Showing papers on "Heuristic (computer science) published in 1981"

On the Mapping Problem

Abstract: In array processors it is important to map problem modules onto processors such that modules that communicate with each other lie, as far as possible, on adjacent processors. This mapping problem is formulated in graph theoretic terms and shown to be equivalent, in its most general form, to the graph isomorphism problem. The problem is also very similar to the bandwidth reduction problem for sparse matrices and to the quadratic assignment problem.

A restricted Lagrangean approach to the traveling salesman problem

Abstract: We describe an algorithm for the asymmetric traveling salesman problem (TSP) using a new, restricted Lagrangean relaxation based on the assignment problem (AP). The Lagrange multipliers are constrained so as to guarantee the continued optimality of the initial AP solution, thus eliminating the need for repeatedly solving AP in the process of computing multipliers. We give several polynomially bounded procedures for generating valid inequalities and taking them into the Lagrangean function with a positive multiplier without violating the constraints, so as to strengthen the current lower bound. Upper bounds are generated by a fast tour-building heuristic. When the bound-strengthening techniques are exhausted without matching the upper with the lower bound, we branch by using two different rules, according to the situation: the usual subtour breaking disjunction, and a new disjunction based on conditional bounds. We discuss computational experience on 120 randomly generated asymmetric TSP's with up to 325 cities, the maximum time used for any single problem being 82 seconds. This is a considerable improvement upon earlier methods. Though the algorithm discussed here is for the asymmetric TSP, the approach can be adapted to the symmetric TSP by using the 2-matching problem instead of AP.

Exact solution of crew scheduling problems using the set partitioning model: Recent successful applications

Abstract: The set partitioning model of the crew rotation problem has been well known for many years. This paper focuses on recent developments that have made this model more attractive and have resulted in several successful implementations. These developments include improved problem conceptualizations and decompositions, as well as new solution techniques employing Lagrangian relaxation and subgradient optimization. Experience is reported from The Flying Tiger Line, Pacific Southwest Airways, Continental Airlines, and Helsinki City Transport. A case is made for work on heuristic decomposition methods to break large problems into moderate sized pieces that can be solved exactly.

Algorithms for optimal material handling in automatic warehousing systems

Abstract: This paper presents four heuristic algorithms for handling orders in automatic warehousing systems. It is assumed that the orders will be handled by the use of an automatic storage and retrieval machine (S/R machine). The algorithms select, the orders that will be hand led in one tour in order to minimize the total distance travelled by the S7sol;R machine within the warehouse system. Computer programs are developed for the four algorithms and the optimal tours are found by using the travelling salesman algorithm. Optimal or near optimal solutions for the handling problem are found.

The Multiregion Dynamic Capacity Expansion Problem, Part I

Abstract: Consider the problem of determining a schedule of capacity expansions for m producing regions and a schedule of shipments from the regions to n markets so as to meet the market demands over a T-period planning horizon at minimum discounted capacity expansion and shipment costs. Both of these costs are assumed to be proportional to the amounts involved. The heuristic algorithm of this paper improves on feasible solutions by exchanging capacities between pairs of regions. The algorithm imbeds an optimization procedure to seek the best feasible solution in the direction specified by the heuristic. Computational results for both real and randomly generated problems show that the heuristic algorithm is computationally efficient and yields close to optimum solutions.

Second-order design sensitivity analysis of structural systems

Abstract: ESIGN sensitivity analysis methods for calculation of first derivatives of structural performance with respect to design parameters have become quite well developed and applied.1>2 It is the purpose of this Note to extend the adjoint method of design sensitivity analysis to calculation of second derivatives of performance with respect to design parameters. The value of second-deriva tive information in design optimization is well known. Using only first-order (gradient) information, optimization algorithms must resort to onedimensional search or heuristic step-size selection methods. If second-derivative information is available, at a reasonable computing cost, much more powerful iterative optimization algorithms are possible.3 Finite-dimensional (matrix) structural models are considered here, even though the methods presented can be extended to distributed parameter (boundary-value problem) structural models. Structural design is presumed to be described by a vector of design parameters b=[b1,b2,...,bk]T. Structural response is described by a vector of nodal displacement coordinates z=[Zi,z2,«.,Zn\7

Analysis of Greedy Solutions for a Replacement Part Sequencing Problem

Abstract: This paper considers the problem of sequencing the installation of replacement parts for the repeated repair of a machine consisting of two working parts. A finite inventory of spares is initially available for each type of part. Each spare has a known deterministic field life, and spares of each type may have different field lives. The inventories are eventually depleted since no replacement or repairs of parts occur. The primary objective is to obtain a sequencing policy which minimizes the total number of installations replacements. This problem is a special case of many opportunistic replacement problems and is called a “build” problem. The motivation for this work is based on the maintenance of modular gas turbine aircraft engines used by domestic airlines and the U.S. Air Force. We show this build problem is NP-hard which indicates the necessity of efficient heuristic solution procedures. This paper considers several “greedy” type algorithms based on grouping parts according to exact matching of field lives. Then, a generalization is presented which allows approximate matches. The focus of the analysis is to obtain tight worst case bounds on the number of replacements obtained by each of the greedy algorithms.

Analysis of a heuristic for full trie minimization

Abstract: A trie is a distributed-key search tree in which records from a file correspond to leaves in the tree. Retrieval consists of following a path from one root to a leaf, where the choice of edge at each node is determined by attribute values of the key. For full tries, those in which all leaves lie at the same depth, the problem of finding an ordering of attributes which yields a minimum size trie is NP-complete.This paper considers a “greedy” heuristic for constructing low-cost tries. It presents simulation experiments which show that the greedy method tends to produce tries with small size, and analysis leading to a worst case bound on approximations produced by the heuristic. It also shows a class of files for which the greedy method may perform badly, producing tries of high cost.

An Experimental Comparison of the Heuristic Methods for Solving Reliability Optimization Problems

Abstract: This paper compares three heuristic methods (Nakagawa-Nakashima, Gopal-Aggarwal-Gupta, Sharma-Venkateswaran) for solving reliability optimization problems with nonlinear constraints. Their effectiveness, measured in terms of computation time, optimality rate, and relative error, is evaluated on several sets of randomly generated test problems with nonlinear constraints for series systems. A FORTRAN program for generating the test problems and best known solutions (some of them are exact optimal) are included.

Technical Note—Analysis of a Preference Order Traveling Salesman Problem

Abstract: Application is made to the preference order dynamic programming solution procedure proposed by Kao for a stochastic traveling salesman problem. Although the procedure is flawed from the myopic interpretation of the monotonicity condition, it may be used as a convenient heuristic tool for solving stochastic problems.

A survey of mathematical optimization models and algorithms for designing and extending irrigation and wastewater networks

Abstract: this paper presents a state-of-the-art survey of network models and algorithms that can be used as a planning tool in irrigation and wastewater systems. it is shown that the problem of designing or extending such systems basically leads tothe same type of mathematical optimization model. the difficulty in solving this model lies mainly in the properties of the objective function. trying to minimize construction and/or operating costs of a system typically results in a concave cost (objective) function, due to economies of scale. a number of ways to attack such models are discussed and compared, including linear programming, integer programming and specially designed exact and heuristic algorithms. the usefulness of each approachis evaluated in terms of the validity of the model, the computational complexity of the algorithm, the properties of the solution, the availability of software and the capability for sensitivity analysis.;

New algorithms for deterministic and stochastic vehicle routing problems

Abstract: In this dissertation, a comprehensive approach to stochastic vehicle routing is developed. Effective solution procedures for various forms of this complex problem are proposed and computationally tested. These solution procedures are adapted from solution procedures that are effective for related problems such as the Traveling Salesman Problem and the Vehicle Routing Problem. In general, given a set of points on a graph (locations on a map) the problem is to route one or more vehicles in such a way that each point and the total distance traveled is minimized. When there is one vehicle which must visit every location and return to its start location, the problem is called the Traveling Salesman Problem. This problem has been widely studied and has many applications in the transportation and scheduling fields. When there are multiple vehicles, each with a specific capacity, and a portion of this capacity is demanded at each point visited (e.g., delivery trucks), the problem is called the Vehicle Routing Problem. Such diverse operations as garbage collection, school busing, small package air mail service, along with a host of commercial distribution systems (e.g., milk, petroleum, etc.) fit this description and have benefited from algorithms designed to efficiently route the vehicles involved. When the demands at the various points are random variables whose values only become known when the vehicle serving that point arrives, the problem is a Stochastic Vehicle Routing Problem and must be treated differently than a deterministic problem above. In stochastic vehicle routing, the problem is to design a route system which has a short overall distance, but at the same time meets the demands on each route with regularity. If too many demand points are placed on one route, the vehicle assigned to that route will often be too small to meet all the demands. When this occurs, either some of the customers will not be served, or a special expense will be incurred in finishing the failed route. Both of these alternatives involve a cost which must be considered when designing the route system. Before specifically addressing the Stochastic Vehicle Routing Problem, this dissertation presents two efficient algorithms for the Traveling Salesman Problem. These algorithms are described in detail and then tested on a set of problems from the literature. The new algorithms produce better solutions to these test problems than several similar heuristic algorithms that have been proposed by other authors. After discussing these algorithms for the Traveling Salesman Problem, a new heuristic algorithm for deterministic vehicle routing is presented. It is based on an effective algorithm for the Traveling Salesman Problem, and has generated the best known solutions to several test problems in the literature. Having presented these new algorithms, the Stochastic Vehicle Routing Problem is formulated in two different forms, a chance constrained model and a penalty function model. These models are developed and tested computationally. The new vehicle routing algorithm presented previously is adapted to handle stochastic demands and is used to generate solutions to some test problems. The final phase of this dissertation involves adapting the stochastic vehicle routing models to the Subscriber Bus Routing Problem. This problem arises when a subscriber bus system in which customers sign up in advance for bus service to and from some large employment center is used as an alternative to the personal car. Such systems have arisen as a result of the recent escalation of automobile and gasoline costs.

Optimization on Refuse Collection Systems

Abstract: A solution to the vehicle routing problem for refuse collection in large cities is presented. The algorithm accommodates real world constraints and employs a combined heuristic and computer approach. The results of a case study in the Municipal Corporation of Greater Bombay brings out the efficacy of the algorithm in identifying the optimal refuse collection routes.

The vehicle scheduling problem: a survey

Abstract: SUMMARY The vehicle scheduling problem is concerned, with routing a fleet of vehicles each with a capacity constraint and which are based at a central depot, to visit a set of delivery points. The optimality criterion is most frequently taken as the total distance travelled which is to be minimized. This paper discusses this problem, surveys the literature on it and presents some new ideas on heuristic solution procedures.

The optimization strategy for query evaluation in RDB/V1

Abstract: RDB/V1 is a fully relational database managenent system that has been developed for end users. In implementing the system, we focused our efforts upon making the system easy to use and efficient in query evaluation. This paper deals with how to gain efficiency in query evaluation; that is, optimization of query evaluation. Our approach for optimization is a heuristic one. Some of the characteristics of our approach are: (1) access cost evaluation based on statistical data, (2) dynamic gathering of data for use in speeding up join operation, (3) integration of facility for optimization into the view mechanism, and (4) global optimization after local optimization.

A Two Stage Solution Procedure for the Lock Box Location Problem

Abstract: New lock box solution techniques have recently been suggested by Stone and Nauss-Markland. This paper briefly discusses these new methodologies and shows how the algorithms can be combined into a third solution procedure which exploits the computational efficiency of the Stone heuristic and retains the optimizing property of the Nauss-Markland algorithm.

A Greedy Heuristic for Single Machine Sequencing with Precedence Constraints

Abstract: We present a greedy heuristic for the n job/1 machine scheduling problem with precedence constraints. This method is useful whenever the manager's optimization criteria is the sum of weighted or unweighted completion times, the sum of weighted or unweighted flow times, with or without release dates, the sum of weighted or unweighted working times, the sum of weighted or unweighted lateness, average completion time, average flow time, average waiting time or average lateness. The greedy heuristic found the optimal solution for 58 of 68 test problems for which a branch and bound method was used to find the optimal solution. The heuristic is, of course, much easier to implement and executes in less time. The greedy heuristic fared well in comparison with a simple myopic heuristic presented by Morton and Dharan Morton. T. E., B. G. Dharan. 1978. Algoristics for single machine sequencing with precedence constraints. Management Sci.24 10 1011-1020..

A Note on Garfinkel, Neebe and Rao's LP Decomposition for the p-Median Problem

Abstract: The convergence problems of Garfinkel, Neebe and Rao's linear programming decomposition algorithm for the relaxed p-median problem are analyzed and traced back to the very degenerate nature of the LP formulation. Extensive computational experience with this algorithm is described. One surprising outcome of the tests conducted with the decomposition algorithm was that convergence was obtained more consistently when a random (and usually worse) initial solution was used instead of a “good” initial solution provided by heuristic methods.

Integer linear programming formulation of the material requirements planning problem

Abstract: Lot sizing procedures for discrete and dynamic demand form a distinct class of inventory control problems, usually referred to asmaterial requirements planning. A general integer programming formulation is presented, covering an extensive range of problems: single-item, multi-item, and multi-level optimization; conditions on lot sizes and time phasing; conditions on storage and production capacities; and changes in production and storage costs per unit. The formulation serves as a uniform framework for presenting a problem and a starting point for developing and evaluating heuristic and tailor-made optimum-seeking techniques.

Integer Linear Programming Formulation of Material Requirements Planning Problem

Abstract: Lot sizing procedures for discrete and dynamic demand form a distinct class of inventory control problems, usually referred to as material requirements planning. A general integer programming formulation is presented, covering an extensive range of problems: single-item, multi-item, and multi-level optimization; conditions on lot sizes and time phasing; conditions on storage and production capacities; and changes in production and storage costs per unit. The formulation serves as a uniform framework for presenting a problem and a starting point for developing and evaluating heuristic and tailor-made optimum- seeking techniques.

A quasi-newton algorithm for solving multiphase equilibrium flash problems

Abstract: A new algorithm has been developed for solving the multicomponent vapor-liquid-liquid equilibrium Mash problem The algorithm is an extension of the “inside-out” approach proposed by Boston and Britt for the vapor-liquid equilibrium flash problem Conventional flash algorithms use temperature, pressure, composition, and phase fraction as the problem independent variables, In the inside-out approach a new set of independent variables is introduced in place of the conventional variables The new variables are chosen to be as independent as possible of the conventional variables and as free as possible of mutual interaction Complex phase equilibrium models are used only to generate parameters for a simple equilibrium ratio model These parameters become the problem independent variables The Quasi-Newton method of Broyden is employed to promote convergence of these variables The algorithm first obtains a solution for the vapor-liquid equilibrium flash By examining the liquid phase, a heuristic al

A Comparison of Dynamic and Static Virtual Memory Allocation Algorithms

Abstract: In this paper we compare the performance of virtual memory allocation algorithms. The primary measure of performance is the space-time product of primary memory occupancy, or space-time cost, used by a program during its execution. Using DMIN, an optimal dynamic aliocation algorithm, we compute the minimum space-time cost achievable for some benchmark program runs. We compare the DMIN space-time cost with the space-time cost from: MIN, an optimal static allocation algorithm, VMIN, an optimal variable space algorithm, and two heuristic dynamic allocation algorithms. the page fault frequency algorithm and the damped working set algorithm.

Adaptive optimization of factory cutting conditions—a heuristic computer simulation applied to single point turning

Abstract: An adaptive optimization scheme for economic machining is developed and tested by a series of experiments. The scheme involves actual shop data and optimization techniques based on computer simulation. The computer simulation model is formulated for stages with one, two and three or more sets of shop data. The results show that the method is practical, valid and independent of the initially selected cutting conditions.

General microprogram width reduction using generator sets

Abstract: The problem of reducing the microinstruction length for a parallel microprogram, by trading off microprogram width (bits) for subsequent logic, is considered. In a generalization of previous methods, it is shown that a considerable reduction of microprogram storage size can be achieved by selecting a subset of the original microorders to serve as inputs to some generating logic in order to provide all the microorders in the original microprogram. Heuristic solution methods are shown, along with ways to control the bounds of the solutions, allowing the designer the choice between a fast solution and an optimal solution. Examples show the effects of using these methods, alone and in conjunction with previously published methods for width reduction. Applications of the width reduction technique to reasonable modern design situations are discussed.