenges for solving it. In this study, after presenting a complete definition of the uncapacitated multiple allocation p-hub center problem (UMApHCP) two well-known metaheuristic algorithms are proposed to solve the problem for small scale and large scale standard data sets. These two algorithms are one single solution-based algorithm, Simulated Annealing (SA), and one population-based metaheuristic, Genetic Algorithm (GA). Because of the particular nature of the problem, Dijkstra's algorithm has been incorporated in the fitness function calculation part of the proposed methods. The numerical results of running the GA and SA for standard test problems show that for smaller scale test problems, single solution-based SA shows greater performance versus GA but for larger scales of data sets the GA generally yield more desirable solutions.

Optimization of production and transport infrastructure based on cluster analysis methods

“…In order to identify the development reserves of the transport services sector, to improve the transport work quality and forecast development, the models of transport systems are created [1][2][3][4][5][6][7][8][9][10].…”

“…-models that determine transport and economic relations [4][5][6]11]; -organization models of the transportation process [8,10,[12][13][14]; -functioning and interaction models of the elements of transport systems [1,3,7,9,[15][16][17][18][19].…”

“…As a rule, production and transportation models when solving are reduced to problems of the transport type (matrix and network transport problem), linear programming, integer programming, network planning [1][2][3][4][5][6][7][8]13]. However, as analysis has shown, a feature of these problems is a large dimension, which does not always allow solving them in a nonlinear setting.…”

“…Solving optimization problems of choosing the location of terminal-logistic objects using graph models and mathematical programming under many combinatorial constraints leads to complex computational procedures of the exhaustive nature, which does not allow their use within the territories of the federal districts or the whole country. An analysis of existing practical methods [4][5][6][7][8][9][10]13] showed that they do not take into account the number of objects, their location relative to industrial production, the volume of cargo flows from individual consignors and consignees, and the existing railroad topology.…”

The capacitated single-allocation p-hub location routing problem: a Lagrangian relaxation and a hyper-heuristic approach

“…The references brought here are sorted by publication year. Rabbani and Kazemi (2015) proposed a genetic algorithm and a simulated annealing for solving an un-capacitated multiple allocation p-hub center problem.…”