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Showing papers on "Heuristic (computer science) published in 1985"


Journal ArticleDOI
TL;DR: It is shown that several known properties of A* retain their form and it is also shown that no optimal algorithm exists, but if the performance tests are confirmed to cases in which the estimates are also consistent, then A* is indeed optimal.
Abstract: This paper reports several properties of heuristic best-first search strategies whose scoring functions ƒ depend on all the information available from each candidate path, not merely on the current cost g and the estimated completion cost h. It is shown that several known properties of A* retain their form (with the minmax of f playing the role of the optimal cost), which helps establish general tests of admissibility and general conditions for node expansion for these strategies. On the basis of this framework the computational optimality of A*, in the sense of never expanding a node that can be skipped by some other algorithm having access to the same heuristic information that A* uses, is examined. A hierarchy of four optimality types is defined and three classes of algorithms and four domains of problem instances are considered. Computational performances relative to these algorithms and domains are appraised. For each class-domain combination, we then identify the strongest type of optimality that exists and the algorithm for achieving it. The main results of this paper relate to the class of algorithms that, like A*, return optimal solutions (i.e., admissible) when all cost estimates are optimistic (i.e., h ≤ h*). On this class, A* is shown to be not optimal and it is also shown that no optimal algorithm exists, but if the performance tests are confirmed to cases in which the estimates are also consistent, then A* is indeed optimal. Additionally, A* is also shown to be optimal over a subset of the latter class containing all best-first algorithms that are guided by path-dependent evaluation functions.

1,059 citations


Journal ArticleDOI
TL;DR: In this article, local search algorithms for routing problems with time windows are presented. But the presence of time windows introduces feasibility constraints, the checking of which normally requires O(N) time.
Abstract: We develop local search algorithms for routing problems with time windows. The presented algorithms are based on thek-interchange concept. The presence of time windows introduces feasibility constraints, the checking of which normally requires O(N) time. Our method reduces this checking effort to O(1) time. We also consider the problem of finding initial solutions. A complexity result is given and an insertion heuristic is described.

595 citations


Journal ArticleDOI
TL;DR: In this article, two types of algorithms are proposed which rely on the assumption that critical points for feasible operation lie at vertices or extreme values of the uncertain parameters, and they are applied to several example problems to demonstrate both the use of the flexibility index in process design and the computational efficiency of the algorithms.
Abstract: Procedures for the numerical computation of an index for operational flexibility in chemical processes are considered. Two types of algorithms are proposed which rely on the assumption that critical points for feasible operation lie at vertices or extreme values of the uncertain parameters. The first algorithm is a direct search procedure that features a heuristic variant to avoid exhaustive enumeration of all vertices. The second algorithm employs an implicit enumeration scheme based on a lower bound for monotonic constraints. These algorithms are applied to several example problems to demonstrate both the use of the flexibility index in process design and the computational efficiency of the algorithms.

254 citations


Journal ArticleDOI
TL;DR: An efficient branch and bound procedure is developed, tested and compared with two previously developed optimal algorithms and can be used as a heuristic for large problems by early termination of the search tree.
Abstract: The multiconstraint 0–1 knapsack problem is encountered when one has to decide how to use a knapsack with multiple resource constraints. Even though the single constraint version of this problem has received a lot of attention, the multiconstraint knapsack problem has been seldom addressed. This paper deals with developing an effective solution procedure for the multiconstraint knapsack problem. Various relaxation of the problem are suggested and theoretical relations between these relaxations are pointed out. Detailed computational experiments are carried out to compare bounds produced by these relaxations. New algorithms for obtaining surrogate bounds are developed and tested. Rules for reducing problem size are suggested and shown to be effective through computational tests. Different separation, branching and bounding rules are compared using an experimental branch and bound code. An efficient branch and bound procedure is developed, tested and compared with two previously developed optimal algorithms. Solution times with the new procedure are found to be considerably lower. This procedure can also be used as a heuristic for large problems by early termination of the search tree. This scheme was tested and found to be very effective.

229 citations


Journal ArticleDOI
TL;DR: In this article, a scheduling problem in a flexible manufacturing system (FMS) is considered to be a composite of two interdependent tasks: loading and sequencing, and heuristic methods are developed and performance is compared with the exact mixed integer programming solutions.
Abstract: A scheduling problem in a flexible manufacturing system (FMS) is considered to be a composite of two interdependent tasks: loading and sequencing. Formulations are presented for the loading problem with two objectives: (i) minimization of the system workload unbalance, and (ii) minimization of system unbalance and the number of late jobs; including constraints such as the number of tools slots with duplications, unique job routing, nonsplitting of jobs and machine capacity. For both the objectives, heuristic methods are developed and performance is compared with the exact mixed integer programming solutions. A simulation model is developed for investigating the system performance for the problem of minimizing the system unbalance using heuristic and sequential loading methods in conjunction with four—FIFO, SPT, LPT and MOPR—dispatching rules.

224 citations


Journal ArticleDOI
T.G. Szymanski1
TL;DR: It is shown that an efficient optimal algorithm for interconnecting two rows of points across an intervening channel is unlikely to exist by establishing that this problem is NP-complete.
Abstract: Interconnecting two rows of points across an intervening channel is an important problem in the design of LSI circuits. The most common methodology for producing such interconnections uses two orthogonal layers of parallel conductors and allows wires to "dogleg" arbitrarily. Although effective heuristic procedures are available for routing channels with this methodology, no efficient optimal algorithm has yet been discovered for the general case problem. We show that such an algorithm is unlikely to exist by establishing that this problem is NP-complete.

209 citations


Journal ArticleDOI
TL;DR: In this article, a heuristic linear programming-based procedure is developed for the least cost layout and design of water distribution networks, which is capable of analyzing a wide range of demand pattern and pipe failure combinations.
Abstract: A heuristic linear programming-based procedure has been developed for the least cost layout and design of water distribution networks. The methodology is capable of analyzing a wide range of demand pattern and pipe failure combinations. Hydraulic consistency is ensured throughout the procedure through the use of the Hardy-Cross network solver technique. The procedure can also be extended for use in the expansion or reinforcement of existing network systems. While the techniques used to reduce the size of the constraint set to enable the procedure to handle a wide range of loading conditions do not guarantee global optimality, a pragmatic “reasonable” optimum is achieved. The method is demonstrated by application to the design of a new network and the expansion of an existing network. In the expansion of the existing network problem the solution obtained was less expensive than any previously published solution.

176 citations


Journal ArticleDOI
TL;DR: In this paper, a primal partitioning scheme with a network flow subproblem is proposed to minimize the processing costs of a multi-item capacitated lot-sizing problem, based on a Lagrangean relaxation of the capacity constraints imposed on the resources.
Abstract: The multi-item capacitated lot-sizing problem consists of determining the magnitude and the timing of some operations of durable results for several items in a finite number of processing periods so as to satisfy a known demand in each period. The subgradient algorithm implemented to minimize the processing costs is based on a Lagrangean relaxation of the capacity constraints imposed on the resources. The method incorporates a primal partitioning scheme—with a network flow subproblem—to obtain good feasible solutions.

156 citations


Journal ArticleDOI
TL;DR: A combination of a subgradient optimization procedure and an augmented Lagrangean-based procedure is used to generate tight lower bounds for capacitated spanning tree problems.
Abstract: Capacitated spanning tree problems appear frequently as fundamental problems in many communication network design problems. An integer programming formulation and a new set of valid inequalities are presented for the linear characterization of the problem. A combination of a subgradient optimization procedure and an augmented Lagrangean-based procedure is used to generate tight lower bounds. The procedure begins with an explicit representation of a subset of the constraints, and the corresponding Lagrangean problem is solved. The solution is examined in order to identify implicit constraints that are violated. Those are added to the Lagrangean problem, forming an expanded problem, and an efficient dual ascent procedure is then applied. When no further improvement is possible through this procedure, a subgradient optimization procedure is invoked in order to further tighten the lower bound value. An exchange heuristic is applied to the nonfeasible Lagrangean solution, in an attempt to generate good feasible solutions to the problem. The procedure has been tested and has generated bounds that are significantly better than ones obtained through previously published procedures.

134 citations


Journal ArticleDOI
TL;DR: Two new exact algorithms are presented for the case where the objective and constraint functions are stagewise separable, both are branch and bound algorithms.
Abstract: This paper discusses allocating redundant components subject to resource constraints so as to optimize some measure of system performance. Two new exact algorithms are presented for the case where the objective and constraint functions are stagewise separable. Both are branch and bound algorithms. The first, BLE1, is based on an underlying knapsack structure, while the second, BLE2, exploits a multiple-choice knapsack structure. BLE1 can solve problems with 100 stages and 10 constraints in just a few seconds of CPU time on an IBM 3033. For larger problems, BLH, a heuristic procedure, is proposed. The heuristic is based on the ``slippery algorithm'' for knapsack problems. Computational testing indicates BLH often finds the optimal solution, and when it doesn't, the solutions are quite close to optimal.

133 citations


Journal ArticleDOI
TL;DR: The PARTAN technique and heuristic variations of the Frank-Wolfe algorithm are described which serve to significantly improve the convergence rate with no significant increase in memory requirements.
Abstract: We discuss methods for speeding up convergence of the Frank-Wolfe algorithm for solving nonlinear convex programs. Models involving hydraulic networks, road networks and factory-warehouse networks are described. The PARTAN technique and heuristic variations of the Frank-Wolfe algorithm are described which serve to significantly improve the convergence rate with no significant increase in memory requirements. Computational results for large-scale models are reported.

Journal ArticleDOI
TL;DR: This paper describes a special case of the general loading problem applied to flexible assembly and develops a discrete optimization model for this problem and presents results for a large scale study.
Abstract: Flexible manufacturing is characterized by versatile work stations with minimum change over times and a versatile material handling system. The loading problem in flexible manufacturing is to assign tools, material, operations and jobs to work stations in order to minimize the total number of job-to-work station assignments. In this paper, we describe a special case of the general loading problem applied to flexible assembly and develop a discrete optimization model. We then discuss approaches for obtaining good heuristic solutions and present results for a large scale study.

Journal ArticleDOI
TL;DR: Approximation methods recently developed for networks of queues are applied to obtain approximation formulas and useful heuristic design principles for queueing systems.
Abstract: An important design problem for queueing systems is to determine the best order for two or more service stations in series. For given external arrival process and given service-time distributions, the object is to determine the order of the stations (to be used by all customers) that minimizes the expected equilibrium sojourn time per customer. Unfortunately, very little is known about this problem because exact analysis is extremely difficult. This paper applies approximation methods recently developed for networks of queues to obtain approximation formulas and useful heuristic design principles.

Journal ArticleDOI
TL;DR: In this paper, a branch-and-bound method was applied to a heuristic circuit-optimization algorithm for electricity distribution planning. But the method was used to produce a family of near-optimal designs to a given planning problem.
Abstract: The application of a branch-and-bound method to a heuristic circuit-optimisation algorithm for electricity distribution planning is described. The intention is to produce a family of near-optimal designs, to a given planning problem. The principal results of this approach are twofold. First, a clearer understanding of the complex network modelling problem is obtained, and secondly the imaginative development of branch-and-bound formulation for optimisation purposes is stimulated.

Journal ArticleDOI
TL;DR: A new algorithm, FLAC (Facility Layout by Analysis of Clusters), is described which emulates the visual methods used by industrial engineers in solving facility layout problems and is found to perform well in problems with high as well as low flow dominance.
Abstract: Due to the combinatorial nature of the facility layout problem, current heuristic computer procedures do not always provide better solutions than visual methods. A new algorithm, FLAC (Facility Layout by Analysis of Clusters), is described which emulates the visual methods used by industrial engineers in solving facility layout problems. Initially side-stepping the combinatorial nature of the problem, FLAC is found to perform well in problems with high as well as low flow dominance, and in the presence and absence of line dominance. Computation time is attractive, especially on larger problems.

Journal ArticleDOI
TL;DR: Two new approaches have been developed for the multipollutant AQMN design that makes use of the index theory and the principles of Pareto optimality.
Abstract: Minimum Spanning Tree (MST) algorithm developed by Modak and Lohani (1984a) has been extended to consider multiple objectives for the optimum siting of ambient air monitors. Two approaches have been proposed, namely one based on the utility function and another based on the principles of sequential interactive compromise. The sequential interactive approach is heuristic but perhaps best suited to consider several objectives at a time, and particularly when professional judgements are also involved. The utility function approach may be normally restricted to two objectives at a time, but could be extended to consider a number of pollutants in the optimum design. For the purpose of illustration, the case of Taipei City, Taiwan has been considered.

Journal ArticleDOI
TL;DR: It is concluded that a heuristic procedure is a suitable way to handle project selection problems in organizational settings by means of an existing heuristic algorithm by Toyoda, and a hierarchical multiperiod multidimensional model is proposed.
Abstract: Decomposable systems, decomposition and 0-1 integer programming techniques are reviewed relative to project selection problems. It is concluded that a heuristic procedure is a suitable way to handle such problems in organizational settings. A hierarchical multiperiod multidimensional model is proposed. Good results are obtained based on an existing heuristic algorithm by Toyoda, by means of a decomposable interactive formulation. Examples and discussions are included that show how the use of this model can improve management decisions. A major advantage of this formulation is its flexibility to handle many different R&D situations, a feature which should increase its usefulness over many other R&D Project Selection Models. The model can be used in a multihierarchy ambience, can use parametric budgeting, and can be used as a control tool. The interactive feature provides the means for improving organizational communications and integrating divergent viewpoints.

Journal ArticleDOI
TL;DR: A new matrix representation of a planar graph and its dual is presented and this is then used to implement a heuristic for facilities layout planning.
Abstract: A new matrix representation of a planar graph and its dual is presented. This is then used to implement a heuristic for facilities layout planning.

Journal ArticleDOI
TL;DR: In this article, the problem of finding the order quantities, or cycle times, for the case of a multi-item inventory system with joint replenishment costs is addressed, where the ordering cost is composed of a fixed cost independent of the number of items ordered and additional ordering costs dependent on the specific items ordered.
Abstract: This paper deals with the problem of finding the order quantities, or cycle times, for the case of a multi-item inventory system with joint replenishment costs. The ordering cost is composed of a fixed cost independent of the number of items ordered and additional ordering costs dependent on the specific items ordered. Different solution procedures suggested for solving this problem are presented. A simulation program is developed comparing the effectiveness of these algorithms. One hundred and thirty two different settings, each consisting of one thousand examples, are analysed. Based on the simulation, two approaches are recommended for solving this problem.

Journal ArticleDOI
TL;DR: In this article, an heuristic for the planning and study of machine-component groups in flexible production cells and flexible manufacturing systems is presented, where the problem of group formation defined on master-component process routes is undertaken in terms of minimum differences between masters and maximum combinations of masters.
Abstract: This paper provides an heuristic for the planning and study of machine-component groups in flexible production cells and flexible manufacturing systems. The problem of group formation defined on master-component process routes is undertaken in terms of minimum differences between masters and maximum combinations of masters. Group formation is a ‘hard’ combinatorial problem subject to exponential growth of complexity as the number of decision-making variables increases. The heuristic is designed to search the solution space of the problem in monotone-increasing order of solution costs so as to avoid the enumeration of solutions for cost minimization.

Journal ArticleDOI
TL;DR: In this article, the authors reformulated the maximum expected covering location problem (MEXCLP) using a separable programming approach, which guarantees optimality and also solves more quickly than previous heuristic approaches.
Abstract: The maximum expected covering location problem (MEXCLP) is reformulated using a separable programming approach. The resulting formulation—nonlinear maximum expected covering location problem (NMEXCLP)—guarantees optimality and also solves more quickly than previous heuristic approaches. NMEXCLP allows two important extensions. First, minor formulation changes allow the specification of the minimum number of times each node is to be covered in order to satisfy expected coverage criteria. Second, coverage matrices can be constructed that consider two different types of coverage simultaneously. Both extensions are useful for ambulance location problems and are demonstrated in that setting.

Journal ArticleDOI
Franz Rendl1
TL;DR: It is shown that decomposing a square matrix into a weighted sum of permutation matrices, such that the sum of the weights becomes minimal, is NP-hard.

Journal ArticleDOI
TL;DR: In this paper, the cost effectiveness of single-stage lot-sizing algorithms in multi-stage settings was evaluated in a series of simulation experiments where the set-up cost, the product structure, and the demand distribution were varied.
Abstract: The purpose of this paper is to determine the cost effectiveness of recently proposed single-stage lot-sizing algorithms in multi-stage settings. Seven different algorithms and six comhinations of methods were examined in conjunction with four cost modification procedures. These procedures attempt to account for the interdependencies across stages by altering the costs employed for decision-making purposes. A series of simulation experiments was conducted where the set-up cost, the product structure, and the demand distribution were varied. It is concluded that the combination methods when used with some of the cost modifications result in enhanced performance in comparison to other sequential approaches.

Journal ArticleDOI
TL;DR: An efficient algorithm is described which necessarily finds a routing in a given grid whenever it exists, and works for a rather large class of grids, called convex grids, including the grids of rectangular, T-, L-, or X-shape boundaries.
Abstract: In this paper, we consider the channel routing problem involving two-terminal nets on rectilinear grids. An efficient algorithm is described which necessarily finds a routing in a given grid whenever it exists. The algorithm is not a heuristic but an exact one, and works for a rather large class of grids, called convex grids, including the grids of rectangular, T-, L-, or X-shape boundaries. Both the running time and required space are linear in the number of vertices of a grid.

Journal ArticleDOI
TL;DR: Efficient distributed query optimization algorithms are presented here for two types of local area networks: address ring networks and broadcast networks.
Abstract: Local area networks are becoming widely used as the database communication framework for sophisticated information systems. Databases can be distributed among stations on a network to achieve the advantages of performance, reliability, availability, and modularity. Efficient distributed query optimization algorithms are presented here for two types of local area networks: address ring networks and broadcast networks. Optimal algorithms are designed for simple queries. Optimization principles from these algorithms guide the development of effective heuristic algorithms for general queries on both types of networks. Several examples illustrate distributed query processing on local area networks.

01 Jun 1985
TL;DR: TALUS is an automatic program debugging system that both detects and corrects nonsyntactic bugs in student programs written to solve small but nontrivial tasks in pure LISP.

Journal ArticleDOI
TL;DR: In this paper, the setup minimization problem for linear extensions of interval orders is considered and a simple greedy heuristic is shown to be never worse than twice the optimum for any linear extension.

01 Jan 1985
TL;DR: Measurements indicate that a hardware-implemented, uniprocessor FAST-1 offers several orders of magnitude speedup over software-IMplemented simulators running on conventional computers built using similar technology.
Abstract: In this dissertation I describe the algorithms, architecture, and performance of a computer called the FAST-1--a special-purpose machine for switch-level simulation of VLSI circuits. The FAST-1 does not implement a previously existing simulation algorithm. Rather its simulation algorithm and its architecture were developed together. The FAST-1 is data-driven, which means that the flow of data determines which instructions to execute next. Data-driven execution has several important attributes: it implements event-driven simulation in a natural way, and it makes parallelism easier to exploit. Although the architecture described in this dissertation has yet to be implemented in hardware, it has itself been simulated using a 'software implementation' that allows performance to be measured in terms of read-modify-write memory cycles. The software-implemented FAST-1 runs at speeds comparable to other software-implemented switch-level simulators. Thus it was possible to collect an extensive set of experimental performance results of the FAST-1 simulating actual circuits, including some with over twenty thousand transistors. These measurements indicate that a hardware-implemented, uniprocessor FAST-1 offers several orders of magnitude speedup over software-implemented simulators running on conventional computers built using similar technology. Additional speedup over a uniprocessor can be obtained using a FAST-1 multiprocessor, that is constructed using multiple FAST-1 uniprocessors that are interconnected by one or more broadcast busses. In order for a FAST-1 multiprocessor to exploit the parallelism available in simulations, the FAST-1 representation of circuits must be carefully partitioned onto the processors. Although, even simple versions of the partitioning problem are NP-complete, I show that an additional order of magnitude speedup can be obtained by using a multiprocessor FAST-1 and fast heuristic partitioning algorithms.

Proceedings Article
21 Aug 1985
TL;DR: This paper model the problem of file reorganization in terms of a hypergraph and shows that this problem is NP-hard, and presents two heuristics which can be classified as incremental reorganization schemes.
Abstract: For many files, reorganization is essential during their lifetime in order to maintain an adequate performance level for users. File reorganization can be defined as the process of changing the physical structure of the file. In this paper we are mainly concerned with changes in the placement of records of a file on pages in secondary storage. We model the problem of file reorganization in terms of a hypergraph and show that this problem is NP-hard. We present two heuristics which can be classified as incremental reorganization schemes. Both algorithms incorporate a heuristic for the traveling salesman problem. The objective of our approach is the minimization of the number of pages swapped in and out of the main memory buffer area during the reorganization process. Synthetic experiments have been performed to compare our heuristics with alternative strategies.

Journal ArticleDOI
TL;DR: In this paper, on-line scheduling which changes the schedule according to the change of operating times is proposed, and their validity is verified by computer simulation that online scheduling using SLACK, EDD, or the Look Ahead heuristic rule is available.
Abstract: Adaptive control is available to adjust the operating speed of machine tools in FMS according to the condition of production, but it changes the time of each operation and disturbs the previously determined schedule. In this paper, on-line scheduling which changes the schedule according to the change of operating times is proposed. It is verified by computer simulation that on-line scheduling using SLACK, EDD, or the Look Ahead heuristic rule is available. The Look Ahead rule is the best for decreasing the lateness of due dates. Algorithms to change the adaptive control mode between optimization for cost performance and that for productivity according to the condition of the schedule are proposed, and their validity is verified by computer simulation.