A hybrid simulated annealing for capacitated vehicle routing problems with the independent route length

A new mathematical model for a competitive vehicle routing problem with time windows solved by simulated annealing

“…However after t ui , d tdi is not carried to the customer definitely. Constraints (15)- (18) are related to that part of the objective function maximizing the amount of sale. Constraint (19) warrantee that a depot is the first and final destination of each vehicle.…”

“…Tavakkoli-Moghaddam et al developed a mathematical model for the VRP with backhauls by a memetic algorithm [17]. Furthermore, Tavakkoli-Moghaddam et al [18] presented a linear-integer model of a capacitated VRP with the independent route length in order to minimize the heterogeneous fleet cost and maximize the capacity utilization. This presented model was solved by a hybrid simulated annealing.…”

An improved ant colony optimization for vehicle routing problem

“…Heuristic algorithms such as simulated annealing (SA) (Chiang and Russell, 1996;Koulamas et al, 1994;Osman, 1993;Tavakkoli-Moghaddam et al, 2006), genetic algorithms (GAs) (Baker and Ayechew, 2003;Osman et al, 2005;Thangiah et al, 1994;Prins, 2004), tabu search (TS) (Gendreau et al, 1999;Semet and Taillard, 1993;Renaud et al, 1996;Brandao and Mercer, 1997;Osman, 1993) and ant colony optimization Reimann et al, 2002;Peng et al, 2005;Mazzeo and Loiseau, 2004;Bullnheimer et al, 1999;Doerner et al, 2004) are widely used for solving the VRP. Among these heuristic algorithms, ant colony optimizations (ACO) are new optimization methods proposed by Italian researchers Dorigo et al (1996), which simulate the food-seeking behaviors of ant colonies in nature.…”

Solving Vehicle Routing Problem Using Ant Colony and Genetic Algorithm

“…Since the process of selecting vehicle routes allows the selection of any combination of customers, VRP is considered as a combinatorial optimization problem where the number of feasible solutions for the problem increases exponentially with the number of customers to be serviced [5]. Heuristic algorithms such as simulated annealing [6], genetic algorithms [7], tabu search [8] and ant colony optimization [9] are widely used for solving the VRP.…”