among numerous np-hard problems, the traveling salesman problem (tsp) has been one of the most explored, yet unknown one. even a minor modification changes the problem’s status, calling for a different solution. the generalized traveling salesman problem (gtsp)expands the tsp to a much more complicated form, replacing single nodes with a group or cluster of nodes, where the objective is to fi...

Among numerous NP-hard problems, the Traveling Salesman Problem (TSP) has been one of the most explored, yet unknown one. Even a minor modification changes the problem’s status, calling for a different solution. The Generalized Traveling Salesman Problem (GTSP)expands the TSP to a much more complicated form, replacing single nodes with a group or cluster of nodes, where the objective is to fi...

Among numerous NP-hard problems, the Traveling Salesman Problem (TSP) has been one of the most explored, yet unknown one. Even a minor modification changes the problem’s status, calling for a different solution. The Generalized Traveling Salesman Problem (GTSP) expands the TSP to a much more complicated form, replacing single nodes with a group or cluster of nodes, where the objective is to fin...

This paper treats of a generalization of the Traveling Salesman Problem (TSP) called Multi-commodity one-to-one Pickup-and-Delivery Traveling Salesman Problem (m-PDTSP) in which cities corresponds to customers providing or requiring known amounts of m different objects, and the vehicle has a given upper-limit capacity. Each object has exactly one origin and one destination, and the vehicle must...

In this chapter we are going to study metaheuristics based on the Automata Theory for the Multi-objective Optimization of Combinatorial Problems. As well known, Combinatorial Optimization is a branch of optimization. Its domain is optimization problems where the set of feasible solutions is discrete or can be reduced to a discrete one, and the goal is to find the best possible solution(Yong-Fa ...

We present an approximation algorithm for the Traveling Salesman Problem when the vehicle is constrained to move forward along paths with bounded curvature (Dubins’ vehicle). A deterministic algorithm returns in time O(n3) a tour within (( 1 + max { 8πρ Dmin , 14 3 }) log n ) of the optimum tour, where n is the number of points to visit, ρ is the minimum turning radius and Dmin is the minimum E...

In this work we investigate two variants of the Stochastic Vehicle Routing Problem: The Vehicle Routing Problem with Stochastic Demands and the Vehicle Routing Problem with Stochastic Demands and Customers. We show that under some moderate conditions there is an asymptotic equivalence between the Vehicle Routing Problem with Stochastic Demands and the Traveling Salesman Problem, as well as betw...

Classical combinatorial optimization problems can be generalized in a natural way by considering a related problem relative to a given partition of the nodes of the graph into node sets. In the literature one can find generalized problems such as: generalized minimum spanning tree, generalized traveling salesman problem, generalized Steiner tree problem, generalized vehicle routing problem, etc...

this article proposes a new algorithm for finding a good approximate set of non-dominated solutions for solving generalized traveling salesman problem. Random gravitational emulation search algorithm (RGES (is presented for solving traveling salesman problem. The algorithm based on random search concepts, and uses two parameters, speed and force of gravity in physics. The proposed algorithm is ...