Showing papers on "Heuristic published in 1976"
01 Feb 1976
TL;DR: An O(n3) heuristic algorithm is described for solving d-city travelling salesman problems (TSP) whose cost matrix satisfies the triangularity condition and a worst-case analysis of this heuristic shows that the ratio of the answer obtained to the optimum TSP solution is strictly less than 3/2.
Abstract: : An O(n sup 3) heuristic algorithm is described for solving n-city travelling salesman problems (TSP) whose cost matrix satisfies the triangularity condition. The algorithm involves as substeps the computation of a shortest spanning tree of the graph G defining the TSP, and the finding of a minimum cost perfect matching of a certain induced subgraph of G. A worst-case analysis of this heuristic shows that the ratio of the answer obtained to the optimum TSP solution is strictly less than 3/2. This represents a 50% reduction over the value 2 which was the previously best known such ratio for the performance of other polynomial-growth algorithms for the TSP.
1,346 citations
TL;DR: The quadratic assignment paradigm developed in operations research is discussed as a general approach to data analysis tasks characterized by the use of proximity matrices in this article, and an extensive set of numerical examples are given illustrating the application of the search procedure to hierarchical clustering, the identification of homogeneous object subsets, linear and circular seriation, and a discrete version of multidimensional scaling.
Abstract: The quadratic assignment paradigm developed in operations research is discussed as a general approach to data analysis tasks characterized by the use of proximity matrices. Data analysis problems are first classified as being either static or non-static. The term ‘static’ implies the evaluation of a detailed substantive hypothesis that is posited without the aid of the actual data. Alternatively, the term ‘non-static’ suggests a search for a particular type of relational structure within the obtained proximity matrix and without the statement of a specific conjecture beforehand. Although the static class of problems is directly related to several inference procedures commonly used in classical statistics, the major emphasis in this paper is on applying a general computational heuristic to attack the non-static problem and in using the quadratic assignment orientation to discuss a variety of research tactics of importance in the behavioral sciences and, particularly, in psychology. An extensive set of numerical examples is given illustrating the application of the search procedure to hierarchical clustering, the identification of homogeneous object subsets, linear and circular seriation, and a discrete version of multidimensional scaling.
831 citations
Book•
01 Jan 1976
TL;DR: A program called 'AM', is described which models one aspect of elementary mathematics research: developing new concepts under the guidance of a large body of heuristic rules, containing great powers and great limitations.
Abstract: : A program called 'AM', is described which models one aspect of elementary mathematics research: developing new concepts under the guidance of a large body of heuristic rules. 'Mathematics' is considered as a type of intelligent behavior, not as a finished product. The local heuristics communicate via an agenda mechanism, a global list of tasks for the system to perform and reasons why each task is plausible. A single task might direct AM to define a new concept, or to explore some facet of an existing concept, or to examine some empirical data for regularities, etc. Repeatedly, the program selects from the agenda the task having the best supporting reasons, and then executes it. Each concept is an active, structured knowledge module. A hundred very incomplete modules are initially provided, each one corresponding to an elementary set-theoretic concept (e.g.,union). This provides a definite but immense 'space' which AM begins to explore. AM extends its knowledge base, ultimately rediscovering hundreds of common concepts (e.g., numbers) and theorems (e.g., unique factorization). This approach to plausible inference contains great powers and great limitations.
294 citations
TL;DR: This paper considers the project scheduling problem with multiple constrained resources and shows that the choice of priority rule is important with the parallel method, but with the sampling method, although it does affect the distribution of the sample, the choices of rule are not significant.
Abstract: This paper considers the project scheduling problem with multiple constrained resources. Two classes of heuristic procedure, both making use of priority rules, are discussed: the parallel method, which generates just one schedule; and the sampling method, which generates a set of schedules using probabilistic techniques and selects the best schedule from this sample. An experimental investigation is described in which a set of projects with different characteristics is scheduled by each of these heuristics with a variety of priority rules. The effects of the heuristic method, the project characteristics and the priority rules are assessed. It is shown that the choice of priority rule is important with the parallel method, but with the sampling method, although it does affect the distribution of the sample, the choice of rule is not significant. The sampling method with sample size 100 is shown to produce samples at least 7% better than those generated by the corresponding parallel method, with 99% confidence. Further results are discussed and conclusions are presented.
180 citations
TL;DR: Individual characteristics of multiple-constrained resource, project scheduling problems are examined in an attempt to predict the solution obtainable with heuristic methods.
Abstract: Individual characteristics of multiple-constrained resource, project scheduling problems are examined in an attempt to predict the solution obtainable with heuristic methods Difficulties encountered in performing this type of research are described, and several multiple regression models are developed for predicting heuristic performance Both single and multiple project data are examined, and results reported demonstrate the efficacy of determining beforehand the method used for problem solution
145 citations
TL;DR: Heuristic methods are presented for scheduling telephone traffic exchange operators to meet demand that varies over a 24-hour operating period, both in terms of solution quality and computational efficiency.
Abstract: Heuristic methods are presented for scheduling telephone traffic exchange operators to meet demand that varies over a 24-hour operating period. Two types of heuristics are described 1 for determining the work shift types to be considered in preparing an operator shift schedule and 2 for constructing an operator shift schedule from a given set of work shift types. These heuristics are evaluated both in terms of solution quality and computational efficiency, using actual operating data.
128 citations
TL;DR: An algorithm is introduced where the role of the heuristic scheduling urgency factor is expanded from one of solely determining the order in which activities are considered for scheduling at a given instant, to one of determining the combination of activities to be scheduled at this instant.
Abstract: This paper extends the field of heuristic algorithms for resource constrained scheduling problems in three important areas. First, an algorithm is introduced where the role of the heuristic scheduling urgency factor is expanded from one of solely determining the order in which activities are considered for scheduling at a given instant, to one of determining the combination of activities to be scheduled at this instant. Second, a new hybrid scheduling urgency factor capitalizing on the fact that this algorithm is sensitive to the absolute value rather than relative sequence of the urgency factors is introduced. Finally, a systematic approach to the evaluation of such algorithms is introduced. This includes the identification of relevant problem attributes and the adoption of evaluative concepts such as computational efficiency and analytic and systems effectiveness.
67 citations
TL;DR: In this article, a computer animated film is used to display the object(s) of analysis in a dynamic temporal setting, which can be used as an heuristic device to aid in suggesting hypotheses which later may be tested in the data.
45 citations
29 Mar 1976
TL;DR: An efficient method to solve the file allocation problem for medium-scale networks is proposed, and a near-optimal heuristic is presented, along with computational results.
Abstract: The problem of allocating files in a computer network is a complex combinatorial problem due to the number of integer design parameters involved. These parameters include system cost, number of copies of each file to be stored, and sites at which the copies should be stored. The tradeoffs between these parameters are discussed. The design problem is formulated as an integer programming problem. A branch and bound algorithm is proposed to solve the problem. A linear programming formulation which ignores integer restrictions (and allows a fraction of a file to reside at a site) is shown to yield integer solutions in most cases. In other words integer restrictions are satisfied automatically. A near-optimal heuristic is presented, along with computational results. An efficient method to solve the file allocation problem for medium-scale networks is proposed.
45 citations
TL;DR: It is shown that the existing model structure is overparameterized and can be simplified by modifying some of the original assumptions and recommendations for further simplification in the human operator model structure are made.
42 citations
TL;DR: An analytical model for location of monitor sites based upon maximizing a sum of coverage factors for each source is developed and is shown to be a valuable addition to the methods available to the air quality monitor network designer.
Abstract: The information presented in this paper is directed to those with the responsibility of designing and operating air quality monitoring networks. An analytical model for location of monitor sites based upon maximizing a sum of coverage factors for each source is developed. An heuristic solution method from the facilities location analysis literature is used for solution of the model. Results of an example problem are presented and compared with the monitoring network currently In place. The model is shown to be a valuable addition to the methods available to the air quality monitor network designer. Needs for further research are pointed out.
TL;DR: In this article, a linear integer programming model and heuristic solution procedure to realign sales territories is described. But this model is not suitable for the real-time optimization of sales territories.
Abstract: A recent article described a mathematical programming model and heuristic solution procedure to realign sales territories. This report presents two linear integer programming models for sales terri...
TL;DR: A description of a simple mathematical framework and modeling process which can be used to study a large class of socio-techno-natural systems.
01 Aug 1976
TL;DR: An approach to modeling human driver behavior in single-lane car following which is based on a finite-state decision structure is considered and the heuristic model behavior matches actual car- following performance better during deceleration and constant velocity phases than during acceleration periods.
Abstract: An approach to modeling human driver behavior in single-lane car following which is based on a finite-state decision structure is considered. The specific strategy at each point in the decision tree was obtained from observations of typical driver behavior. The synthesis of the decision logic is based on position and velocity thresholds and four states defined by regions in the phase plane. The performance of the resulting assumed intuitively logical model was compared with actual freeway data. The match of the model to the data was optimized by adapting the model parameters using a modified PARTAN algorithm. The results indicate that the heuristic model behavior matches actual car-following performance better during deceleration and constant velocity phases than during acceleration periods.
TL;DR: By utilizing unique attributes associated with real-life problems and using small incisive modifications it is demonstrated how a heuristic procedure can be significantly improved.
Abstract: The limited ability of schematic procedures, constraints of linear programming techniques, inflexibility of construction methods and inadequacy of dynamic programming approaches to provide acceptable solutions to realistic size layout design problems has led to an ever increasing interest in heuristic procedures. Comparative studies have shown that heuristic procedures can satisfy more desirable qualities in an ‘ideal algorithm’ to a greater extent than competitive techniques. Excessive computational effort, which has been one of the main criticisms levelled against heuristic approaches in the past, proves to be less of a problem in relation to layout design. By utilizing unique attributes associated with real-life problems and using small incisive modifications it is demonstrated how a heuristic procedure can be significantly improved.
TL;DR: In this article, the authors developed a method for choosing advertising media plans for the next T-periods in order to maximize net discounted profits using the discrete maximum principle of Optimal Control Theory.
Abstract: This paper develops a method for choosing advertising media plans for the next T-periods in order to maximize net discounted profits. Using the discrete maximum principle of Optimal Control Theory, it is shown that under certain conditions a T-period media model can be decomposed into a sequence of T one-period models together with the determination of the corresponding carry-over effects using an iterative procedure. The single period models with their objective functions modified to include the carry-over effects can be solved by conventional methods. Although the conditions for decomposition are not always satisfied, the heuristic solution procedure defined by the decomposition approach has been found to give close to optimal solutions in randomly generated test problems. The solutions obtained in these tests are usually better than the corresponding solutions obtained by the Little and Lodish type of heuristic applied to the present model. Finally, the T-period model is specialized to derive a steady-state formulation of an infinite horizon media planning problem.
TL;DR: It can be shown that even in a world governed by this system M nontrivial self-reproduction can be established, thus illuminating what simple combinatorial structures allow for the handling of such logical somewhat difficult phenomenas as self-organization, self- reproduction, etc.
Abstract: An abstract research on self-reproduction from the viewpoint of systems theory is made, investigating the problem of how simple the combinatorial laws of formal systems can be chosen and to still ensure nontrivial self-reproduction. We take as a base the heuristic of the theory of cellular automata in the sense of von Neumann. We operate in a formal, microscopic, submolecular world as our patterns of cells shall represent some kind of artificial molecules. Computation- and construction-universal, self-reproducing systems are regarded as artificial living beings according to the common heuristic. A simple combinatorial system M of only four very simple dynamic laws is introduced and it can be shown that even in a world governed by this system M nontrivial self-reproduction can be established, thus illuminating what simple combinatorial structures allow for the handling of such logical somewhat difficult phenomenas as self-organization, self-reproduction, etc. To receive a model slightly more adapt...
TL;DR: Network structures provide heuristic vehicles by which population models can be de- veloped and modified, and allow explicit incorporation of key processes in the life cycle of the organism being modeled.
Abstract: The well-established methods of network construction and analysis are adapted to the problem of modeling single populations. A major advantage of the resulting approach is that it allows explicit incorporation of key processes in the life cycle of the organism being modeled, with feedback loops providing economy of representation where they are allowed. Thus, network structures provide heuristic vehicles by which population models can be de- veloped and modified. When a model is linear and has parameters that do not vary with time, a characteristic dynamic function can be derived by inspection from a simple transform of the network representation. The zeros of the function can be found (analytically or by commonly available numerical methods) and used directly to deduce the modeled population's dominant growth pattern and its propensity to sustain oscillations. In addition, under certain conditions (i.e., that the network model not contain both time delays and integrators), a straightforward method (partial fraction expansion) is available for deduction of the modeled population's specific responses to a variety of perturbations.
TL;DR: The use of heuristic strategies for searching problem spaces of various types of problem representations is discussed, and geometric analysis provides an intuitive alternative to the algebraic analysis which appears in the literature.
TL;DR: In this article, a simple heuristic argument based on the method of dimensions is used to derive the formula nu =(d+2)/4(d-1), for d or=4, for the correlation length exponent of a scalar field Ising-type model.
Abstract: A simple heuristic argument based on the method of dimensions is used to derive the formula nu =(d+2)/4(d-1), for d or=4, for the correlation length exponent of a scalar field Ising-type model.
TL;DR: A construction approach due to Graves and Whinston produced the best results, both when used to generate starting solutions for the improvement methods and when evaluated on its own merit against the improved methods using other starts.
Abstract: The purpose of this study is to examine the relative efficacy of several promising heuristic approaches to a classic problem of component placement. Four "construction" and nine "improvement" algorithms were chosen for investigation and compared experimentally on a CDC 6400 computer. The improvement methods were selected to test some basic strategies of pairwise-interchanging of components and the construction procedures were chosen primarily to evaluate the effects of the quality of starting solution on the improvement methods. The algorithms were tested on 75 problems generated from the literature and compared with respect to the produced solution quality and CPU run-time requirements. A construction approach due to Graves and Whinston produced the best results, both when used to generate starting solutions for the improvement methods and when evaluated on its own merit against the improvement methods using other starts. Construction approaches have previously been regarded in the the past as relatively inferior techniques.
TL;DR: The alpha beta heuristic has been used extensively as a means for reducing the tree-searching effort in computer game-playing programs as discussed by the authors, and it is well known that if the number of terminal nodes in a tree is N, then under optimal circumstances the alpha-beta heuristic reduces the actual number of nodes examined to about 2N?.
Abstract: The alpha beta heuristic has been used extensively as a means for reducing the tree-searching effort in computer game-playing programs. It is well known that if the number of terminal nodes in a tree is N, then under optimal circumstances the alpha beta heuristic reduces the actual number of nodes examined to about 2N?. This is a substantial reduction in the case that N is on the order of ten thousand to a million. Unfortunately these optimal conditions are equivalent, in the case of game playing, to having immediate knowledge for every position in the tree as to which alternative is the best one; and this amount of foreknowledge would make tree searching unnecessary in the first place! This paper explores quantitively the performance of the alpha beta heuristic under a wide variety of conditions other than the optimal one, including several situations occurring in actual game-playing programs.
TL;DR: In this article, the authors investigate the effects of various modes of presentation of general heuristic processes on students' problem-solving ability and evaluate the effect of this instruction on their ability to solve problems.
Abstract: It was the purpose of this study to investigate the effects of various modes of presentation of general heuristic processes on students' problem-solving ability. It was felt that if students are to become effective problem solvers they must be formally instructed in the established techniques of, and approaches to, problem solving. It was hypothesized that these techniques would both facilitate students' efficiency in solving problems and improve their ability to solve various kinds of problems. This study, then, was an attempt to formally instruct students in a particular heuristic problemsolving process so that awareness and ability could be developed, and subsequently to evaluate the effects of this instruction on their ability to solve problems.
TL;DR: Two heuristic self-organization methods for construction of a non-linear prediction model of river flows have multi-layered structures of the perceptron type and provide the optimally complex non- linear equation of the input-output relation.
Abstract: This paper presents two heuristic self-organization methods for construction of a non-linear prediction model of river flows. The self-organization algorithms have multi-layered structures of the perceptron type and provide the optimally complex non-linear equation of the input-output relation. The algorithms are applied to the river-flow prediction of Karasu JRiver and Katsura River in Japan. The performance of the prediction models by the self-organization methods is compared with that of the hydrological models. The numerical comparison shows that without any hydrological and geographical knowledge the prediction models presented here aro superior to the elaborate hydrological models.
TL;DR: Methods for improving the rate of convergence are presented, and heuristic reasons for this approach are presented along with a simple example which illustrates why such an approach is effective.
Abstract: Gradient-type methods which employ penalty functions typically have difficulties in solving optimal control problems with variable final time. Methods for improving the rate of convergence are presented. The first approach involves simply guaranteeing that the initial iterate final time is less than the optimal final time. Heuristic reasons for this approach are presented along with a simple example which illustrates why such an approach is effective. The second approach involves the use of a two-dimensional search routine, with a final time parameter and the control vector correction length as the parameters. The number of function evaluations is reasonable because of the availability of J(0,0), Ja(0,0), and JT(0,0), where J(a,T) is the two-parameter function to be minimized, and since a recursive quadratic surface fitting procedure is employed. The approach is illustrated on two aerospace trajectory optimization problems.
TL;DR: In this paper, an on-the-shop floor experiment is carried out to determine the price-quality relationship for a number of toiletries and three different and distinct demand curves are obtained.
Abstract: An on-the-shop-floor experiment is carried out to determine the price-quality relationship for a number of toiletries. Three different and distinct demand curves are obtained. A heuristic model to describe these curves is constructed. The implications of this model for the profit-orientated businessman are then analysed.
01 Jul 1976
TL;DR: A heuristic technique is presented for detecting the presence of an unknown signal in noise and estimating its waveshape using the most recent estimate as a template against which new observations are matched.
Abstract: A heuristic technique is presented for detecting the presence of an unknown signal in noise and estimating its waveshape. The heuristic utilizes the most recent estimate of the waveshape as a template against which new observations are matched. If the match is "good," the observation is used to update the estimate, and the procedure is repeated. If the match is "poor," the observation is discarded. It is the decisions of the detector which direct the evolution of the estimate while simultaneously the current estimate directs the detector's performance. The mutual interactions of the estimator/detector are conducted without external supervision and without the benefit of training samples, and thus the system falls into the category of a self-learning decision directed adaptive system.