New heuristic algorithms for the windy rural postman problem

In this paper we deal with the windy rural postman problem. This problem generalizes several important arc routing problems and has interesting real-life applications. Here, we present several heuristics whose study has lead to the design of a scatter search algorithm for the windy rural postman problem. Extensive computational experiments over different sets of instances, with sizes up to 988 nodes and 3952 edges, are also presented.     

Heuristics for the rural postman problem

When addressing the problem of snow removal for secondary roads, a tool for solving the rural postman problem can be very useful. We present some ideas for heuristics for this problem. The heuristics are of the same type as the classical Frederickson heuristic. The ideas concern the order of the main steps in such a method, namely constructing a connected graph with all vertices having even degree, containing all the required edges. We also propose two postprocessing heuristics for improving the tours and removing unnecessary detours. The computational tests show that the ideas are interesting alternatives to the classical approach, and that running times are acceptable. We study problem characteristics that may indicate which method to choose.     

The time-dependent rural postman problem: polyhedral results

The Chinese postman problem is a famous and classical problem in graph theory. This paper introduces a new variant of this problem, namely, the time-dependent rural postman problem, which is motivated by applications, involving scheduling with time-dependent processing time. We present an arc-path formulation for the problem with a constraint set that is divided into two parts. The first part is linear and has a strong combinatorial structure, which defines the polytope of the arc-path alternation sequence (APAS), while the second part is nonlinear and is closely related to time-dependent travel time. First, we investigate the facial structure of the APAS polytope and present several facet inequalities. Second, considering the travel and service time functions as piecewise functions, we linearize the nonlinear inequalities and propose several strong, valid inequalities. Finally, we propose a cutting plane algorithm and report numerical results on several randomly generated instances.     

A new algorithm for the directed chinese postman problem

The directed Chinese Postman Problem can be transformed into a minimum cost flow problem over a derived network, or be transformed into a transportation problem in which the coefficients are determined by a shortest path problem over an extended network. Based on the Complementary Slackness Theorem, this paper will present an algorithm for the directed Chinese Postman Problem, which can be applied directly to the original network and, compared with the existing algorithms, has a better computational complexity O(kn²) where k depends on the structure of the network. The algorithm is extended to the directed m-CPP case.     

Privatized rural postman problems

In this work we analyze the privatized rural postman problem which is the edge version of the traveling salesman problems with profits.The problem is defined on a undirected graph G(V,E) with a distinguished vertex d, called the Depot. There are two non-negative real functions on the edge set E, which define the value of a cycle in G: one is the profit function, b, and the other one is the cost function, c. They have different meanings when a cycle C traverses an edge e (possibly more than once), because we pay a cost c_e every time e is traversed, but we collect the profit b_e only the first time e is traversed. The privatized rural postman problem is to find a cycle C, passing through d and not necessarily simple, which maximizes the sum of the values of the edges traversed in C. That is, where t_e is the number of times that edge e is traversed in C.We study some properties of the problem: we show that it is NP-hard, its relation with known and new problems, and special cases with good algorithms. We also analyze several integer linear systems of inequalities, which define the polyhedral structure of the problem, and we give dominance and preprocessing conditions. We finish with some remarks and comments about future research.     

A heuristic approach for a scheduling problem with periodic maintenance and sequence-dependent setup times

In this paper we study a problem of sequencing jobs in a machine with programmed preventive maintenance and sequence-dependent setup times. To the authors’ knowledge, this problem has not been treated as such in the operations research literature. Computational experiments show that it is very hard to solve the problem by exact methods. Therefore, the contribution of this paper is to design and implement a solution approach based on metaheuristic procedures. The proposed method finds high quality solutions in very short computational times.     

A heuristic for the label printing problem

Label printing finds many applications in industry. However, this task is still labor intensive in many printing factories. Since each template can only accommodate a fixed number of labels, an important task is to work out the compositions of templates by allocating suitable labels to each template in order to fulfill the order requirements effectively. The template design could be rather arbitrary, which usually ends up with a lot of excessive printed labels. Enhancing the template design will significantly improve the efficiency of the printing process, and, at the same time, reduce the waste of resources. This motivates the study of more automatic design methods. In this paper, the problem is first formulated as a nonlinear integer programming problem. The main variables in the formulation are the compositions and the printing frequencies of templates. For practical purpose, each type of label is confined to one template only which allows automated packing and handling. The structure of the problems is carefully analyzed and a new algorithm is proposed. Numerical results show that the proposed method is a simple but effective way of generating good template designs.     

Approximate solutions for the maximum benefit chinese postman problem

The Maximum Benefit Chinese Postman Problem (MBCPP) is an interesting and practical generalization of the classical Chinese Postman Problem, which has many real-world applications. Each arc on the MBCPP network is associated with a service cost for the traversal with service, a deadhead cost for the traversal with no service, and a set of benefits. Each time an arc is traversed, a benefit is generated. The objective of the MBCPP is to find a postman tour traversing a selected set of arcs with the total net benefit maximized. Such a generalization reflects real-world situations more closely. The MBCPP has been shown to be more complicated than the Rural Postman Problem, which is an NP-hard problem. Therefore, it is difficult to find polynomial-time bounded algorithms to solve the problem exactly. In this paper, we first review an existing exact solution procedure, and introduce several heuristic algorithms including the Branch-Scan algorithm, the Connection algorithm with various connection strategies, and the Directed Tree algorithm, to solve the MBCPP approximately. We also apply one-opt, two-opt, component exchange, and component-drop procedures to improve the solutions. The proposed algorithms are tested and compared. Extensive computational results are provided and analysed.     

A decomposition-based heuristic for the multiple-product inventory-routing problem

The inventory-routing problem is an integrated logistics planning problem arising in situations where customers transfer the responsibility for inventory replenishment to the vendor. The vendor must then decide when to visit each customer, how much to deliver and how to sequence customers in vehicle routes. In this paper, we focus on the case where several different products have to be delivered by a fleet of vehicles over a finite and discrete planning horizon. We present a three-phase heuristic based on a decomposition of the decision process of the vendor. In the first phase, replenishment plans are determined by using a Lagrangian-based method. These plans do not specify delivery sequences for the vehicles. The sequencing of the planned deliveries is performed in the second phase in which a simple procedure is employed to construct vehicle routes. The third phase incorporates planning and routing decisions into a mixed-integer linear programming model aimed at finding a good solution to the integrated problem. Computational experiments show that our heuristic is effective on instances with up to 50 customers and 5 products.     

A hybrid heuristic for the traveling salesman problem

The combination of genetic and local search heuristics has been shown to be an effective approach to solving the traveling salesman problem (TSP). This paper describes a new hybrid algorithm that exploits a compact genetic algorithm in order to generate high-quality tours, which are then refined by means of the Lin-Kernighan (LK) local search. The local optima found by the LK local search are in turn exploited by the evolutionary part of the algorithm in order to improve the quality of its simulated population. The results of several experiments conducted on different TSP instances with up to 13,509 cities show the efficacy of the symbiosis between the two heuristics     

A multi-phase heuristic for the production routing problem

This study considers the production routing problem where a plant produces and distributes a single item to multiple retailers over a multi-period time horizon. The problem is to decide on when and how much to produce and stock at the plant, when and how much to serve and stock at each retailer, and vehicle routes for shipments such that the sum of fixed production setup cost, variable production cost, distribution cost, and inventory carrying cost at the plant and retailers is minimized. A multi-phase heuristic is proposed for the problem. The proposed heuristic is a mathematical programming-based heuristic that relies on formulating and solving restricted versions of the problem as mixed integer programs. The computational experiments on benchmark instances show favorable results with regard to the quality of the solutions found at the expense of higher computing times on large instances. In particular, the heuristic managed to find new best solutions for the 65% of benchmark instances.     

Plowing with precedence: A variant of the windy postman problem

In winter, a common problem is to determine the route that a snowplow should take in order to minimize the distance traveled. We propose a variant of this arc routing problem that is motivated by the fact that deadhead travel over streets that have already been plowed is significantly faster than the time it takes to plow the street. This problem differs from most arc routing problems because the cost of traversing a street changes depending on the order of the streets on a route. We develop a method that generates near-optimal solutions to instances as large as 200 nodes.     

A heuristic manipulation technique for the sequential ordering problem

The sequential ordering problem is a version of the asymmetric travelling salesman problem where precedence constraints on vertices are imposed. A tour is feasible if these constraints are respected, and the objective is to find a feasible solution with minimum cost.The sequential ordering problem models many real-world applications, mainly in the fields of transportation and production planning.A problem manipulation technique to be used in conjunction with heuristic algorithms is discussed. The aim of the technique is to make the search space associated with each problem more attractive for the underlying heuristic algorithms.This novel methodology is tested in combination with the state-of-the-art method for the sequential ordering problem. Improved results are obtained, particularly for the largest problems considered.     

A simulated annealing heuristic for the open location-routing problem

This paper introduces the open location-routing problem (OLRP) that is a variant of the capacitated location-routing problem (CLRP). OLRP is motivated from the rise in contracting with third-party logistic (TPL) companies and is different from CLRP in that vehicles do not return to the distribution center after servicing all customers. The goal of OLRP is to minimize the total cost, consisting of facility operation costs, vehicle fixed costs, and traveling costs. We propose a simulated annealing (SA)-based heuristic for solving OLRP, which is tested on OLRP instances that have been adopted from three sets of well-known CLRP benchmark instances with up to 318 customers and 4 potential depots. The computational results indicate that the proposed heuristic efficiently solves OLRP.     

A tabu search heuristic for the concentrator location problem

The concentrator location problem (CLP) is a classical problem in the network design literature. Given a set of candidate locations and the concentrator capacities, the problem is to answer the following related questions. How many concentrators should be used? Where should they be located? Which users are to be assigned to each concentrator? A Lagrangian relaxation is used to obtain lower bounds for this problem. The Lagrangian relaxation is complemented by a tabu search (TS) metaheuristic. Computational results are given for a set of randomly generated problems and for test problems available in the literature. The tabu search heuristic (TSH) is shown to be competitive with other solution procedures available for the problem.     

A TABU search heuristic for the team orienteering problem

This paper describes a tabu search heuristic for the Team Orienteering Problem (TOP). The TOP is a variant of the well-known Vehicle Routing Problem in which a set of vehicle tours are constructed such that the total collected reward received from visiting a subset of customers is maximized and the length of each vehicle tour is restricted by a pre-specified limit. The tabu search heuristic is embedded in an adaptive memory procedure that alternates between small and large neighborhood stages during the solution improvement phase. Both random and greedy procedures for neighborhood solution generation are employed and infeasible, as well as feasible, solutions are explored in the process. Results from computational experiments conducted on a set of published test problems show that the proposed technique consistently produces high-quality solutions and outperforms other published heuristics for the TOP.     

A new directed branching heuristic for the pq-median problem

The pq-median problem, of Serra and ReVelle seeks to locate hierarchical facilities at two levels so as to obtain a coherent structure. Coherence requires that the entire area assigned to a facility at the inferior level be assigned to one and the same facility at the next higher level of the hierarchy. Although optimal solutions can be obtained by means of solving biobjective integer linear programs, large problems are likely to require heuristics. Here we present a new heuristic that combines the generation of points, by means of a “directed” branching procedure with the final selection of points, using the FDH-technique. We further compare our new heuristic with the two most relevant heuristics proposed by Serra and ReVelle.