This paper studies parsimonious, intuitive, and effective formulas to approximate the length of Traveling Salesman Problems (TSP) and Vehicle Routing Problems (VRP). Using intuition derived from continuous models and graph theory, a formula to approximate the length of vehicle routes is proposed. In instances with different patterns of customer spatial distribution, time windows, customer deman...

Operations research (OR) practitioners are accustomed to dealing with variants of classic OR problems. Indeed, an industrial problem often looks like a traveling salesman problem, vehicle routing shortest path etc., but has additional constraint or different objective that prevent the use powerful algorithms produced by decades on This situation can be frustrating, notably when we realize catch...

Vehicle Routing Problems are generalizations of the well known Traveling Salesman Problem; we focus on the on-line version of these problems, where requests are not known in advance and arrive over time. We introduce a model of lookeahead for this class of problems, the time lookahead ∆, which allows an on-line algorithm to foresee all the requests that will be released during next ∆ time units...

Throughout the history, Genetic Algorithms (GA) have been widely applied to a broad range of combinatorial optimization problems. Its easy applicability to areas such as transport or industry has been one of the reasons for its great success. In this paper, we propose a new Adaptive Multi-Crossover Population Algorithm (AMCPA). This new technique changes the philosophy of the basic genetic algo...

We study how to set the vehicle capacity for traveling Salesman Problems where some of the customer demands are stochastic. The analyses are done for the one-commodity pickup-and-delivery TSP, as this problem also includes the setting of the initial load. We first consider feasibility issues. This includes finding the smallest vehicle capacity and some initial load such that a given tour is fea...

Vehicle Routing Problem (VRP) is a real life constraint satisfaction problem to find minimal travel distances of vehicles to serve customers. Capacitated VRP (CVRP) is the simplest form of VRP considering vehicle capacity constraint. Constructive and clustering are the two popular approaches to solve CVRP. A constructive approach creates routes and attempts to minimize the cost at the same time...

Drone delivery is drawing increasing attention in last-mile delivery. Effective solution methods to solve decision-making problems arising drone allow run and assess systems. In this paper, we focus on systems with a single traditional vehicle multiple drones working tandem fulfill customer requests. We address the Traveling Salesman Problem Multiple Drones (TSP-MD) investigate modeling challen...

This paper will address an innovative bio-inspired algorithm able to incrementally grow decision graphs in multiple directions for discrete multi-objective optimisation. The algorithm takes inspiration from the slime mould Physarum Polycephalum, an amoeboid organism that in its plasmodium state extends and optimizes a net of veins looking for food. The algorithm is here used to solve multi-obje...

this paper considers the multi-depot vehicle routing problem with time window in which each vehicle starts from a depot and there is no need to return to its primary depot after serving customers. the mathematical model which is developed by new approach aims to minimizing the transportation cost including the travelled distance, the latest and the earliest arrival time penalties. furthermore, ...

We consider a generalized Path Traveling Salesman Problem where the distances are defined by a 2-edge-connected graph metric and a constant number of salesmen have to cover all the destinations by traveling along paths of minimum total length. We show that for this problem there is a polynomial algorithm with asymptotic approximation ratio of 2 .