Consider the following restricted (symmetric or asymmetric) traveling-salesman problem (TSP): given an initial ordering of the n cities and an integer k > 0, find a minimum-cost feasible tour, where a feasible tour is one in which city i precedes city j whenever j ≥ i+ k in the initial ordering. Balas (1996) has proposed a dynamic-programming algorithm that solves this problem in time linear in...

In the single objective period traveling salesman problem (SOPTSP), each of given n cities has to be visited by the traveling salesman a fixed number of times according to some allowable day combinations over a given m day planning period with the objective to minimize the total traveling distance over the whole period. The existing solution methods for the SOPTSP always generate a set of unbal...

In this paper, a new approach to risk minimizing vehicle routing and scheduling problem is presented. Forwarding agents or companies have two main concerns for the collection of high-risk commodities like cash or valuable commodities between the central depot and the customers: one; because of the high value of the commodities transported, the risk of ambush and robbery are very high. Two; the ...

Imperial competitive algorithm (ICA) simulates a multi-agent algorithm. Each agent is like a kingdom has its country, and the strongest country in each agent is called imperialist, others are colony. Countries are competitive with imperialist which in the same kingdom by evolving. So this country will move in the search space to find better solutions with higher fitness to be a new imperialist....

The vehicle routing problem (VRP) is an important aspect of transportation logistics with many variants. This paper studies the VRP with backhauls (VRPB) in which the set of customers is partitioned into two subsets: linehaul customers requiring a quantity of product to be delivered, and backhaul customers with a quantity to be picked up. The basic VRPB involves finding a collection of routes w...

The Generalized Traveling Salesman Problem (GTSP) is a well-known combinatorial optimization problem with a host of applications. It is an extension of the Traveling Salesman Problem (TSP) where the set of cities is partitioned into so-called clusters, and the salesman has to visit every cluster exactly once. While the GTSP is a very important combinatorial optimization problem and is well stud...

Our goal is to design simple and asymptotically optimal heuristic algorithms for a class of bottleneck and capacity optimization problems. Our approach is applied to a wide variety of bottleneck problems including vehicle routing problems, location problems, and communication network problems. In particular, we present simple and asymptotically optimal heuristic algorithms that solve the bottle...

Multiple Traveling Salesman Problem (MTSP) is an important combinatorial optimization problem. However, it is applicable to only the cases in which multiple executing individuals (traveling salesman) share the common workspace (city set). It cannot be used to handle many multi-machine engineering systems where multiple machines’ workspaces are not the same and partially overlap with each other....

The paper examines applications of combinatorial optimization in logistics and transport, and considers some mathematical optimization problems from the perspective of Operational Research (OR). It also lists some of the numerous applications of these problems in economic reality, describes how such problems can be mathematically modelled, proposes algorithms for their solution, and presents th...