A hybrid GRASP/VND algorithm for two- and three-dimensional bin packing

The three-dimensional bin packing problem consists of packing a set of boxes into the minimum number of bins. In this paper we propose a new GRASP algorithm for solving three-dimensional bin packing problems which can also be directly applied to the two-dimensional case. The constructive phase is based on a maximal-space heuristic developed for the container loading problem. In the improvement phase, several new moves are designed and combined in a VND structure. The resulting hybrid GRASP/VND algorithm is simple and quite fast and the extensive computational results on test instances from the literature show that the quality of the solutions is equal to or better than that obtained by the best existing heuristic procedures.     

A Tabu Search Heuristic Procedure for Solving the Transportation Problem with Exclusionary Side Constraints

A new heuristic procedure for the transportation problem with exclusionary side constraints is developed and implemented. Tabu search, a meta-heuristic method, is used to guide the search to follow a path selectively to prevent from being trapped at local optimal solutions in order to find a global optimal or near global optimal solution. The simplex method on a graph is employed to lead the search from one solution to an adjacent solution in order to take advantage of the underlying network structure of the problem. In the procedure, net changes in cost and in infeasibility are used to measure the attractiveness of a move, and strategic oscillation is used to implement the intensification and diversification functions. A computational experiment was conducted to test the performance of the heuristic procedure and substantial computational results are reported. These results show that the new heuristic procedure finds very good quality solutions and outperforms an existing heuristic procedure in terms of both solution quality and CPU time.     

An efficient heuristic approach for a multi-period logistics network redesign problem

In this paper, a multi-period logistics network redesign problem arising in the context of strategic supply chain planning is studied. Several aspects of practical relevance are captured, namely, multiple echelons with different types of facilities, product flows between facilities in the same echelon, direct shipments to customers, and facility relocation. A two-phase heuristic approach is proposed to obtain high-quality feasible solutions to the problem, which is initially modeled as a large-scale mixed-integer linear program. In the first phase of the heuristic, a linear programming rounding strategy is applied to find initial values for the binary location variables. The second phase of the heuristic uses local search to correct the initial variable choices when a feasible solution is not identified, or to improve the initial feasible solution when its quality does not meet given criteria. The results of a computational study are reported for randomly generated instances comprising a variety of logistics networks.     

An Application of Tabu Search Heuristic for the Maximum Edge-Weighted Subgraph Problem

The purpose of this article is to describe an efficient search heuristic for the Maximum Edge-weighted Subgraph (MEwS) problem. This problem requires to find a subgraph such that the sum of the weights associated with the edges of the subgraph is maximized subject to a cardinality constraint. In this study a tabu search heuristic for the MEwS problem is proposed. Different algorithms to obtain an initial solution are presented. One neighborhood search strategy is also proposed. Preliminary computational results are reported for randomly generated test problems of MEwS problem with different densities and sizes. For most of test problems, the tabu search heuristic found good solutions. In addition, for large size test problems, the tabu search outperformed the local search heuristic appearing in the literature.     

Using Lagrangian dual information to generate degree constrained spanning trees

In this paper, a Lagrangian-based heuristic is proposed for the degree constrained minimum spanning tree problem. The heuristic uses Lagrangian relaxation information to guide the construction of feasible solutions to the problem. The scheme operates, within a Lagrangian relaxation framework, with calls to a greedy construction heuristic, followed by a heuristic improvement procedure. A look ahead infeasibility prevention mechanism, introduced into the greedy heuristic, allowed us to solve instances of the problem where some of the vertices are restricted to having degrees 1 or 2. Furthermore, in order to cut down on CPU time, a restricted version of the original problem is formulated and used to generate feasible solutions. Extensive computational experiments were conducted and indicate that the proposed heuristic is competitive with the best heuristics and metaheuristics in the literature.     

A penalty-shift-insertion-based algorithm to minimize total flow time in no-wait flow shops

This paper proposes a penalty-shift-insertion (PSI)-based algorithm for the no-wait flow shop scheduling problem to minimize total flow time. In the first phase, a penalty-based heuristic, derived from Vogel’s approximation method used for the classic transportation problem is used to generate an initial schedule. In the second phase, a known solution is improved using a forward shift heuristic. Then the third phase improves this solution using a job-pair and a single-job insertion heuristic. Results of the computational experiments with a large number of randomly generated problem instances show that the proposed PSI algorithm is relatively more effective and efficient in minimizing total flow time in a no-wait flow shop than the state-of-the-art procedures. Statistical significance of better results obtained by the proposed algorithm is also reported.     

A multi-heuristic approach for solving the pre-marshalling problem

Minimizing the number of reshuffling operations at maritime container terminals incorporates the pre-marshalling problem (PMP) as an important problem. Based on an analysis of existing solution approaches we develop new heuristics utilizing specific properties of problem instances of the PMP. We show that the heuristic performance is highly dependent on these properties. We introduce a new method that exploits a greedy heuristic of four stages, where for each of these stages several different heuristics may be applied. Instead of using randomization to improve the performance of the heuristic, we repetitively generate a number of solutions by using a combination of different heuristics for each stage. In doing so, only a small number of solutions is generated for which we intend that they do not have undesirable properties, contrary to the case when simple randomization is used. Our experiments show that such a deterministic algorithm significantly outperforms the original nondeterministic method. The improvement is twofold, both in the quality of found solutions, and in the computational effort.     

A Genetic Algorithm for the Multidimensional Knapsack Problem

In this paper we present a heuristic based upon genetic algorithms for the multidimensional knapsack problem. A heuristic operator which utilises problem-specific knowledge is incorporated into the standard genetic algorithm approach. Computational results show that the genetic algorithm heuristic is capable of obtaining high-quality solutions for problems of various characteristics, whilst requiring only a modest amount of computational effort. Computational results also show that the genetic algorithm heuristic gives superior quality solutions to a number of other heuristics.     

A fast heuristic for solving a large-scale static dial-a-ride problem under complex constraints

This paper presents a heuristic, which concentrates on solving a large-scale static dial-a-ride problem bearing complex constraints. In this heuristic, a properly organized local search strategy and a diversification strategy are used to improve initial solutions. Then the improved solutions can be refined further by an intensification strategy. The performance of this heuristic was evaluated by intensive computational tests on some randomly generated instances. Small gaps to the lower bounds from the column generation method were obtained in very short time for instances with no more than 200 requests. Although the result is not sensitive to the initial solution, the computational time can be greatly reduced if some effort is spent to construct a good initial solution. With this good initial solution, larger instances up to 2000 requests were solved in less than 10 hours on a popular personal computer.     

Vehicle routing problem with simultaneous deliveries and pickups

The vehicle routing problem with backhauls involves the delivery and pickup of goods at different customer locations. In many practical situations, however, the same customer may require both a delivery of goods from the distribution centre and a pickup of recycled items simultaneously. In this paper, an insertion-based procedure to generate good initial solutions and a heuristic based on the record-to-record travel, tabu lists, and route improvement procedures are proposed to resolve the vehicle routing problems with simultaneous deliveries and pickups. Computational characteristics of the insertion-based procedure and the hybrid heuristic are evaluated through computational experiments. Computational results show that the insertion-based procedure obtained better solutions than those found in the literature. Computational experiments also show that the proposed hybrid heuristic is able to reduce the gap between initial solutions and optimal solutions effectively and is capable of obtaining optimal solutions very efficiently for small-sized problems.     

A Lagrangian relaxation approach to the mixed-product assembly line sequencing problem: A case study of a door-lock company in Taiwan

In mixed-product assembly line sequencing, the production resources required for the assembly lines should be scheduled to minimize the overall cost and meet customer demand. In this paper, we study an assembly line sequencing problem for the door-lock industry in Taiwan and develop an integer programming formulation with realistic constraints. The complex solution space makes the resulting program difficult to solve using commercial optimization packages. Therefore, a heuristic based on the Lagrangian relaxation principle is developed to solve this problem efficiently. We evaluate the efficiency of the developed Lagrangian relaxation heuristic by comparing its solutions with those obtained using a commercial optimization package: the computational results show that the developed heuristic solves the real-world problem faster than the optimization package by almost 15 times in CPU time at a comparable solution quality.     

An improved decomposition-based heuristic to design a water distribution network for an irrigation system

In this paper the authors address a pressurized water distribution network design problem for irrigation purposes. Two mixed binary nonlinear programming models are proposed for this NP-hard problem. Furthermore, a heuristic algorithm is presented for the problem, which considers a decomposition sequential scheme, based on linearization of the second model, coupled with constructive and local search procedures designed to achieve improved feasible solutions. To evaluate the robustness of the method we tested it on several instances generated from a real application. The best solutions obtained are finally compared with solutions provided by standard software. These computational experiments enable the authors to conclude that the decomposition sequential heuristic is a good approach to this difficult real problem.     

An artificial bee colony algorithm for the capacitated vehicle routing problem

This paper introduces an artificial bee colony heuristic for solving the capacitated vehicle routing problem. The artificial bee colony heuristic is a swarm-based heuristic, which mimics the foraging behavior of a honey bee swarm. An enhanced version of the artificial bee colony heuristic is also proposed to improve the solution quality of the original version. The performance of the enhanced heuristic is evaluated on two sets of standard benchmark instances, and compared with the original artificial bee colony heuristic. The computational results show that the enhanced heuristic outperforms the original one, and can produce good solutions when compared with the existing heuristics. These results seem to indicate that the enhanced heuristic is an alternative to solve the capacitated vehicle routing problem.     

A Heuristic Approach for Antenna Positioning in Cellular Networks

The antenna-positioning problem concerns finding a set of sites for antennas from a set of pre-defined candidate sites, and for each selected site, to determine the number and types of antennas, as well as the associated values for each of the antenna parameters. All these choices must satisfy a set of imperative constraints and optimize a set of objectives. This paper presents a heuristic approach for tackling this complex and highly combinatorial problem. The proposed approach is composed of three phases: a constraint-based pre-processing phase to filter out bad configurations, an optimization phase using tabu search, and a post-optimization phase to improve solutions given by tabu search. To validate the approach, computational results are presented using large and realistic data sets.     

An Improved Heuristic for the Quadratic Assignment Problem

A technique is described whereby the computational efficiency of the Lashkari-Jaisingh heuristic for the quadratic assignment problem is greatly enhanced. Results for the modified heuristic are presented which demonstrate that it provides solutions of consistently high quality at relatively small computational cost.     

An Almost Optimal Heuristic for Preemptive C max Scheduling of Dependent Tasks on Parallel Identical Machines

We consider the problem of scheduling preemptable, dependent tasks on parallel, identical machines to minimize the makespan. The computational complexity of this problem remains open if the number of machines is fixed and larger than 2. The aim of this paper is to compare two heuristic algorithms on a basis of a computational experiment. The solutions generated by the heuristics are compared with optimal solutions obtained by a branch-and-bound algorithm. Computational results show that the heuristic based on node ordering finds optimal schedules for 99.9% of instances with the maximum relative deviation from optimum of 4.8%.     

A resource investment problem with time/resource trade-offs

In this study, we consider a Resource Investment Problem with time/resource trade-offs in project networks. We assume that there is a single renewable resource and the processing requirement of an activity can be reduced by investing extra resources. Our aim is to minimize the maximum resource usage, hence, the total amount invested for the single resource, while meeting the pre-specified deadline. We formulate the problem as a mixed integer linear model and find optimal solutions for small-sized problem instances. For large-sized problem instances, we propose a heuristic solution procedure. We develop several lower bounds and use them to evaluate the performance of our heuristic procedure. The results of our computational experiments have revealed the satisfactory behaviour of our optimality properties, lower bounds and heuristic procedure.     

The prize-collecting generalized minimum spanning tree problem

We introduce the prize-collecting generalized minimum spanning tree problem. In this problem a network of node clusters needs to be connected via a tree architecture using exactly one node per cluster. Nodes in each cluster compete by offering a payment for selection. This problem is NP-hard, and we describe several heuristic strategies, including local search and a genetic algorithm. Further, we present a simple and computationally efficient branch-and-cut algorithm. Our computational study indicates that our branch-and-cut algorithm finds optimal solutions for networks with up to 200 nodes within two hours of CPU time, while the heuristic search procedures rapidly find near-optimal solutions for all of the test instances.     

A mathematical formulation and complexity considerations for the blocks relocation problem

The blocks relocation problem (BRP) may be defined as follows: given a set of homogeneous blocks stored in a two-dimensional stock, which relocations are necessary to retrieve the blocks from the stock in a predefined order while minimizing the number of those relocations? In this paper, we first prove NP-hardness of the BRP as well as a special case, closing open research questions. Moreover, we propose different solution approaches. First, a mathematical model is presented that provides optimal solutions to the general BRP in cases where instances are small. To overcome such limitation, some realistic assumption taken from the literature is introduced, leading to the definition of a binary linear programming model. In terms of computational time, this approach is reasonably fast to be used to solve medium-sized instances. In addition, we propose a simple heuristic based upon a set of relocation rules. This heuristic is used to generate “good” quality solutions for larger instances in very short computational time, and, consequently, is proposed for tackling problem instances where solutions are required (almost) immediately. Solution quality of the heuristic is measured against optimal solutions obtained using a state-of-the-art commercial solver and both of them are compared with reference results from literature.     

Multistart Tabu Search Strategies for the Unconstrained Binary Quadratic Optimization Problem

This paper describes and experimentally compares five rather different multistart tabu search strategies for the unconstrained binary quadratic optimization problem: a random restart procedure, an application of a deterministic heuristic to specially constructed subproblems, an application of a randomized procedure to the full problem, a constructive procedure using tabu search adaptive memory, and an approach based on solving perturbed problems. In the solution improvement phase a modification of a standard tabu search implementation is used. A computational trick applied to this modification – mapping of the current solution to the zero vector – allowed to significantly reduce the time complexity of the search. Computational results are provided for the 25 largest problem instances from the OR-Library and, in addition, for the 18 randomly generated larger and more dense problems. For 9 instances from the OR-Library new best solutions were found.