We consider the classical minimum Travelling Salesman Problem on the class of 3-edge-connected cubic graphs. More specifically we consider their (shortest path) metric completions. The well-known conjecture states that the subtour elimination LP relaxation on the min TSP yields a 4/3 approximation factor, yet the best known approximation factor is 3/2. The 3-edge-connected cubic graphs are inte...

Travelling Repairman Problem (TRP) is one variant of the Travelling Salesman Problem (TSP) with the objective function minimizing the total waiting time for customers served by the repairman. Finding TRP solution is very important because it is often encountered in real world cases. In the TRP, a customer requires a fast service that he was satisfied. TRP is a combinatorial problem that require...

The Royal Australian Air Force (RAAF) conducts maritime surveillance operations in order to deter non-state threats such as terrorism or illegal fishing. RAAF aircraft search various areas of ocean in order to classify as many ships as possible in the shortest possible time. This resembles the traditional Travelling Salesman Problem (TSP) but with many interesting variations – the “cities” (shi...

We study the Travelling Salesman Problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NP-hard. The problem is of interest because of its relation to the famous 4/3 conjecture for metric TSP, which says that the integrality gap, i.e., the worst case ratio between the optimal values of the TSP and its linear programming relaxation, is 4/3. Using polyhedral tec...

The real life problems deal with imperfectly specified knowledge and some degree of imprecision, uncertainty or inconsistency is embedded in the problem specification. The well-founded theory of fuzzy sets is a special way to model the uncertainty. The rules in a fuzzy model contain a set of propositions, each of which restricts a fuzzy variable to a single fuzzy value by means of the predicate...

Permasalahan yang sering dijumpai dalam optimasi pengiriman sebuah produk adalah Travelling Salesman Problem (TSP). TSP merupakan masalah pencarian rute terpendek dari sejumlah node, di satu kali perjalanan. Perusahaan Es Batu melakukan menginginkan terpendek, untuk mengurangi keterlambatan pengiriman. Dampak terhadap kualitas es batu dapat menurunkan kepuasan pelanggan. Rute tidak diatur akan ...

The purpose of this article is to describe several applications of the clustered travelling salesman problem (CTSP), a variant of the well-known travelling salesman problem (TSP). The CTSP is defined on a complete graph G 1⁄4 ðV ;EÞ in the undirected case or (V, A) in the directed case, where V 1⁄4 fv1; . . . ; vng is a vertex set partitioned into m clusters V1; . . . ;Vm. The set E 1⁄4 fðvi; v...

Here we present a hybrid system that uses a reinforcement learning agent to improve the performance of a genetic algorithm on the travelling salesman problem (TSP). The agent uses Q(λ) learning to estimate state-action utility values, which it uses to implement high-level adaptive control over the genetic algorithm. In this way the agent influences selection of both crossover and mutation opera...

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. ...

Abstract Travelling salesman problem (TSP) is a well known combinatorial optimization which has drawn colossal attention due to its eclectic range of applications. In this article, we have proposed two modified versions intelligent water drops (IWD) algorithm. The first one the enhanced IWD (e-IWD) algorithm solve single objective TSP. second modification, e-IWD been extended multi-objective IW...