This paper presents a new class of heuristics which embed an exact algorithm within the framework of a local search heuristic. This approach was inspired by related heuristics which we developed for a practical problem arising in electronics manufacture. The basic idea of this heuristic is to break the original problem into small subproblems having similar properties to the original problem. Th...

Travelling Salesman Problem is an intensively studied problem in the field of Combinatorial Optimization. Being an NP-Hard problem it is widely studied in the area of optimization. A problem is NP-Hard if its approximate solution is derived from the solution of NP problem, i.e. an algorithm that is used to solve NP problem can be modified to find the approximate solution to NP-hard problem.The ...

The travelling salesman problem (TSP) is an NP-hard in combinatorial optimization. It has assumed significance operations research and theoretical computer science. was first formulated 1930 since then, been one of the most extensively studied problems In fact, it used as a benchmark for many optimization methods. This paper represents new method to addressing TSP using improved version cuckoo ...

Travelling Salesman Problem (TSP) is a discrete hybrid optimization problem considered NP-hard. TSP aims to discover the shortest Hamilton route that visits each city precisely once and then returns starting point, making it feasible. This paper employed Farmland Fertility Algorithm (FFA) inspired by agricultural land fertility hyper-heuristic technique based on Modified Choice Function (MCF). ...

The Generalized Traveling Salesman Problem (GTSP) consists of finding a least cost Hamiltonian circuit or cycle through several clusters of vertices. In this paper we propose a new tabu search algorithm which uses the problem’s configuration to guide the search and reduce the solution space. A new way to manage the tabu restrictions, specially adapted to this problem, is also proposed. Results ...

The Generalized Traveling Salesman Problem (GTSP) is stated as follows. Given a weighted complete digraph K∗ n and a partition V1, . . . , Vk of its vertices, find a minimum weight cycle containing exactly one vertex from each set Vi, i = 1, . . . , k. We study transformations from GTSP to TSP. The ’exact’ Noon-Bean transformation is investigated in computational experiments. We study the ’non-...

This paper is concerned with polynomial time approximations schemes for the generalized geometric problems with geographic clustering. We illustrate the approach on the generalized traveling salesman problem which is also known as Group-TSP or TSP with neighborhoods. We prove that under the condition that all regions are non-intersecting and have comparable sizes and shapes, the problem admits ...

---------------------------------------------------------------------***--------------------------------------------------------------------Abstract In this paper, we have used two algorithms, i.e. the Nearest Neighbor algorithm and Genetic Algorithm to solve the Travelling Salesman problem. The Travelling Salesman problem is a widely studied problem in computational mathematics. In the Travell...

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Abstract An O( n 3 ) heuristic algorithm is described for solving d -city travelling salesman problems (TSP) whose cost matrix satisfies the triangularity condition. The involves as substeps computation of a shortest spanning tree graph G defining TSP and finding minimum perfect matching certain induced subgraph . A worst-case analysis this shows that ratio answer obtained to optimum solution s...