Showing papers on "Heuristic published in 1995"

Balancing and Sequencing of Assembly Lines

Abstract: I Decision Problems.- 1 Introduction.- 2 Single-Model Assembly Lines.- 3 Mixed-Model Assembly Lines.- II Solution Methods.- 4 Exact Procedures for Single-Model Assembly Line Balancing Problems.- 5 Heuristic Procedures for Single - Model Assembly Line Balancing Problems.- 6 Solution Methods for Mixed-Model Balancing and Sequencing Problems.- 7 Computational Experiments.- 8 Summary and Conclusions.- References.

An exchange heuristic for routeing problems with time windows

Abstract: In this paper, we compare different exchange heuristics for vehicle routeing problems with time windows. We also introduce a new 2-opt* exchange heuristic, and show that a hybrid approach, based on Or-opt and 2-opt* exchanges, is particularly powerful for problems with time windows. Computational results are reported for randomly generated problems and for a standard test set.

An empirical study of algorithms for point-feature label placement

Abstract: A major factor affecting the clarity of graphical displays that include text labels is the degree to which labels obscure display features (including other labels) as a result of spatial overlap. Point-feature label placement (PFLP) is the problem of placing text labels adjacent to point features on a map or diagram so as to maximize legibility. This problem occurs frequently in the production of many types of informational graphics, though it arises most often in automated cartography. In this paper we present a comprehensive treatment of the PFLP problem, viewed as a type of combinatorial optimization problem. Complexity analysis reveals that the basic PFLP problem and most interesting variants of it are NP-hard. These negative results help inform a survey of previously reported algorithms for PFLP; not surprisingly, all such algorithms either have exponential time complexity or are incomplete. To solve the PFLP problem in practice, then, we must rely on good heuristic methods. We propose two new methods, one based on a discrete form of gradient descent, the other on simulated annealing, and report on a series of empirical tests comparing these and the other known algorithms for the problem. Based on this study, the first to be conducted, we identify the best approaches as a function of available computation time.

Robust scheduling to hedge against processing time uncertainty in single-stage production

Abstract: Schedulers confronted with significant processing time uncertainty often discover that a schedule which is optimal with respect to a deterministic or stochastic scheduling model yields quite poor performance when evaluated relative to the actual processing times. In these environments, the notion of schedule robustness, i.e., determining the schedule with the best worst-case performance compared to the corresponding optimal solution over all potential realizations of job processing times, is a more appropriate guide to schedule selection. In this paper, we formalize the robust scheduling concept for scheduling situations with uncertain or variable processing times. To illustrate the development of solution approaches for a robust scheduling problem, we consider a single-machine environment where the performance criterion of interest is the total flow time over all jobs. We define two measures of schedule robustness, formulate the robust scheduling problem, establish its complexity, describe properties of the optimal schedule, and present exact and heuristic solution procedures. Extensive computational results are reported to demonstrate the efficiency and effectiveness of the proposed solution procedures.

A Location Based Heuristic for General Routing Problems

Abstract: We present a general framework for modeling routing problems based on formulating them as a traditional location problem called the capacitated concentrator location problem. We apply this framework to two classical routing problems: the capacitated vehicle routing problem and the inventory routing problem. In the former case, the heuristic is proven to be asymptotically optimal for any distribution of customer demands and locations. Computational experiments show that the heuristic performs well for both problems and, in most cases, outperforms all published heuristics on a set of standard test problems.

SEM: a system for enumerating models

Abstract: Model generation can be regarded as a special case of the Constraint Satisfaction Problem (CSP). It has many applications in AI, computer science and mathematics. In this paper, we describe SEM, a System for Enumerating finite Models of first-order many-sorted theories. To the best of our knowledge, SEM outperforms any other finite model generation system on many test problems. The high performance of SEM relies on the following two techniques: (a) an efficient implementation of constraint propagation which requires little dynamic allocation of storage; (b) a powerful heuristic which eliminates many isomorphic partial models during the search. We will present the basic algorithm of SEM along with these two techniques. Our experimental results show that general purpose finite model generators are indeed useful in many applications.

Near optimal solutions for product line design and selection: beam search heuristics

Abstract: Many practical product line design problems have large numbers of attributes and levels. In this case, if most attribute level combinations define feasible products, constructing product lines directly from part-worths data is necessary. For three typical formulations of this important problem, Kohli and Sukumar Kohli, R., R. Sukumar. 1990. Heuristics for product-line design using conjoint analysis. Management Sci.36 1464-1478. present state-of-the-art heuristics to find good solutions. In this paper, we develop improved heuristics based on a beam search approach for solving these problems. In our computations for 435 simulated problems, significant improvements occur in five important performance measures used. Our heuristic solutions are closer to the optimal, have smaller standard deviation over replicates, take less computation time, obtain optimal solutions more often and identify a number of "good" product lines explicitly. Computation times for these problems are no more than 22 seconds on a PC, small enough for adequate sensitivity analysis. We also apply the heuristics to a real data set and clarify computational steps by giving a detailed example.

An improved heuristic for the period vehicle routing problem

Abstract: In the period vehicle routing problem, each customer requires a certain number of deliveries per week. Given these frequency requirements, customers must be allocated to days. A vehicle routing problem is solved over each day. We have improved upon best-known solutions to problems from the literature using a new heuristic procedure. The heuristic also works well on 19 newly generated test problems.

Note: A local-search heuristic for large set-covering problems

Abstract: In this note we describe a local-search heuristic (LSH) for large non-unicost set-covering problems (SCPs). The new heuristic is based on the simulated annealing algorithm and uses an improvement routine designed to provide low-cost solutions within a reasonable amount of CPU time. The solution costs associated with the LSH compared very favorably to the best previously published solution costs for 20 large SCPs taken from the literature. In particular, the LSH yielded new benchmark solutions for 17 of the 20 test problems. We also report that, for SCPs where column cost is correlated with column coverage, the new heuristic provides solution costs competitive with previously published results for comparable problems. © 1995 John Wiley & Sons, Inc.

Design Heuristic for Globally Minimum Cost Water-Distribution Systems

Abstract: Two standard test problems that are nonconvex with multiple local minima are considered An outer flow search–inner optimization procedure is proposed for choosing better local minima Each pipe network is judiciously subjected to the outer-search scheme that chooses alternative flow configurations to find an optimal flow division among pipes An inner linear program is used for the design of least-cost diameters The algorithm can also be used for the optimal design of parallel expansion of existing networks Because the problem is nonconvex, two global-search schemes, MULTISTART and ANNEALING, are used to permit a local-optimum-seeking method to migrate among various local minima MULTISTART selectively saturates portions of the feasible region to identify the local minima ANNEALING iteratively improves the objective function by finding successive better points, and, to escape out of a local minimum, it exercises the metropolis step, which requires an occasional acceptance of a worse point The optimal

Computing near‐optimal solutions to the steiner problem in a graph using a genetic algorithm

Abstract: A new genetic algorithm (GA) for the Steiner Problem in a Graph (SPG) is presented. The algorithm is based on a bitstring encoding of selected Steiner vertices and the corresponding Steiner tree is computed using a deterministic SPG heuristic. The GA is tested on all SPG instances from the OR-Library having from 500 to 2500 vertices and up to 62,500 edges. For these graphs, the algorithm finds a global optimum in 70% of all program executions and is within 1% from the global optimum value in 90% of all executions. The performance is compared to that of two branch-and-cut algorithms and two of the very best deterministic heuristics : an iterated version of the Takahashi and Matsuyama heuristic (ITM) and an iterated version of the Kou, Markowsky, and Berman heuristic (IKMB). In almost all cases, even the worst result ever found by the GA is equal to or better than the best result of ITM and IKMB. Furthermore, while none of the deterministic heuristics or the branch-and-cut algorithms are capable of solving all problem instances within a reasonable time limit, the GA finds a near-optimal solution to every problem in a moderate amount of time.

Dynamic Variable Ordering in CSPs

Abstract: We investigate the dynamic variable ordering (DVO) technique commonly used in conjunction with tree-search algorithms for solving constraint satisfaction problems. We first provide an implementation methodology for adding DVO to an arbitrary tree-search algorithm. Our methodology is applicable to a wide range of algorithms including those that maintain complicated information about the search history, like backmarking. We then investigate the popular reordering heuristic of next instantiating the variable with the minimum remaining values (MRV). We prove some interesting theorems about the MRV heuristic which demonstrate that if one wants to use the MRV heuristic one should use it with forward checking. Finally, we investigate the empirical performance of 12 different algorithms with and without DVO. Our experiments and theoretical results demonstrate that forward checking equipped with dynamic variable ordering is a very good algorithm for solving CSPs.

Degree-constrained multicasting in point-to-point networks

Abstract: Establishing a multicast tree in a point-to-point network of switch nodes, such as a wide-area ATM network, is often modeled as the NP-complete Steiner problem in networks. In this paper, we study algorithms for finding efficient multicast trees in the presence of constraints on the copying ability of the individual switch nodes in the network. We refer to this problem as the degree-constrained multicast tree problem and model it as the degree-constrained Steiner problem in networks. Steiner heuristics for the degree-constrained case are proposed and their simulation results for sparse, point-to-point networks are presented. The results are compared with respect to their quality of solution, cost (running time), and the number of test cases for which no solution could be found. The results of our research indicate that efficient multicast frees can be found in large, sparse networks with small multicast groups even with limited multicast capability in the individual switches. Some of the Steiner heuristics tested yielded degree-constrained multicast trees within 5% of the best heuristic solution found in most of the cases. Even when the fanout of each switch node was restricted to 2, the heuristics we used were able to generate efficient multicast trees in almost all our test networks. Surprisingly few test networks were unsolvable. In those cases where no solution was found by a heuristic, backtracking solved many of the remaining cases. Among the heuristics we used, degree-constrained versions of simple path-distance heuristics such as SPH and SPH-R provided the best tradeoffs between quality of solution and cost.

An improved spectral bisection algorithm and its application to dynamic load balancing

Abstract: The efficient parallel execution of grid-oriented scientific calculations requires a partitioning of the grid that minimises both load imbalance and interprocessor communication. For unstructured static grids, good partitions are obtained with the recursive spectral bisection heuristic, applied to the interdependency graph of the grid. We will describe an alternative spectral bisection algorithm that yields better partitions than the standard algorithm, especially for interdependency graphs with a large variation in the weights of the edges. We will further describe how even in case of dynamically changing grids, grid-oriented problems can be formulated as graph partitioning problems for the purpose of load balancing. We will then partition these dynamically changing grids with the alternative spectral algorithm.

Artificial Planning Experience by Means of a Heuristic Cell-Space Model: Simulating International Migration in the Urban Process:

Abstract: We suggest considering the city as a complex, open, and thus self-organized system, and describing it by means of a cell-space model. A central property of self-organizing systems is that they are not controllable—not by individuals, nor by economic, political, and planning institutions. The city, in this respect, is complex and untamable. Inability to recognize and accept this property is one of the reasons for the difficulties and problems of modernist town planning. The theory and model we present are built to describe the urban process as a historical one in which, given identical initial conditions, each simulation run is unique and never fully repeats itself. From the point of view of urban policy and planning, our heuristic model can guide decisionmakers by answering the following question: ‘given the initial conditions of an inflow of new immigrants (that is, from the ex-USSR), what possible urban scenarios can result, and what are their global structural properties?’.

On the Bounded-Skew Clock and Steiner Routing Problems

Abstract: We study theminimum-cost bounded-skewrouting tree (BST) problem under the linear delay model. This problem captures several engineering tradeoffs in the design of routing topologies with controlled skew. We propose three tradeoff heuristics. (1) For a fixed topology Extended-DME (Ex-DME) extends the DME algorithm for exact zero-skew trees via the concept of a merging region. (2) For arbitrary topology and arbitrary embedding, Extended Greedy-DME (ExG-DME) very closely matches the best known heuristics for the zero-skewcase,and for the infinite-skewcase (i.e., the Steiner minimal tree problem). (3) For arbitrary topology and single-layer (planar) embedding, the Extended Planar-DME (ExP-DME) algorithm exactly matches the best known heuristic for zero-skewplanar routing, and closely approaches the best known performance for the infinite-skewcase. Ourwork provides unifications of the clock routing and Steiner tree heuristic literatures and gives smooth cost-skew tradeoff that enable good engineering solutions.

Methods of graph searching for border detection in image sequences with applications to cardiac magnetic resonance imaging

Abstract: Automated border detection using graph searching principles has been shown useful for many biomedical imaging applications. Unfortunately, in an often unpredictable subset of images, automated border detection methods may fail. Most current edge detection methods fail to take into account the added information available in a temporal or spatial sequence of images that are commonly available in biomedical image applications. To utilize this information the authors extended their previously reported single frame graph searching method to include data from a sequence. The authors' method transforms the three-dimensional surface definition problem in a sequence of images into a two-dimensional problem so that traditional graph searching algorithms may be used. Additionally, the authors developed a more efficient method of searching the three-dimensional data set using heuristic search techniques which vastly improve execution time by relaxing the optimality criteria. The authors have applied both methods to detect myocardial borders in computer simulated images as well as in short-axis magnetic resonance images of the human heart. Preliminary results show that the new multiple image methods may be more robust in certain circumstances when compared to a single frame method and that the heuristic search techniques may reduce analysis times without compromising robustness. >

The finite horizon nonstationary stochastic inventory problem: near-myopic bounds, heuristics, testing

Abstract: Nonstationary stochastic periodic review inventory problems with proportional costs occur in a number of industrial settings with seasonal patterns, trends, business cycles, and limited life items. Myopic policies for such problems order as if the salvage value in the current period for ending inventory were the full purchase price, so that information about the future would not be needed. They have been shown in the literature to be optimal when demand "is increasing over time," and to provide upper bounds for the stationary finite horizon problem and in some other situations. Some results are also known, given special salvaging assumptions, about lower bounds on the optimal policy which are near-myopic. Here analogous but stronger bounds are derived for the general finite horizon problem, without such special assumptions. The best upper bound is an extension of the heuristic used by industry for some years for end of season EOS problems; the lower bound is an extension of earlier analytic methods. Four heuristics were tested against the optimal obtained by stochastic dynamic programming for 969 problems. The simplest heuristic is the myopic heuristic itself: it is good especially for moderately varying problems without heavy end of season salvage costs and averages only 2.75% in cost over the optimal. However, the best of the heuristics exceeds the optimal in cost by an average of only 0.02%, at about 0.5% of the computational cost of dynamic programming.

Optimal Asset Allocation using Adaptive Dynamic Programming

Abstract: In recent years, the interest of investors has shifted to computerized asset allocation (portfolio management) to exploit the growing dynamics of the capital markets. In this paper, asset allocation is formalized as a Markovian Decision Problem which can be optimized by applying dynamic programming or reinforcement learning based algorithms. Using an artificial exchange rate, the asset allocation strategy optimized with reinforcement learning (Q-Learning) is shown to be equivalent to a policy computed by dynamic programming. The approach is then tested on the task to invest liquid capital in the German stock market. Here, neural networks are used as value function approximators. The resulting asset allocation strategy is superior to a heuristic benchmark policy. This is a further example which demonstrates the applicability of neural network based reinforcement learning to a problem setting with a high dimensional state space.

A Branch-and-Bound Approach for a Two-machine Flowshop Scheduling Problem

Abstract: In this paper, we present a branch-and-bound approach for solving a two-machine flow shop scheduling problem, in which the objective is to minimize a weighted combination of job flowtime and schedule makespan. Experimental results show that the algorithm works very well for certain special cases and moderately well for others. In fact, it is able to produce optimal schedules for 500-job problems in which the second machine dominates the first machine. It is also shown that the algorithm developed to provide an upper bound for the branch-and-bound is optimal when processing times for jobs are the same on both machines. The primary reason for developing the branch-and-bound approach is that its results can be used to guide other heuristic techniques, such as simulated annealing, tabu search and genetic algorithms, in their search for optimal solutions for larger problems.

Branch predictor using multiple prediction heuristics and a heuristic identifier in the branch instruction

Abstract: In a computer program, a branch instruction selects a prediction heuristic from a plurality of prediction heuristics for predicting whether the branch will be taken during execution of the program by a computer. A current pattern comprises a number of consecutive identical branch decisions for the instruction. A prior pattern comprises a number of consecutive identical prior branch decisions for the instruction, the prior branch decisions occurring prior to the branch decisions comprised by the current pattern. The selected prediction heuristic generates a branch prediction using the current pattern and the prior pattern. The selected prediction heuristic is identified by adding profiling instructions to the program to compute history information for the branch instruction. The profiling instructions input the branch history information to a plurality of prediction heuristics, and each prediction heuristic outputs a prediction of whether the branch instruction will be taken. The program is executed with a sample data set, and the output of each prediction heuristic is compared to the branch decision for the instruction to identify which heuristic most accurately predicts the branch decision for the branch instruction.

Exact and approximate algorithms for the index selection problem in physical database design

Abstract: The index selection problem (ISP) is an important optimization problem in the physical design of databases. The aim of this paper is to show that ISP, although NP-hard, can in practice be solved effectively through well-designed algorithms. We formulate ISP as a 0-1 integer linear program and describe an exact branch-and-bound algorithm based on the linear programming relaxation of the model. The performance of the algorithm is enhanced by means of procedures to reduce the size of the candidate index set. We also describe heuristic algorithms based on the solution of a suitably defined knapsack subproblem and on Lagrangian decomposition. Finally, computational results on several classes of test problems are given. We report the exact solution of large-scale ISP instances involving several hundred indexes and queries. We also evaluate one of the heuristic algorithms we propose on very large-scale instances involving several thousand indexes and queries and show that it consistently produces very tight approximate (and sometimes provably optimal) solutions. Finally, we discuss possible extensions and future directions of research.

A Multiple-rule Heuristic for Assembly Line Balancing

Abstract: This paper introduces a four-rule heuristic method for production/assembly line balancing which seeks to minimize the number of workstations for a given cycle time. To evaluate its performance, the proposed method was compared with 15 other heuristic methods ranging in complexity from random assignment of work elements to Hoffmann's enumeration procedure. The results, based on both randomly generated problems and problems taken from the literature, indicate that the proposed heuristic outperformed other procedures. Further, the suggested method was able to find the optimal solution for 57 (85%) of the 67 literature problems.