The Quadratic Travelling Salesman Problem (QTSP) is to find a least cost Hamilton cycle in an edge-weighted graph, where costs are defined on all pairs of edges contained in the Hamilton cycle. This is a more general version than the commonly studied QTSP which only considers pairs of adjacent edges. We define a restricted version of QTSP, the k-neighbour TSP (TSP(k)), and give a linear time al...

The x-and-y-axes travelling salesman problem forms a special case of the Euclidean TSP, where all cities are situated on the x-axis and on the y-axis of an orthogonal coordinate system of the Euclidean plane. By carefully analyzing the underlying combinatorial and geometric structures, we show that this problem can be solved in polynomial time. The running time of the resulting algorithm is qua...

Routing problems are optimization problems that consider a set of goals in a graph to be visited by a vehicle (or a fleet of them) in an optimal way, while numerous constraints have to be satisfied. We present a solution based on multidimensional scaling which significantly reduces computational time of a self-organizing neural network solving a typical routing problem – the Travelling Salesman...

This paper deals with the optimization of the capacity of a terminal railway station using the Ant Colony Optimization algorithm. The capacity of the terminal station is defined as the number of trains that depart from the station in unit interval of time. The railway capacity optimization problem is framed as a typical symmetrical Travelling Salesman Problem (TSP), with the TSP nodes represent...

Let tsp(G) denote the length of a shortest travelling salesman tour in a graph G. We prove that for any ε > 0, there exists a simple 2-connected planar cubic graph G1 such that tsp(G1) ≥ (1.25 − ε) · |V (G1)|, a simple 2-connected bipartite cubic graph G2 such that tsp(G2) ≥ (1.2 − ε) · |V (G2)|, and a simple 3-connected cubic graph G3 such that tsp(G3) ≥ (1.125− ε) · |V (G3)|.

In this paper a modification of the Hopfield neural network solving the Travelling Salesman Problem (TSP) is proposed. Two strategies employed to achieve the solution and results of the computer simulations are presented. The network exhibits good performance in escaping from local minima of the energy surface of the problem. With a judicious choice of network internal parameters nearly 100% co...

Nature inspired algorithms for their powerfulness, acquire a unique place among the algorithms for optimization. This paper intends to provide a comparison of firefly algorithm (FA) with 3 other nature inspired algorithms; genetic algorithms (GA), particle swarm optimization algorithm (PSO) and ant colony systems (ACS). Traveling salesman problem (TSP) has been used as the problem to be solved ...

Abstract We define a geometric transformation of Euclidean Travelling Salesman Problem (TSP) tours that leads to new formulation the TSP. For every TSP n-city tour, it is possible construct an inscribed n-polygon (Equivalent Cyclic Polygon, ECP) such lengths edges are equal corresponding tour links and follow same sequence order. The analysis ECP elicits possibility defining objective function ...

TSP has been considered the most complex algorithmic problem because of its time complexity. TSP comes under the NP Complete problem that becomes more critical as the number of cities increases. In this present work, an effective solution to TSP is provided using genetic approach. The work has presented genetic based model to generate the TSP path in effective time. The improvement is here perf...