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Showing papers on "Heuristic (computer science) published in 1980"


Journal ArticleDOI
TL;DR: An algorithm for the 0-1 knapsack problem (KP), which relies mainly on three new ideas, one of which is a binary search-type procedure for solving LKP which, unlike earlier methods, does not require any ordering of the variables.
Abstract: We describe an algorithm for the 0-1 knapsack problem (KP), which relies mainly on three new ideas. The first one is to focus on what we call the core of the problem, namely, a knapsack problem equivalent to KP, defined on a particular subset of the variables. The size of this core is usually a small fraction of the full problem size, and does not seem to increase with the latter. While the core cannot be identified without solving KP, a satisfactory approximation can be found by solving the associated linear program (LKP). The second new ingredient is a binary search-type procedure for solving LKP which, unlike earlier methods, does not require any ordering of the variables. The computational effort involved in this procedure is linear in the number of variables. Finally, the third new feature is a simple heuristic which under certain conditions finds an optimal solution with a probability that increases with the size of KP. Computational experience with an algorithm based on the above ideas, on several ...

468 citations


Journal ArticleDOI
TL;DR: One of the major conclusions is that it is not difficult to get within 2–3% of optimality using a composite heuristic which requires on the order of n3 computations where n is the number of nodes in the network.
Abstract: There have been a multitude of heuristic algorithms proposed for the solution of large scale traveling salesman problems. Our intent in this paper is to examine some of these well known heuristics, to introduce some new heuristics, and to compare these approximate techniques on the basis of efficiency and accuracy. We emphasize the strengths and weaknesses of each algorithm tested. One of our major conclusions is that it is not difficult to get within 2–3% of optimality using a composite heuristic which requires on the order of n3 computations where n is the number of nodes in the network.

290 citations


Book
01 Nov 1980
TL;DR: In this article, the linear sum assignment problem and the cardinality matching problem are used to solve the Chinese Postman Problem. But the linear Sum Matching Problem is not one of the problems we consider in this paper.
Abstract: 1. The Linear Sum Assignment Problem.- 2. The Linear Bottleneck Assignment Problem.- 3. The Cardinality Matching Problem.- 4. The Sum Matching Problem.- 5. The Bottleneck Matching Problem.- 6. The Chinese Postman Problem.- 7. Quadratic Assignment Problems.- 8. QAP Heuristic 1: The method of increasing degree of freedom.- 9. QAP Heuristic 2: Cutting plane and exchange method.- 10. General Subroutines.

203 citations


Journal ArticleDOI
TL;DR: The heuristic solutions are compared with optimal solutions obtained by branch and bound in numerous randomly generated problems and are found to be optimal in most cases.
Abstract: This paper treats the problem of minimizing the total weighted flow cost plus job-processing cost in a single machine sequencing problem for jobs having processing costs which are linear functions of processing times. The optimal job sequence and processing times are obtainable from the solution of an associated problem of optimal row and column selection in a symmetric matrix. Some sufficient conditions for expediting certain jobs are proved. In order to handle cases in which these conditions fail to complete the solution to the problem a heuristic algorithm with a provable performance bound is developed. The heuristic solutions are compared with optimal solutions obtained by branch and bound in numerous randomly generated problems and are found to be optimal in most cases.

197 citations


Journal ArticleDOI
TL;DR: In this paper, the basic ground rules of worst-case analysis of heuristics are reviewed, and a large variety of the existing types of worstcase results are described in terms of the knapsack problem.
Abstract: The increased focus on heuristics for the approximate solution of integer programs has led to more sophisticated analysis methods for studying their performance. This paper is concerned with the worst-case approach to the analysis of heuristic performance. A worst-case study establishes the maximum deviation from optimality that can occur when a specified heuristic is applied within a given problem class. This is an important piece of information that can be combined with empirical testing and other analyses to provide a more complete evaluation of a heuristic. In this paper the basic ground rules of worst-case analysis of heuristics are reviewed, and a large variety of the existing types of worst-case results are described in terms of the knapsack problem. A selected sample of results for four other problems is given. The paper concludes with a discussion of possibilities for further research.

132 citations


Journal ArticleDOI
TL;DR: This paper defines a heuristic method as a procedure for solving a well-defined mathematical problem by an intuitive approach in which the structure of the problem can be interpreted and exploited intelligently to obtain a reasonable solution.

107 citations


Journal ArticleDOI
TL;DR: An extension of the Lin-Kernighan local search algorithm for the solution of the asymmetric traveling salesman problem is presented and computational results suggest that the heuristic is feasible for fairly large instances.
Abstract: We present an extension of the Lin-Kernighan local search algorithm for the solution of the asymmetric traveling salesman problem. Computational results suggest that our heuristic is feasible for fairly large instances. We also present some theoretical results which guided our design of the heuristic.

103 citations


Journal ArticleDOI
TL;DR: An algorithm, based on the "bounded branch and bound" integer programming technique, has been developed to obtain the optimal solution of the model, and it is found to be more efficient than several existing general nonlinear integer programming algorithms.
Abstract: In this paper a model is developed for the optimization of distributed information systems. Compared with the previous work in this area, the model is more complete, since it considers simultaneously the distribution of processing power, the allocation of programs and databases, and the assignment of communication line capacities. It also considers the return flow of information, as well as the dependencies between programs and databases. In addition, an algorithm, based on the "bounded branch and bound" integer programming technique, has been developed to obtain the optimal solution of the model. The algorithm is more efficient than several existing general nonlinear integer programming algorithms. Also, it avoids some of the disadvantages of heuristic and decomposition algorithms which are used widely in the optimization of computer networks and distributed databases. The algorithm has been implemented in Fortran, and the computation times of the algorithm for several test problems have been found very reasonable.

90 citations


Book ChapterDOI
C. N. Potts1
01 Jan 1980
TL;DR: The single machine sequencing problem is considered, in which each job has a processing time and a weight, and there are precedence constraints on the jobs.
Abstract: The single machine sequencing problem is considered, in which each job has a processing time and a weight, and there are precedence constraints on the jobs. The objective is to find a sequence of jobs which minimises the weighted sum of completion times. A new lower bound is derived and used in a branch and bound algorithm. Computational results for up to forty jobs are given.

83 citations


01 Nov 1980
TL;DR: The major result presented in this dissertation is a polynomial time algorithm for a restricted case of the routing problem, which minimizes the area of a rectangle circumscribing the component and the wire paths.
Abstract: In this thesis, the problem of designing the layout of integrated circuits is examined. The layout of an integrated circuit specifies the position of the chip of functional components and wires interconnecting the components. We use a general model under which components are represented by rectangles, and wires are represented by lines. This model can be applied to circuit components defined at any level of complexity, from a transistor to a programmable logic array (PLA). We focus on the standard decomposition of the layout problem into a placement problem and a routing problem. We examine problems encountered in layout design from the point of view of complexity theory. The general layout problem under our model is shown to be NP-complete. In addition, two problems encountered in a restricted version of the routing problem --channel routing--are shown to be NP-complete. The analysis of heuristic algorithms for NP-complete problems is discussed, and the analysis of one common algorithm is presented. The major result presented in this dissertation is a polynomial time algorithm for a restricted case of the routing problem. Given one rectangular component with terminals on its boundary, and pairs of terminals to be connected, the algorithm will find a two-layer channel routing which minimizes the area of a rectangle circumscribing the component and the wire paths. Each terminal can appear in only one pair of terminals to be connected, and the rectangle used to determine the area must have its boundaries parallel to those of the component. If any of the conditions of the problem are removed, the algorithm is no longer guaranteed to find the optimal solution.

83 citations


Journal ArticleDOI
TL;DR: A class of heuristic algorithms are developed for the solution of a centralized telecommunication network comprised of multipoint lines given a set of terminal locations, traffic requirements, and a common central site by imbedding existing heuristics inside a loop where small, carefully chosen sets of arcs are alternately forced in and out of the solution.
Abstract: We consider the problem of designing a centralized telecommunication network comprised of multipoint lines given a set of terminal locations, traffic requirements, and a common central site. The optimal solution to this problem is a capacitated minimal spanning tree. We develop a class of heuristic algorithms for the solution of this problem by imbedding existing heuristics, referred to as first-order greedy algorithms, inside a loop where small, carefully chosen sets of arcs are alternately forced in and out of the solution. The resultant procedure is shown to be superior to existing techniques, producing solutions typically 2 percent better, while requiring only a modest amount of additional computer time.

Book ChapterDOI
01 Jan 1980
TL;DR: Computational experience is reported on with the branch-and-bound algorithm proposed there for determining a track for a single searcher while searching for a moving target in discrete space and time.
Abstract: In a recent paper (Stewart [19 79]), we have introduced the problem of search for a moving target when there are practical constraints on the rate of movement of the searcher and have suggested approaches to a solution. In the present paper, we report, in particular, on computational experience with the branch-and-bound algorithm proposed there for determining a track for a single searcher while searching for a moving target in discrete space and time. Although the method was developed for a single searcher, a heuristic adaptation was also suggested for use when there are multiple searchers.

Journal ArticleDOI
TL;DR: An interactice, computer based procedure for solving the variant of the vehicle loading problem encountered when loading containers and pallets into an aircraft is described.

Journal ArticleDOI
TL;DR: The process draws upon the problem solver's disease centered and data centered knowledge and can be made more effective through the use of various heuristic rules and strategies that the physician develops with increasing expertise.

Journal ArticleDOI
Tamotsu Hayase1, Hiroshi Motoda1
TL;DR: It has been demonstrated that the proposed heuristic algorithm is capable of finding a feasible rod pattern, even starting from an all-rods-out pattern, in the method of approximation programming (MAP).
Abstract: OPROD, a computer code for automatic generation of control rod programming that has successfully been applied to an older boiling water reactor (BWR), has experienced some difficulties when applied to a BWR of larger power density and stronger heterogeneity. To improve the performance, a heuristic algorithm that is derived from accumulated experience has been introduced to search for a feasible rod pattern that satisfies all constraints. Application of this algorithm to an initial cycle of an 800-MW(e) BWR of high heterogeneity has been very successful. It has been demonstrated that the proposed algorithm is capable of finding a feasible rod pattern, even starting from an all-rods-out pattern. Some improvement was also made in the method of approximation programming (MAP) algorithm. The temporal constraint relaxation method is shown to be effective in finding an optimal control rod pattern in MAP starting from a guess pattern that is not feasible.

Journal ArticleDOI
TL;DR: In this paper, the authors compared several existing methods for identifying GUB structure and developed bounds for the maximum size of GUB sets in order to evaluate the effectiveness of the heuristic algorithms.
Abstract: To solve contemporary large-scale linear, integer and mixed integer programming problems, it is often necessary to exploit intrinsic special structure in the model at hand. One commonly used technique is to identify and then to exploit in a basis factorization algorithm a generalized upper bound GUB structure. This report compares several existing methods for identifying GUB structure. Computer programs have been written to permit comparison of computational efficiency. The GUB programs have been incorporated in an existing optimization system of advanced design and have been tested on a variety of large-scale real-life optimization problems. The identification of GUB sets of maximum size is shown to be among the class of NP-complete problems; these problems are widely conjectured to be intractable in that no polynomial-time algorithm has been demonstrated for solving them. All the methods discussed in this report are polynomial-time heuristic algorithms that attempt to find, but do not guarantee, GUB sets of maximum size. Bounds for the maximum size of GUB sets are developed in order to evaluate the effectiveness of the heuristic algorithms.

Journal ArticleDOI
TL;DR: In this study a heuristic algorithm is proposed dealing with the assignment to individual days of the weekly requirements of the time-table requirements, using five British schools as examples.

Journal ArticleDOI
TL;DR: Two heuristic solution methods and a branch and bound algorithm for solving single source transportation problems and Computational experience with the solution of randomly generated problems having up to 40,000 integer variables are reported.

Journal ArticleDOI
TL;DR: A heuristic algorithm developed to schedule a group of individuals such that every person performs each of the different activities they desire at some point during the time-frame of the schedule and the difference between the exogenously given number of people desired at each available location-activity-period position and those allocated to these positions is minimized.
Abstract: This paper describes a heuristic algorithm developed to schedule a group of individuals such that every person performs each of the different activities they desire at some point during the time-frame of the schedule and the difference between the exogenously given number of people desired at each available location-activity-period position and those allocated to these positions is minimized. The contribution of the present work is in the formulation of the problem, and the resulting ease with which good solutions to large-scale problems can be generated, rather than in the mechanics of the algorithm itself. The mathematic formulation of the scheduling problem is presented first, and subsequently, the solution strategy is elaborated. Experimental results on some reasonably large problems are also presented.

Journal ArticleDOI
TL;DR: In this article, two versions of a heuristic algorithm are presented to solve a model of the capital-budgeting problem in a decentralized multidivision firm involving no more than two exchanges of information between headquarters and divisions.
Abstract: This paper presents two versions of a heuristic algorithm to solve a model of the capital-budgeting problem in a decentralized multidivision firm involving no more than two exchanges of information between headquarters and divisions. Headquarters makes an allocation of funds to each division based upon its cash demand and its potential growth rate. Each division determines which projects to accept. Then, an additional iteration is performed to define the solution. More than one thousand examples were simulated resulting in an average relative error of less than one percent.

01 Sep 1980
TL;DR: The problem of identifying the maximum size embedded pure network rows within the coefficient matrix of such models is shown to be among the class of NP-hard problems, therefore, the polynomially-bounded algorithms presented here do not guarantee network sets of maximum size.
Abstract: : The solution of contemporary large-scale linear, integer, and mixed integer programming problems is often facilitated by the exploitation of intrinsic special structure in the model. This paper deals with the problem of identifying embedded pure network rows within the coefficient matrix of such models and presents two heuristic algorithms for identifying such structure. The problem of identifying the maximum size embedded pure network is shown to be among the class of NP-hard problems, therefore, the polynomially-bounded algorithms presented here do not guarantee network sets of maximum size. However, upper bounds on the size of the maximum network set are developed and used to evalaute the algorithms. Finally, the algorithms were tested with a number of large-scale, real-world models and the results of these benchmark runs are presented. (Author)

Journal ArticleDOI
Reeves1, Bruner
TL;DR: A general scheme is described for generating efficient programs to implement arbitrary functions on bit-serial-arithmetic processors, based on logic design methodology and involves designing a logic network to realize a desired function.
Abstract: Parallel processors with bit-serial processing elements (PE's) usually implement arithmetic functions by a sequence of word-level arithmetic operations; however, basic operations must be specified at the bit level. In this correspondence the possibility of more efficiently implementing a function with a special tailored sequence of bit-serial operations is considered. A general scheme is described for generating efficient programs to implement arbitrary functions on bit-serial-arithmetic processors. This scheme is based on logic design methodology and involves designing a logic network to realize a desired function. The parallel processor is then used to efficiently simulate a set of these networks. Heuristic design algorithms are used to generate the logic networks; several algorithms are described and compared with some benchmark functions. Several efficient PE designs are described and analyzed.



01 Jan 1980
TL;DR: This paper deals with performance evaluation of several heuristic algorithms and keeps track of each algorithms performance for varying assumptions such as the shape of the demand function and the cost-capacity characteristics for individual projects, to establish a performance profile for each algorithm.
Abstract: One of the problems faced by planners when designed an expansion plan for water resources systems is selecting the sequence of projects that satisfies a given demand at minimum cost, some prescribed time into the future. This problem is indeed closely related to what is generally known as the capacity expansion problem although unique local conditions at each project site result in a somewhat different problem formulation. To ensure an optimal solution to the project sequencing problem the usual approach has been to use dynamic programming techniques, although it suffers from the commonly known limits on problem size due to the associated excessive computational requirements. The need of planners in search of a practical screening method useful at all stages in the planning process, involving possibly a large number of projects, has led to the introduction of several heuristic algorithms. While such algorithms do not guarantee an optimal solution, their usefulness is based on the assumption that the solution obtained is close enough to being optimal for some practical purposes. Little has, however, been written about their performance in general. This paper deals with performance evaluation of several such algorithms. The algorithms are tested by creating a number of sequencing problems which are in turn solved by each of them as well as by dynamic programming. By keeping track of each algorithms performance for varying assumptions such as the shape of the demand function and the cost-capacity characteristics for individual projects, a performance profile is established for each algorithm. Such performance measure should be helpful when selecting the appropriate solution procedure to a project-sequencing problem for instance in a practical setting.

Journal ArticleDOI
TL;DR: It is shown that nonserial problems can be solved by the use of dynamic programming incorporating algorithms based on heuristics, and two such algorithms are developed using artificial intelligence concepts of estimating the likelihood of future results on present decisions.
Abstract: Dynamic programming is an extremely powerful optimization approach used for the solution of problems which can be formulated to exhibit a serial stage-state structure. However, many design problems are not serial but have highly connected interdependent structures. Existing methods, for the solution of nonserial problems require the problem to possess a certain structure or limit the size of the problem due to storage and computational time requirements. The aim of this paper is to show that nonserial problems can be solved by the use of dynamic programming incorporating algorithms based on heuristics. Two such algorithms are developed using artificial intelligence concepts of estimating the likelihood of future results on present decisions. The algorithms are explained in detail, A small problem is solved and the results of testing them on large scale problems are given. The method is then used to solve a problem drawn from the literature.

Journal ArticleDOI
TL;DR: In this paper, a model of the feeder route for which a good allocation of feeder pairs is derived using a combination of heuristic and mathematical programming techniques is presented, which is flexible enough to handle allocation problems on routes with pair gain systems and conventional resistance design cable routes with multiple paths from some customers to the central office.
Abstract: Loop feeder allocation is the process of planning for economic use of the spare capacity in a feeder route, which supplies a central office. This paper presents a model of the feeder route for which a good allocation of feeder pairs is derived using a combination of heuristic and mathematical programming techniques. The model of the route reflects the factors relevant to making allocation decisions: subscriber growth, operating costs due to subscriber movement, transmission requirements, relief, and rearrangement costs. The model is flexible enough to handle allocation problems on routes with pair gain systems as well as conventional resistance design cable routes with multiple paths from some customers to the central office. An iterative separable linear programming algorithm is used to find the feasible allocation with the minimum expected operating expense. The need to reserve existing pairs in the feeder route to connect to the pairs placed in future relief jobs requires the solution of a multi-time period model. To save on computation time, a heuristic algorithm is used to solve the dynamic problem approximately.

Journal ArticleDOI
TL;DR: Three new algorithms and modifications based on the same basic approach will resolve all of the technical difficulties remaining in the development of algorithms for producing cutting schedules for the paper and board industry.

Book ChapterDOI
01 Jan 1980
TL;DR: Adaptive control of a class of distributed-parameter systems is considered using the heuristic approach of separating identification and optimization, and features of the complete parameter-adaptive procedure are compared with results for state- Adaptive algorithms known from literature.
Abstract: Adaptive control of a class of distributed-parameter systems is considered using the heuristic approach of separating identification and optimization. Both subproblems are solved using known optimization results. — In identification, the problem of cyclic identification is treated with respect to the choice of a suitable error-weighting function. — Features of the complete parameter-adaptive procedure are compared with results for state-adaptive algorithms known from literature. — As an application, adaptive control of a bubble-column fermenter producing single-cell protein is discussed in detail.