We present a map from the travelling salesman problem (TSP), prototypical NP-complete combinatorial optimisation task, to ground state associated with system of many-qudits. Conventionally, TSP is cast into quadratic unconstrained binary (QUBO) problem, that can be solved on an Ising machine. The size corresponding physical system's Hilbert space $2^{N^2}$, where $N$ number cities considered in...

We propose a new genetic algorithm with optimal recombination for the asymmetric instances of travelling salesman problem. The algorithm incorporates several new features that contribute to its effectiveness: (i) Optimal recombination problem is solved within crossover operator. (ii) A new mutation operator performs a random jump within 3-opt or 4-opt neighborhood. (iii) Greedy constructive heu...

Symmetri Generalized Travelling Salesman Problem Matteo Fis hetti Juan Jos e Salazar Gonz alezy Paolo Tothz January 1994; Revised May 1995 Abstra t We onsider a variant of the lassi al symmetri Travelling Salesman Problem in whi h the nodes are partitioned into lusters and the salesman has to visit at least one node for ea h luster. This NP-hard problem is known in the literature as the symmetr...

Traveling Salesman Problem (TSP) is about finding a Hamiltonian path with minimum cost. Travelling salesman problem (TSP) finds its application in many real world industrial applications including the areas such as logistics, transportation, and semiconductor industries. few potential applications of TSP includes finding an optimized scan chains route in integrated chip testing, parcels collect...

In the classical Travelling Salesman Problem (TSP), the objective function sums the costs for travelling from one city to the next city along the tour. In the q-stripe TSP with [Formula: see text], the objective function sums the costs for travelling from one city to each of the next q cities in the tour. The resulting q-stripe TSP generalizes the TSP and forms a special case of the quadratic a...

Solving NP hard problem like Travelling Salesman Problem (TSP) is a major challenge faced by analysts even though many techniques are available. Many versions of Genetic Algorithms are introduced by researchers to improve its performance in solving TSP. Clustering Genetic Algorithm (CGA) was recently introduced and this paper analyzes the results obtained by implementing it for TSP. It is obser...

The arc costs are assumed to be online parameters of the network and decisions should be made while the costs of arcs are not known. The policies determine the permitted nodes and arcs to traverse and they are generally defined according to the departure nodes of the current policy nodes. In on-line created tours arc costs are not available for decision makers. The on-line traversed nodes are f...

Evolutionary Multi-Objective Optimization is becoming a hot research area and quite a few papers regarding these algorithms have been published. However the role of local search techniques has not been expanded adequately. This paper studies the role of a local search technique called 2opt for the Multi-Objective Travelling Salesman Problem (MOTSP). A new mutation operator called Jumping Gene (...

Graphs (1-skeletons) of Traveling-Salesman-related polytopes have attracted a lot of attention. Pedigree polytopes are extensions of the classical Symmetric Traveling Salesman Problem polytopes (Arthanari 2000) whose graphs contain the TSP polytope graphs as spanning subgraphs (Arthanari 2013). Unlike TSP polytopes, Pedigree polytopes are not “symmetric”, e.g., their graphs are not vertex trans...

We show that the random insertion method for the traveling salesman problem (TSP) may produce a tour (log log n= log log log n) times longer than the optimal tour. The lower bound holds even in the Euclidean Plane. This is in contrast to the fact that the random insertion method performs extremely well in practice. In passing we show that other insertion methods may produce tours (log n= log lo...