Showing papers on "Heuristic (computer science) published in 1977"

Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane

Abstract: We consider partitioning algorithms for the approximate solution of large instances of the traveling-salesman problem in the plane. These algorithms subdivide the set of cities into small groups, construct an optimum tour through each group, and then patch the subtours together to form a tour through all the cities. If the number of cities in the problem is n, and the number of cities in each group is t, then the worst-case error is $O\sqrt{n/t}$ . If the cities are randomly distributed, then the relative error is Ot-1/2 with probability one. Hybrid schemes are suggested, in which partitioning is used in conjunction with existing heuristic algorithms. These hybrid schemes may be expected to give near-optimum solutions to problems with thousands of cities.

On the Topological Design of Distributed Computer Networks

Abstract: The problem of data transmission in a network environment involves the design of a communication subnetwork. Recently, significant progress has been made in this technology, and in this article we survey the modeling, analysis, and design of such computercommunication networks. Most of the design methodology presented has been developed with the packet-switched Advanced Research Projects Agency Network (ARPANET) in mind, although the principles extend to more general networks. We state the general design problem, decompose it into simpler subproblems, discuss the solutions to these subproblems, and then suggest a heuristic topological design procedure as a solution to the original problem.

Large-Scale Network Topological Optimization

Abstract: A cost-effective structure for a large network is a multilevel hierarchy consisting of a backbone network and a family of local access networks. The backbone network is generally a distributed network, while the local access networks are typically centralized systems. In special cases, the network may consist primarily of either centralized or distributed portions. This paper discusses topological design problems for such systems, including the concentrator location problem, the terminal assignment problem, the terminal layout problem (the constrained minimum spanning tree problem), the distributed network topological layout problem, and the backbone node location problem. Recent algorithm research, including exact and heuristic problem solutions, are described and computational experience is given. Finally, open problems in large-scale topological design are reported.

An efficient heuristic cluster algorithm for tearing large-scale networks

Abstract: An efficient heuristic algorithm for solving a cluster problem associated with the tearing of an undirected graph is presented via the concept of a contour tableau. The required computation time is shown to be bounded by \theta (nb) , where n and b are the number of nodes and branches of the input graph, respectively. Experimental results show that our algorithm is highly efficient and yields near optimal solutions.

An Effective Heuristic for the M-Tour Traveling Salesman Problem with Some Side Conditions

Abstract: This note presents a heuristic for determining very good solutions for the symmetric M-tour traveling salesman problem with some side conditions. These side conditions pertain to load, distance and time, or sequencing restrictions. The heuristic is an extension of the highly successful one of Lin and Kernighan for the single traveling salesman problem. Computational experience with widely tested vehicle dispatch problems indicates that the proposed heuristic consistently yields better solutions than existing heuristics that have appeared in the literature. Run times grow approximately as N2 3, where N is the number of cities. The heuristic is generally slower than the modified SWEEP heuristic except on problems having a large number of points per route. THIS NOTE presents a heuristic algorithm that generates very good solutions to the symmetric M-tour traveling salesman problem with some side conditions. The specific problem is: Given an n by n symmetric matrix of distances between n cities, m salesmen, and a "load" associated with each city, find M tours of minimum total length that leave a depot, visit each city only once, return to the depot, and satisfy certain side conditions. These side conditions pertain to an upper bound on the total load or distance associated with each tour. We also consider time or sequencing restrictions in which individual cities may have due dates or interval constraints requiring that they be visited only during certain time intervals. The above node routing problem is a generalization of the well-known vehicle dispatch problem [9]. Exact optimization techniques exist [4, 17] for vehicle dispatch problems but are severely limited by the size of the problem that can be solved. Good solutions to this class of combinatorial

Technical Note—An Effective Heuristic for the M-Tour Traveling Salesman Problem with Some Side Conditions

Abstract: This note presents a heuristic for determining very good solutions for the symmetric M-tour traveling salesman problem with some side conditions. These side conditions' pertain to load, distance and time, or sequencing restrictions. The heuristic is an extension of the highly successful one of Lin and Kernighan for the single traveling salesman problem. Computational experience with widely tested vehicle dispatch problems indicates that the proposed heuristic consistently yields better solutions than existing heuristics that have appeared in the literature. Run times grow approximately as N2.3, where N is the number of cities. The heuristic is generally slower than the modified SWEEP heuristic except on problems having a large number of points per route.

A Hierarchical Approach to the Control of a Prosthetic Arm

Abstract: A hierarchical method combining analytical techniques from control theory and heuristic techniques from artificial intelligence is presented and applied to the decentralized control of a prosthetic arm. The dynamic model of the arm is derived, and two complementary performance criteria are suggested for the kinematic and the dynamic evaluation for the system response. The "principle of minimum interaction" is used to decompose the prosthetic system into seven subsystems, one per mechanical degree of freedom. A "suboptimal" control structure for nonlinear systems is proposed in conjunction with a performance adaptive self-organizing control algorithm. Syntactic pattern classification is used for the dynamic coordination of the subsystems. The syntax of the man-machine commands is also examined as part of the function of highest level of the hierarchy, the organizer.

Network Design: An Algorithm for the Access Facility Location Problem

Abstract: In any network where a large number of widely dispersed "users" share a limited number of "resources," the strategy for access will play a large part in determining the cost and performance of the network. In this paper we consider a topological design aspect of the access problem. In particular, we consider the problem of locating "access facilities," or concentration points, to obtain an economic connection of users to resources. The problem is formulated as the locating of generic access facilities (GAF's) to obtain an economic connection of nodes (users) to a resource connection point (RESCOP). The nodes may be connected through multipoint lines, but with a constraint on the number of nodes which may share a single line. The GAF's are constrained in capacity, expressed as the number of nodes they can support, and have a cost associated with them. The basic solution technique presented is a heuristic algorithm characterized by the following four steps. 1) Simplify the problem to a point-to-point problem by replacing clusters of nodes by single "center-of-mass" (COM) nodes. 2) Partition the reduced set of COM nodes by applying an Add algorithm, resulting in one of the COM nodes selected as a GAF site. 3) Select one of the original nodes as a real GAF site in each partition by examining the original nodes closest to the COM node selected in the Add algorithm, and selecting the best. 4) Apply a line-layout algorithm to each partition, with its selected GAF site serving as the central node.

An Effective Subgradient Procedure for Minimal Cost Multicommodity Flow Problems

Abstract: This paper presents a heuristic technique for obtaining good solutions to large multicommodity network flow problems. The general approach is to allocate the arc capacities among the individual commodities and hence decompose the problem into a set of one-commodity problems. The one-commodity problems are solved and the combined solution is compared to a lower bound. If the solution is within an acceptable deviation from the lower bound, the procedure terminates. Otherwise, the arc capacities are reallocated and the subprograms are resolved. The reallocation is based on a subgradient optimization approach. Hence, the heuristic technique involves no matrix operations which may lead to round-off errors, the storage requirements are modest, and almost all operations are carried out directly on one-commodity networks. The technique has been coded and the initial computational experience is encouraging.

A general packing algorithm for multidimensional resource requirements

Abstract: Many problems in resource allocations, memory allocation, and distributed computer system design can be formulated as problems of packing variablesized items into fixed-sized containers in order to minimize the total number of containers used. In this paper, a generalized packing algorithm that encompasses many well-known heuristic packing algorithms is proposed. Simulation results on this generalized packing algorithm are described, and their implications are discussed. The objective of this paper is to investigate the performance of various heuristic packing algorithms within a general framework, to obtain numerical estimates on their efficiency, and to provide guidelines on the use of these algorithms.

A Discrete-Convex Programming Approach to the Simultaneous Optimization of Land Use and Transportation

Abstract: Three design problems are discussed in this article. First, it is shown that the network design problem with congestion reduces to an all-or nothing traffic assignment problem under some assumptions on the congestion function and the investment cost function. Second, the land use design problem is formulated as an extension of the Koopmans-Beckmann problem and a heuristic is proposed to solve this problem. Third, it is shown that the seemingly more complex problem of designing jointly a land-use plan and a transportation network reduces to a pure land-use design problem. All that is needed to solve the joint optimization problem is a shortest path algorithm and a heuristic to solve the land use design problem. Computational experience is reported for each algorithm.

Discrete link capacity and priority assignments in communication networks

Abstract: This paper deals with the problem of discrete link capacity assignment in store-and-forward packet switching communication networks. Our problem formulation calls for minimizing the network cost while satisfying all the average packet delay constraints specified for different classes of packets. Heuristic algorithms which give near-optimal solutions of the problem are developed. We first describe a discrete link capacity assignment algorithm for networks with arbitrarily defined classes of packets having individual delay constraints. The problem of priority assignment on different classes of packets is then investigated, and an algorithm is developed which assigns suboptimal priorities on classes of packets based on parameters such as delay requirement, path length, packet length, and packet rate. These two algorithms for capacity assignment and priority assignment are combined and tested over a number of examples. It is found that a substantial reduction on network cost can be achieved by the use of a simple priority queuing discipline.

Solving Large Zero-One Knapsack Problems.

Abstract: : An algorithm for the 0-1 knapsack problem (KP) is described which relies mainly on three new ideas. The first one is to focus on 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 (LKP), the associated linear program. 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. Finally, the third new feature is a simple-minded heuristic whose accracy under certain conditions grows exponentially with the problem size. Computational experience with an algorithm based on the above ideas, on 200 randomly generated test problems with 1,000-10,000 variables and with coefficients ranging from between 10-100 to be between 10-10,000, indicates that for such problems the computational effort grows linearly with the number of variables and logarithmically with the range of coefficients. Total time for the 200 problems was 160 UNIVAC 1108 seconds, and the maximum time for any single problem was 3 seconds.

The Optimal Interconnection of Circuit Modules in Microprocessor and Digital System Design

Abstract: This paper studies the problem of interconnecting circuit modules in microprocessor and digital system design. This problem is ever-present and has generally been handled in a heuristic manner.

Note—Plant Layout: Computers Versus Humans

Abstract: This work offers a critique of the methodology used by Scriabin and Vergin [Scriabin, Michael, Roger C. Vergin. 1975. Comparison of computer algorithms and visual based methods for plant layout. Management Sci. 22 (2, October) 172–181] in their study of computer algorithms versus humans in designing plant layouts. It attempts to show that Scriabin's and Vergin's experiments do not provide a useful comparison of computers and humans, and to point out several experimental procedures that would make comparisons of heuristic computer algorithms and humans more valid.

A two-dimensional trim-loss problem with sequencing constraints

Abstract: A two-dimensional trim-loss problem is considered in which the cutting is two-stage but there are constraints on the sequencing of the cutting of orders, A method is developed in which problem reduction is used to generate a set of possible cutting patterns at each step and an heuristic choice made of a pattern from that set The sequences of patterns produced, although slightly sub-optimal as regards trimloss, fully satisfy the sequencing constraints

The ubiquity of discovery: computers and thought lecture

Abstract: As scientists interested in studying the phenomenon of "intelligence", we first choose a view of Man, develop a theory of how intelligent behavior is managed, and construct some models which can test out and refine that, theory The view we choose is that Man is a symbolic information processor The theory is that sophisticated cognitive tasks can be cast as searches or explorations, and that each human possesses (and efficiently accesses) a large body of infoimal uiles of thumb (heinistics) which constrain his search The source of what we colloquially call "intelligence" is seen to be very efficient searching of an a priori immense space Some computational models which incorporate this theory arc described. Among them is AM, a computer program which develops new mathematical concepts and conjectures' involving them, AM is guided in this exploration by a collection of 250 more or less general heuristic rules. The operational nature of such models allows experiments to be performed upon them, experiments which help us test and develop hypotheses about intelligence. One interesting result has been the ubiquity of this kind of heuristic guidance: intelligence permeates everyday problem solving and invention, as well as the kind of problem solving and invention that scientists and artists perform.

A comparison of three problem-solving methods

Abstract: This paper is a comparison of ABSTRIPS, planning (as defined in Newell and Simon, 1972) and GPS. Each of these methods has parameters chat contain heuristic information which is problem dependent. These parameters are used to guide the methods, search and usually cause them to be incomplete in the sense that they cannot solve some problems that have solutions. We show that the parameters of the methods serve the same function in the following sense: Given the parameters for one method we can formulate the parameters for the other two such that all three can solve the same class of problem; i.e. those which have totally ordered solutions. This result is somewhat surprising because the search spaces of the methods are different. The Implications of this result to the efficiency of search Is discussed at some length.

A manual solution procedure for the school bus routing problem

Abstract: In the school bus routing problem a fleet of buses, each with known capacity, must be scheduled to visit stops, collect pupils and transport them to a school. It is assumed that each bus begins its first trip at a unique location termed the 'driver's home'. The problem is to minimise the total cost (in terms of time, distance, or money) incurred in transporting all the pupils to the school. This paper presents a manual heuristic solution procedure for the problem. The method requires the use of a map of the area concerned. It is suitable for use by school planners who are not going to employ a computer (a).

General systems problem solving packages

Abstract: Various approaches to general systems research have been suggested during the last two decades or so. One of the approaches, to which this author has become commiteed since the late 1960's, is oriented toward general systems problem solving. This approach aims at the characterization of systems problems, their classification, and the development of mathematical, computational or heuristic methodological tools for solving the individual classes of systems problems.

Combinatorial analysis of an efficient algorithm for processor and storage allocation

Abstract: A combinatorial problem related to storage allocation is analyzed. The problem falls into a class of NP-complete, one-dimensional bin-packing problems. We propose an iterative approximation algorithm and show that it is superior to an earlier heuristic presented for this problem. The bulk of the paper is devoted to the proof of a worst-case performance bound.

A family of heuristic solution methods for a class of nonlinear programming problems

Abstract: A heuristic algorithm has been developed which is shown to be applicable to any nonlinear programming problem whose variables can be partitioned into two disjoint sets with a corresponding partition of the problem constraints. A number of applications of this heuristic method to specific problem types are discussed and computational results presented. In addition a Markov chain analysis of the performance of the algorithm for the transportation-location problem has been made to indicate why the algorithm performs well in practice. The relationship between problem structure and ease of solution is discussed, based on the results of this analysis.

Simulation as an alternative to linear programming

Abstract: It is commonly accepted that general classes of problems are best solved using particular techniques. For example, critical path scheduling problems can often be formulated for solution by linear programming, but this approach would not recommend itself for cost reasons to the vast majority of those having access to a PERT or CPM heuristic package. Likewise, the classic product mix or blending problem which pervades the end-of-chapter exercises following a discussion of linear programming is assumed to be "best" solved using graphical methods or the Simplex algorithm. Simulation might offer a reasonable alternative solution vehicle in many circumstances like these, yet some operations research analysts tend to consider its use only "when all else fails". That is, simulation is the technique of last resort.

A Computer Simulation Model for Determining Fleet Size and Composition

Abstract: A heterogeneous vehicle fleet is one that is composed of several types of vehicles. The number of each type of vehicle in the fleet is called the fleet’s composition. The problem of determining the best fleet size and composition for an in-house heterogeneous company fleet having a known demand was solved in this paper. A computer model was developed which tied a fleet simulation model to two different search algorithms. One of the search algorithms is a complete factorial nonsequential search and the other is a combination of a partial factorial nonsequential search and a heuristic sequential hill-climbing search. The objective of both searches is to select the fleet size and composition which provides the lowest total vehicle travel costs to the company. Several examples were used to demonstrate the use of the model.

On state estimation for uncertain discrete-time systems

Abstract: A combined detection-estimation scheme for the estimation of the state of a linear discrete-time system with unknown noise covariances is considered. It is a heuristic extension of the standard minimax scheme to the case when multiple bounds on the unknown parameters are available. The convergence of the scheme is discussed and an example is considered for illustration.