We present an approximation algorithm for the traveling salesman problem when the vehicle is constrained to move forward along paths with bounded curvatures (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 turn radius and Dmin is the minimum Euc...

vehicle routing problem (vrp) is one of the major problems in the transportation and distribution planning. in the most previous studies, the objective of vrp models was distance and vehicle related costs. however in many industrial cases along with routing distance, vehicle loading amount is a factor of cost function. in this paper, we formulate a mixed integer non-linear programming (minlp) m...

This paper deals with evolutionary algorithms for solving the vehicle routing problem. More precisely, the paper is concerned with eight evolutionary crossover operators, which have originally been designed for the traveling salesman problem but can also be used for vehicle routing. The considered crossovers are tested on a set of well known benchmark problem instances. The obtained experimenta...

Many real-world optimization problems today are multi-objective multi-constraint generalizations of NP-hard problems. A classic case we study in this paper is the Inventory Routing Problem with Time Windows (IRPTW). IRPTW considers inventory costs across multiple instances of Vehicle Routing Problem with Time Windows (VRPTW). The latter is in turn extended with time-windows constraints from the...

This paper describes a polynomial transformation for a class of unit-demand vehicle routing problems, named node-balanced routing problems (BRP), where the number of nodes on each route is restricted to be in an interval such that the workload across the routes is balanced. The transformation is general in that it can be applied to single or multiple depot, homogeneous or heterogeneous fleet BR...

In this paper, the fuzzy multi-depot vehicle routing problem with simultaneous pickup and delivery (FMDVRP-SPD) is investigated. The FMDVRP-SPD is the problem of allocating customers to several depots, so that the optimal set of routes is determined simultaneously to serve the pickup and the delivery demands of each customer within scattered depots. In the problem, both pickup and delivery dema...

The single vehicle routing problem with multiple routes is a variant of the vehicle routing problem where the vehicle can be dispatched to several routes during its workday to serve a number of customers. In this paper we propose a goal programming model for multi-objective single vehicle routing problem with time windows and multiple routes. To solve the model, we present a heuristic method wh...

We consider the Ordered Cluster Traveling Salesman Problem (OCTSP). In this problem, a vehicle starting and ending at a given depot must visit a set of n points. The points are partitioned intoK,K n, prespeci ed clusters. The vehicle must rst visit the points in cluster 1, then the points in cluster 2, : : :, and nally the points in cluster K so that the distance traveled is minimized. We prese...

The Generalized Traveling Salesman Problem is one of a well known complex combinatorial optimization problems. Equality-Generalized Traveling Salesman Problem is a particular case of it. Themain objective of the problem it is to find a minimum cost tour passing through exactly one node from each cluster of a large-scale undirected graph. Multi-agent approaches are successfully used nowadays for...

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 one target in each cluster is visited by some salesman. The GMDTSP is an NP-hard problem as it generalizes the MDTSP and has practical applications in desig...