The traveling salesman problem (TSP) is the problem of finding the shortest tour through all the nodes that a salesman has to visit. The TSP is probably the most famous and extensively studied problem in the field of combinatorial optimization. Because this problem is an NP-hard problem, practical large-scale instances cannot be solved by exact algorithms within acceptable computational times. ...

Genetic algorithms, Evolutionary strategies and many variants of local search algorithms are being applied directly on a fitness function. Such direct search algorithms require minimal knowledge of a problem and can be applied to a wide variety of different domains. This paper suggests to apply a simple mapping on the fitness function – which we refer to as a “preprocessing” step. Any direct se...

Travelling Salesman Problem (TSP) is a classical combinatorial optimization problem. This problem is NP-hard in nature. Meta-heuristic approaches have proved to be quite useful for approximate solution of difficult combinatorial optimization problems. Ant colony optimization is one of the popular Meta-heuristics and is unique on the basis of its distributed computation and indirect communicatio...

The quadratic travelling salesman problem (QTSP) is to find a least cost Hamiltonian cycle in an edge-weighted graph. We define a restricted version of QTSP, the kneighbour TSP (TSP(k)), and give a linear time algorithm to solve TSP(k) on a Halin graph for k ≤ 3. This algorithm can be extended to solve TSP (k) on any fully reducible class of graphs for any fixed k in polynomial time. This resul...

In this paper three heuristic algorithms using the Divide-and-Conquer paradigm are developed and assessed for integer optimizations problems: Multidimensional Knapsack Problem (d-KP), Bin Packing (BPP) Travelling Salesman (TSP). For each case, algorithm is introduced, together with design of numerical experiments, in order to empirically establish its performance from both points view: computat...

Real world problems like Travelling Salesman Problem (TSP) belong to NP-hard optimization problems which are difficult to solve using classical mathematical methods. Therefore, many alternate solutions have been developed to find the optimal solution in shortest possible time. Nature-inspired algorithms are one of the proposed solutions which are successful in finding the solutions that are ver...

The travelling salesman problem (TSP) is the most well-known combinatorial optimization problem. TSP is used to find a routing of a salesman who starts from a home location, visits a prescribed set of cities and returns to the original location in such a way that the total distance travelled is minimized and each city is visited exactly once . This problem is known to be NP-hard, and cannot be ...

The travelling salesman problem (TSP) is the most well-known combinatorial optimization problem. TSP is used to find a routing of a salesman who starts from a home location, visits a prescribed set of cities and returns to the original location in such a way that the total distance travelled is minimized and each city is visited exactly once . This problem is known to be NP-hard, and cannot be ...

Tourism industries are rapidly increased for the last few years especially in Malaysia. In order to attract more tourists, Malaysian Governance encourages any effort to increase Malaysian tourism industry. One of the efforts in attracting more tourists in Malacca, Malaysia is a duck tour. Duck tour is an amphibious sightseeing tour that works in two types of engines, hence, it required a huge c...

The Selective Travelling Salesman Problem (STSP) is a modified version of the Travelling Salesman Problem (TSP) where it is not necessary to visit all vertices. Instead of it, with each vertex a number meaning a profit is associated. The problem is to find a cycle which maximizes collected profit but does not exceed a given cost constraint. A direct application of the STSP, e.g. in Intelligent ...