相关论文: A Conjecture Related to the Traveling Salesman Pro…
Hougardy and Schroeder (WG 2014) proposed a combinatorial technique for pruning the search space in the traveling salesman problem, establishing that, for a given instance, certain edges cannot be present in any optimal tour. We describe an…
The traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization. Several semidefinite programming relaxations have been proposed recently that exploit a variety of mathematical structures including, e.g.,…
We present an exact formulation of the symmetric Traveling Salesman Problem (TSP) that replaces the classical edge-selection view with a surface-building approach. Instead of selecting edges to form a cycle, the model selects a set of…
The Traveling-Salesperson-Problem (TSP) is arguably one of the best-known NP-hard combinatorial optimization problems. The two sophisticated heuristic solvers LKH and EAX and respective (restart) variants manage to calculate close-to…
The Traveling Salesman Problem is one of the most intensively studied combinatorial optimization problems due both to its range of real-world applications and its computational complexity. When combined with the Set Covering Problem, it…
The question of whether all problems in NP class are also in P class is generally considered one of the most important open questions in mathematics and theoretical computer science as it has far-reaching consequences to other problems in…
The Traveling Salesman Problem (TSP) is one of the classic and hard problems in combinatorial optimization. We develop a new heuristic that uses a connection between Minimum Cost Flow Problems and the TSP to improve on a given suboptimal…
The cutting plane method is an augmentative constrained optimization procedure that is often used with continuous-domain optimization techniques such as linear and convex programs. We investigate the viability of a similar idea within…
The Multiple Travelling Salesman Problem (MTSP) is among the most interesting combinatorial optimization problems because it is widely adopted in real-life applications, including robotics, transportation, networking, etc. Although the…
Deep learning has shown significant potential in solving combinatorial optimization problems such as the Euclidean traveling salesman problem (TSP). However, most training and test instances for existing TSP algorithms are generated…
This paper presents a novel and straight formulation, and gives a complete insight towards the understanding of the complexity of the problems of the so called NP-Class. In particular, this paper focuses in the Searching of the Optimal…
The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization problem that aims to find the shortest possible route that visits each city exactly once and returns to the starting point. This paper explores the application…
The Traveling Salesperson problem asks for the shortest cyclic tour visiting a set of cities given their pairwise distances and belongs to the NP-hard complexity class, which means that with all known algorithms in the worst case instances…
TSP (Traveling Salesman Problem), a classic NP-complete problem in combinatorial optimization, is of great significance in multiple fields. Exact algorithms for TSP are not practical due to their exponential time cost. Thus, approximate…
The Clustered Traveling Salesman Problem (CTSP) is a variant of the popular Traveling Salesman Problem (TSP) arising from a number of real-life applications. In this work, we explore a transformation approach that solves the CTSP by…
For some weighted $NP$-complete problems, checking whether a proposed solution is optimal is a non-trivial task. Such is the case for the celebrated traveling salesman problem, or the spin-glass problem in 3 dimensions. In this letter, we…
Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based…
In this work we revisit the Hopfield-Tank algorithm for the traveling salesman problem (TSP) and report encouraging results, with a different dynamics, that makes the algorithm more efficient finding better solutions in much less…
For many problems, the important instances from practice possess certain structure that one should reflect in the design of specific algorithms. As data reduction is an important and inextricable part of today's computation, we employ one…
The generalized multiple depot traveling salesmen problem (GMDTSP) is a variant of the multiple depot traveling salesmen problem (MDTSP), where each salesman starts at a distinct depot, the targets are partitioned into clusters and at least…