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A recently formulated statistical mechanics method is used to study the phase transition occurring in a generalisation of the Traveling Salesman Problem (TSP) known as the centred TSP. The method shows that the problem has clear signs of a…

We present a new approximation algorithm for the (metric) prize-collecting traveling salesperson problem (PCTSP). In PCTSP, opposed to the classical traveling salesperson problem (TSP), one may not include a vertex of the input graph in the…

The paper provides a description of the two recent approximation algorithms for the Asymmetric Traveling Salesman Problem, giving the intuitive description of the works of Feige-Singh[1] and Asadpour et.al\ [2].\newline [1] improves the…

While traditional optimization problems were often studied in isolation, many real-world problems today require interdependence among multiple optimization components. The traveling thief problem (TTP) is a multi-component problem that has…

We study integrality gaps and approximability of two closely related problems on directed graphs. Given a set V of n nodes in an underlying asymmetric metric and two specified nodes s and t, both problems ask to find an s-t path visiting…

A generalization of the classical TSP is the so-called quadratic travelling salesman problem (QTSP), in which a cost coefficient is associated with the transition in every vertex, i.e. with every pair of edges traversed in succession. In…

We initiate the study of online routing problems with predictions, inspired by recent exciting results in the area of learning-augmented algorithms. A learning-augmented online algorithm which incorporates predictions in a black-box manner…

A solution to the benchmark ATT48 Traveling Salesman Problem (from the TSPLIB95 library) results from isolating the set of vertices into ten open-ended zones with nine lengthwise boundaries. In each zone, a minimum-length Hamiltonian Path…

We propose a learning algorithm for solving the traveling salesman problem based on a simple strategy of trial and adaptation: i) A tour is selected by choosing cities probabilistically according to the ``synaptic'' strengths between…

The Steiner Traveling Salesman Problem (STSP) is a variant of the classical Traveling Salesman Problem. The STSP involves incorporating steiner nodes, which are extra nodes not originally part of the required visit set but that can be added…

Meta-heuristics are frequently used to tackle NP-hard combinatorial optimization problems. With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem…

Discrete version of state transition algorithm is proposed in order to solve the traveling salesman problem. Three special operators for discrete optimization problem named swap, shift and symmetry transformations are presented. Convergence…

We provide exact and approximation methods for solving a geometric relaxation of the Traveling Salesman Problem (TSP) that occurs in curve reconstruction: for a given set of vertices in the plane, the problem Minimum Perimeter Polygon (MPP)…

This paper presents a method for calculating Region of Attraction of a target set (not necessarily an equilibrium) for controlled polynomial dynamical systems, using a hierarchy of semidefinite programming problems (SDPs). Our approach…

Given a complete edge-weighted graph G, we present a polynomial time algorithm to compute a degree-four-bounded spanning Eulerian subgraph of 2G that has at most 1.5 times the weight of an optimal TSP solution of G. Based on this algorithm…

In this paper we use marker method and propose a new mutation operator that selects the nearest neighbor among all near neighbors solving Traveling Salesman Problem.

The Travelling Salesman Problem - TSP is one of the most explored problems in the scientific literature to solve real problems regarding the economy, transportation, and logistics, to cite a few cases. Adapting TSP to solve different…

The travelling salesman problem (TSP) of space trajectory design is complicated by its complex structure design space. The graph based tree search and stochastic seeding combinatorial approaches are commonly employed to tackle the…

In this note, we polynomially reduce an instance of the partition problem to a dynamic lot sizing problem, and show that solving the latter problem solves the former problem. By solving the dynamic program formulation of the dynamic lot…

This paper has been merged into 1110.4604.