Background Many combinatorial optimization problems are NP-hard, and the theory of NP-completeness has reduced hopes that NP-hard problems can be solved within polynomially bounded computation times (Dahlke 2008; Dunne 2008). Nevertheless, sub-optimal solutions are sometimes easy to find. Consequently, there is much interest in approximation and heuristic algorithms that can find near optimal s...

This paper studies the pickup and delivery traveling salesman problem with multiple stacks. The vehicle contains a number of (horizontal) stacks of finite capacity for loading items from the rear of the vehicle. Each stack must satisfy the last-in-first-out constraint which states that any new item must be loaded on top of a stack and any unloaded item must be on top of its stack. A branch-and-...

The best worst case complexity ofO(n2) to solve optimally the Traveling Salesman Problem is achieved by the Dynamic Programming algorithm of Held and Karp from 1962. This is exponentially better than an exhaustive enumeration of all O(n!) feasible solutions. For the Vehicle Routing Problem we were unable to find similar results in the literature. We present a Dynamic Programming algorithm for t...

The Multiple Traveling Salesman problem (mTSP) is an extension of the well-known Traveling Salesman Problem (TSP), where more than one salesman is allowed to be used in order to visit some cities just once. Furthermore, the formulation of the mTSP applies to a wide range of reallife applications, and can be extended to a wide variety of Vehicle Routing Problems (VRPs) by incorporating some addi...

The Probabilistic Traveling Salesman Problem with Deadlines (PTSPD) is a Stochastic Vehicle Routing Problem with a computationally demanding objective function. Currently heuristics using an approximation of the objective function based on Monte Carlo Sampling are the state-of-the-art methods for the PTSPD. We show that those heuristics can be significantly improved by using statistical tests i...

We introduce a new extension of Punnen’s exponential neighborhood for the traveling salesman problem (TSP). In contrast to an interesting generalization of Punnen’s neighborhood by De Franceschi, Fischetti and Toth (2005), our neighborhood is searchable in polynomial time, a feature that invites exploitation by heuristic and metaheuristic procedures for the TSP and related problems, including t...

Nowadays, the development of new metaheuristics for solving optimization problems is a topic of interest in the scientific community. In the literature, a large number of techniques of this kind can be found. Anyway, there are many recently proposed techniques, such as the artificial bee colony and imperialist competitive algorithm. This paper is focused on one recently published technique, the...

Nested Rollout Policy Adaptation (NRPA) is a Monte Carlo search algorithm for single player games. In this paper we propose to generalize NRPA with temperature and bias analyze theoretically the algorithms. The generalized named GNRPA. Experiments show it improves on different application domains: SameGame Traveling Salesman Problem Time Windows.

We introduce a new extension of Punnen’s exponential neighborhood for the traveling salesman problem (TSP). In contrast to an interesting generalization of Punnen’s neighborhood by De Franceschi, Fischetti and Toth (2005), our neighborhood is searchable in polynomial time, a feature that invites exploitation by heuristic and metaheuristic procedures for the TSP and related problems, including t...

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 ...