Abstract
The traveling salesman problem (TSP), can be used as a typical combinatorial optimization problem, to describe a wide variety of practical engineering optimization problems in various fields. In this study, the problem of personnel and equipment utilization in the transportation industry was abstracted, a more general class of TSPs with replenishment arcs was proposed, an optimization model to minimize the total travel time was established, the ant colony optimization algorithm to solve the standard TSP was improved, and an improved ant colony algorithm based on dynamic heuristic information was designed. Simulation experiments showed that the algorithm can account for the cumulative mileage constraint and search for the shortest path, effectively solving the TSP with replenishment arcs.
Highlights
The travelling salesman problem (TSP) is a typical combinatorial optimisation problem whose general description, finding the shortest Hamiltonian cycle in a fully connected graph with n nodes, has been proven to be an NP-hard problem [1]
For a kind of travelling salesman problem with supply arc proposed in this paper, when it is inversely transformed into the EMU Operation planning problem, the city nodes can be transformed into the train operation lines that need to be undertaken, and the businessmen can be transformed into the utilized EMUs; When the cumulative mileage and time of EMUs are considered at the same time, we can use the method proposed in this paper to describe and solve the EMU operation problem
In this paper, the personnel and equipment utilisation problem in the transportation industry with cumulative working time or utilisation mileage constraints was abstracted and extended to obtain a class of RATSP with cumulative travel constraints and dynamic replenishment arcs, and the constraints that should be satisfied in the journey of the travelling salesman were provided by analyzing the cumulative travel time of the travelling salesman upon entering and leaving the city node
Summary
The travelling salesman problem (TSP) is a typical combinatorial optimisation problem whose general description, finding the shortest Hamiltonian cycle in a fully connected graph with n nodes, has been proven to be an NP-hard problem [1]. From the current research results of the TSP, a variety of proven methods has been derived from the research of various experts and scholars to obtain better solutions, or even the optimal solution On this basis, a TSP-like problem with a cumulative travel time (mileage) constraint was proposed in this paper by abstracting and extending the problem of personnel and equipment utilisation in the transportation industry, and the improvement and application of the ant colony algorithm in solving this problem were investigated. By summarising the results of the abovementioned research on the problem of personnel and equipment utilisation in the transportation industry, the common features of their research approaches were obtained: the tasks to be accomplished were abstracted as city nodes when the problem was modeled, and the connections between tasks were considered as intercity connections; thereby, a connected network was established. Where viin denotes the virtual starting point of the corresponding node, v out i denotes the virtual ending point of the corresponding node, i denotes the weight of node vi , and ij denotes the arc weight from node vout i to node v in j
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