A hybrid algorithm for the manufacturing cell formation problem

In this paper we compare different heuristic methods for the manufacturing cell formation problem considering part process sequence: a GRASP algorithm, a reactive GRASP algorithm and a hybrid algorithm which combines reactive GRASP and tabu search. All algorithms are tested with a set of instances from the literature. The results from the GRASP algorithm are compared to those of the reactive GRASP in order to evaluate the advantages of automatically adjusting the parameter value within the randomized greedy procedure. Also the reactive GRASP results are compared to those of the hybrid algorithm to evaluate the contribution to solution quality of replacing the local search phase of the GRASP algorithm with tabu search.     

GRASP heuristic with path-relinking for the multi-plant capacitated lot sizing problem

This paper addresses the independent multi-plant, multi-period, and multi-item capacitated lot sizing problem where transfers between the plants are allowed. This is an NP-hard combinatorial optimization problem and few solution methods have been proposed to solve it. We develop a GRASP (Greedy Randomized Adaptive Search Procedure) heuristic as well as a path-relinking intensification procedure to find cost-effective solutions for this problem. In addition, the proposed heuristics is used to solve some instances of the capacitated lot sizing problem with parallel machines. The results of the computational tests show that the proposed heuristics outperform other heuristics previously described in the literature. The results are confirmed by statistical tests.     

A GRASP for the biquadratic assignment problem

The biquadratic assignment problem (BiQAP) is a generalization of the quadratic assignment problem (QAP). It is a nonlinear integer programming problem where the objective function is a fourth degree multivariable polynomial and the feasible domain is the assignment polytope. BiQAP problems appear in VLSI synthesis. Due to the difficulty of this problem, only heuristic solution approaches have been proposed. In this paper, we propose a new heuristic for the BiQAP, a greedy randomized adaptive search procedure (GRASP). Computational results on instances described in the literature indicate that this procedure consistently finds better solutions than previously described algorithms.     

A heuristic for multiple-feeder PCB manufacturing

In the considered printed circuit board (PCB) manufacturing problem, the objective is to minimize production time by allocating components to capacitated feeders and sequencing the placement of these components on a printed circuit board by a robot arm. A number of applications outside the computer industry illustrate the importance of the PCB problem also in other areas. We report the development and implementation of a new heuristic and a related lower bound. Computational results are given for test instances up to 13 feeders and 140 locations.     

An optimization-based heuristic for the robotic cell problem

This study investigates an optimization-based heuristic for the robotic cell problem. This problem arises in automated cells and is a complex flow shop problem with a single transportation robot and a blocking constraint. We propose an approximate decomposition algorithm. The proposed approach breaks the problem into two scheduling problems that are solved sequentially: a flow shop problem with additional constraints (blocking and transportation times) and a single machine problem with precedence constraints, time lags, and setup times. For each of these problems, we propose an exact branch-and-bound algorithm. Also, we describe a genetic algorithm that includes, as a mutation operator, a local search procedure. We report the results of a computational study that provides evidence that the proposed optimization-based approach delivers high-quality solutions and consistently outperforms the genetic algorithm. However, the genetic algorithm delivers reasonably good solutions while requiring significantly shorter CPU times.     

A matheuristic for the cell formation problem

In this paper we propose a GRASP matheuristic coupled with an Integer Programming refinement based on Set Partitioning to solve the Cell Formation Problem. We use the grouping efficacy measure to evaluate the solutions. As this measure is nonlinear, we propose a fractional Set Partitioning approach and its linearization. Our method is validated on a set of 35 instances from the literature. The experiments found four unknown solutions. For all instances with known optima, our method is able to determine the optimum solutions.     

A gamma heuristic for the p-median problem

Heuristic concentration (HC) is a two-stage metaheuristic that can be applied to a wide variety of combinatorial problems. It is particularly suited to location problems in which the number of facilities is given in advance. In such settings, the first stage of HC repeatedly applies some random-start interchange (or other) heuristic to produce a number of alternative facility configurations. A subset of the best of these alternatives is collected and the union of the facility sites in them is called a concentration set (CS). Among the component elements of the CS are likely to be included those sites which are members of the optimal solution. In earlier studies the second stage of HC has consisted of an exact procedure to extract the best possible solution from the CS. In this paper we demonstrate, for the p-median problem, the use of two sequentially active heuristics in the second stage of HC. That is, we offer two additional layers of heuristics to improve solutions which are found in the first stage of HC. Thus we are describing a variant of the HC metaheuristic consisting of three layers of heuristics which are utilized in sequence. We propose for this procedure the name of Gamma Heuristic.     

A GRASP + ILP-based metaheuristic for the capacitated location-routing problem

In this paper we present a three-phase heuristic for the Capacitated Location-Routing Problem. In the first stage, we apply a GRASP followed by local search procedures to construct a bundle of solutions. In the second stage, an integer-linear program (ILP) is solved taking as input the different routes belonging to the solutions of the bundle, with the objective of constructing a new solution as a combination of these routes. In the third and final stage, the same ILP is iteratively solved by column generation to improve the solutions found during the first two stages. The last two stages are based on a new model, the location-reallocation model, which generalizes the capacitated facility location problem and the reallocation model by simultaneously locating facilities and reallocating customers to routes assigned to these facilities. Extensive computational experiments show that our method is competitive with the other heuristics found in the literature, yielding the tightest average gaps on several sets of instances and being able to improve the best known feasible solutions for some of them.     

A GRASP algorithm for the multi-criteria minimum spanning tree problem

This paper proposes a GRASP (Greedy Randomized Adaptive Search Procedure) algorithm for the multi-criteria minimum spanning tree problem, which is NP-hard. In this problem a vector of costs is defined for each edge of the graph and the problem is to find all Pareto optimal or efficient spanning trees (solutions). The algorithm is based on the optimization of different weighted utility functions. In each iteration, a weight vector is defined and a solution is built using a greedy randomized constructive procedure. The found solution is submitted to a local search trying to improve the value of the weighted utility function. We use a drop-and-add neighborhood where the spanning trees are represented by Prufer numbers. In order to find a variety of efficient solutions, we use different weight vectors, which are distributed uniformly on the Pareto frontier. The proposed algorithm is tested on problems with r=2 and 3 criteria. For non-complete graphs with n=10, 20 and 30 nodes, the performance of the algorithm is tested against a complete enumeration. For complete graphs with n=20, 30 and 50 nodes the performance of the algorithm is tested using two types of weighted utility functions. The algorithm is also compared with the multi-criteria version of the Kruskal’s algorithm, which generates supported efficient solutions. This work was funded by the Municipal Town Hall of Campos dos Goytacazes city. The used computer was acquired with resource of CNPq.     

GRASP with path relinking for the orienteering problem

In this paper, we address an optimization problem resulting from the combination of the well-known travelling salesman and knapsack problems. In particular, we target the orienteering problem, originated in the context of sport, which consists of maximizing the total score associated with the vertices visited in a path within the available time. The problem, also known as the selective travelling salesman problem, is NP-hard and can be formulated as an integer linear program. Since the 1980s, several solution methods for this problem have been developed and applied to a variety of fields, particularly in routing and tourism. We propose a heuristic method—based on the Greedy Randomized Adaptive Search Procedure (GRASP) and the Path Relinking methodologies—for finding approximate solutions to this optimization problem. We explore different constructive methods and combine two neighbourhoods in the local search of GRASP. Our experimentation with 196 previously reported instances shows that the proposed procedure obtains high-quality solutions employing short computing times.     

A hybrid heuristic for the maximum clique problem

In this paper we present a heuristic based steady-state genetic algorithm for the maximum clique problem. The steady-state genetic algorithm generates cliques, which are then extended into maximal cliques by the heuristic. We compare our algorithm with three best evolutionary approaches and the overall best approach, which is non-evolutionary, for the maximum clique problem and find that our algorithm outperforms all the three evolutionary approaches in terms of best and average clique sizes found on majority of DIMACS benchmark instances. However, the obtained results are much inferior to those obtained with the best approach for the maximum clique problem.     

A heuristic for the Steiner problem in graphs

In this paper, we present a heuristic for the Steiner problem in graphs (SPG) along with some experimental results. The heuristic is based on an approach similar to Prim's algorithm for the minimum spanning tree. However, in this approach, arcs are associated with preference weights which are used to break ties among alternative choices of shortest paths occurring during the course of the algorithm. The preference weights are calculated according to a global view which takes into consideration the effect of all the regular nodes, nodes to be connected, on determining the choice of an arc in the solution tree.     

A heuristic for the three-dimensional strip packing problem

The contribution presents a heuristic for the three-dimensional strip packing problem (3D-SPP) with rectangular pieces (boxes). The considered 3D-SPP can be formulated as follows: for a given set of boxes and a given longitudinal open container, determine an arrangement of all boxes within the container so that the required container length is minimized.     

A hybrid heuristic for the maximum dispersion problem

In this paper we propose a hybrid heuristic for the Maximum Dispersion Problem of finding a balanced partition of a set of objects such that the shortest intra-part distance is maximized. In contrast to clustering problems, dispersion problems aim for a large spread of objects in the same group. They arise in many practical applications such as waste collection and the formation of study groups. The heuristic alternates between finding a balanced solution, and increasing the dispersion. Balancing is achieved by a combination of a minimum cost flow algorithm to find promising pairs of parts and a branch-and-bound algorithm that searches for an optimal balance, and the dispersion is increased by a local search followed by an ejection chain method for escaping local minima. We also propose new upper bounds for the problem. In computational experiments we show that the heuristic is able to find solutions significantly faster than previous approaches. Solutions are close to optimal and in many cases provably optimal.     

A heuristic algorithm for the strip packing problem

The two-dimensional strip packing problem is to pack a given set of rectangles into a strip with a given width and infinite height so as to minimize the required height of the packing. From the computational point of view, the strip packing problem is an NP-hard problem. With the B*-tree representation, this paper first presents a heuristic packing strategy which evaluates the positions used by the rectangles. Then an effective local search method is introduced to improve the results and a heuristic algorithm (HA) is further developed to find a desirable solution. Computational results on randomly generated instances and popular test instances show that the proposed method is efficient for the strip packing problem.     

A dynamic programming heuristic for the P-median problem

A new heuristic algorithm is proposed for the P-median problem. The heuristic restricts the size of the state space of a dynamic programming algorithm. The approach may be viewed as an extension of the myopic or greedy adding algorithm for the P-median model. The approach allows planners to identify a large number of solutions all of which perform well with respect to the P-median objective of minimizing the demand weighted average distance between customer locations and the nearest of the P selected facilities. In addition, the results indicate regions in which it is desirable to locate facilities. Computational results from three test problems are discussed.     

A heuristic method for the multi-story layout problem

In this paper we present a heuristic procedure designed expressly for solving a large layout problem in a multi-story setting, where the objective is to minimize total fixed and interaction costs. This is achieved by decomposing the original facilities layout problem into several similar but smaller problems, thus enabling solution of problems with as many as 150 facilities in reasonable time. Some of the novel features of the procedure described are the use of a heuristic K-median subroutine to obtain groupings of facilities, and a simple and fast exchange-improvement method. Computational results for randomly generated problems compare the effectiveness of this method with the space planning heuristic method of Liggett and Mitchell.     

A heuristic procedure for the Capacitated m-Ring-Star problem

In this paper we propose a heuristic method to solve the Capacitated m-Ring-Star Problem which has many practical applications in communication networks. The problem consists of finding m rings (simple cycles) visiting a central depot, a subset of customers and a subset of potential (Steiner) nodes, while customers not belonging to any ring must be “allocated” to a visited (customer or Steiner) node. Moreover, the rings must be node-disjoint and the number of customers allocated or visited in a ring cannot be greater than the capacity Q given as an input parameter. The objective is to minimize the total visiting and allocation costs. The problem is a generalization of the Traveling Salesman Problem, hence it is NP-hard. In the proposed heuristic, after the construction phase, a series of different local search procedures are applied iteratively. This method incorporates some random aspects by perturbing the current solution through a “shaking” procedure which is applied whenever the algorithm remains in a local optimum for a given number of iterations. Computational experiments on the benchmark instances of the literature show that the proposed heuristic is able to obtain, within a short computing time, most of the optimal solutions and can improve some of the best known results.     

A new heuristic approach for the P-median problem

The Euclidean p-median problem is concerned with the decision of the locations for public service centres. Existing methods for the planar Euclidean p-median problems are capable of efficiently solving problems of relatively small scale. This paper proposes two new heuristic algorithms aiming at problems of large scale. Firstly, to reflect the different degrees of proximity to optimality, a new kind of local optimum called level-m optimum is defined. For a level-m optimum of a p-median problem, where m<p, each of its subsets containing m of the p partitions is a global optimum of the corresponding m-median subproblem. Starting from a conventional local optimum, the first new algorithm efficiently improves it to a level-2 optimum by applying an existing exact algorithm for solving the 2-median problem. The second new algorithm further improves it to a level-3 optimum by applying a new exact algorithm for solving the 3-median problem. Comparison based on experimental results confirms that the proposed algorithms are superior to the existing heuristics, especially in terms of solution quality.     

A water flow-like algorithm for manufacturing cell formation problems

Available research on the manufacturing cell formation problem shows that most solution approaches are either single- or multiple-solution-agent-based, with a fixed size of solution agents. Frequent problems encountered during the process of solving the cell formation problem include solutions being easily trapped in local optima and bad solution efficiency. Yang and Wang [Yang, F.-C., Wang, Y.-P., 2007. Water flow-like algorithm for object grouping problems. Journal of the Chinese Institute of Industrial Engineers, 24 (6), 475–488] proposed the water flow-like algorithm (WFA) to overcome the shortcomings of single- and multiple-solution -agent-based algorithms. WFA has the features of multiple and dynamic numbers of solution agents, and its mimicking of the natural behavior of water flowing from higher to lower levels coincides exactly with the process of searching for optimal solutions. This paper therefore adopts the WFA logic and designs a heuristic algorithm for solving the cell formation problem. Computational results obtained from running a set of 37 test instances from the literature and newly created have shown that the proposed algorithm has performed better than other benchmarking approaches both in solution effectiveness and efficiency, especially in large-sized problems. The superiority of the proposed WFACF over other approaches from the literature should be attributed to the collaboration of the WFA logic, the proposed prior estimation of the cell size, and the insertion-move. The WFA is a novel heuristic approach that deserves more attention. More attempts on adopting the WFA logic to solve many other combinatorial optimization problems are highly recommended.