Showing papers on "Heuristic published in 1986"

The dynamics of plant layout

Abstract: The problem of plant layout has generally been treated as a static one. In this paper, we deal with the dynamic nature of this problem. Both optimal and heuristic procedures are developed for this problem and are based on a dynamic programming formulation. The use of one of these approaches depends on the ability to solve the static problem efficiently. Finally, we briefly discuss the issue of extending the planning horizon, and how to resolve system nervousness when previously planned layouts need to be changed.

A comparative evaluation of heuristic line balancing techniques

Abstract: In this paper, we report on a computational experiment designed to assess the efficacy of 26 heuristic decision rules which group work tasks into work stations along an assembly line such that the number of work stations required is minimized. The heuristic decision rules investigated vary from simple list processing procedures that consider a single attribute of each work task for assignment, to procedures which are optimal seeking, but which have had their search terminated through the imposition of a limit on the amount of computation time that can be devoted to each search. Also included are heuristic decision rules which backtrack in an attempt to locate an improved solution, and decision rules which probabilistically search for improved solutions. Our investigation differs from those reported previously, in that the objective in balancing each line is to determine the minimum number of work stations for a given limit on the time available for assembly at each work station the cycle time. Previous approaches have investigated the problem of determining the minimum cycle time for a given line length. We also compare the results obtained with the optimal solution for a subset of the problems investigated. Both problems which have appeared in the open literature and problems which have been solved for the first time are included. Because a portion of our results differ from those reported previously, we suggest why these differences have occurred. Guidelines are also given to those balancing industrial assembly lines on the choice of the heuristic decision rule to use whether one is attempting to obtain a minimum station balance given a limit on the time available for assembly at each work station, or whether one is attempting to minimize the time devoted to assembly at a work station given a limit on the number of work stations available.

Finding a shortest solution for the N x N extension of the 15- Puzzle is intractable

Abstract: The 8-puzzle and the 15-puzzle have been used for many years as a domain for testing heuristic search techniques. From experience it is known that these puzzles are "difficult" and therefore useful for testing search techniques. In this paper we give strong evidence that these puzzles are indeed good test problems. We extend the 8-puzzle and the 15-puzzle to a nxn board and show that finding a shortest solution for the extended puzzle is NP-hard and thus computationally infeasible. We also present an approximation algorithm for transforming boards that is guaranteed to use no more than c L (SP) moves, where L (SP) is the length of the shortest solution and c is a constant which is independent of the given boards and their size n.

A Lagrangian Relaxation Heuristic for Capacitated Facility Location with Single-Source Constraints

Abstract: Facility location models are applicable to problems in many diverse areas, such as distribution systems and communication networks. In capacitated facility location problems, a number of facilities with given capacities must be chosen from among a set of possible facility locations and then customers assigned to them. We describe a Lagrangian relaxation heuristic algorithm for capacitated problems in which each customer is served by a single facility. By relaxing the capacity constraints, the uncapacitated facility location problem is obtained as a subproblem and solved by the well-known dual ascent algorithm. The Lagrangian relaxations are complemented by an add heuristic, which is used to obtain an initial feasible solution. Further, a final adjustment heuristic is used to attempt to improve the best solution generated by the relaxations. Computational results are reported on examples generated from the Kuehn and Hamburger test problems.

Simulated Annealing and Combinatorial Optimization

Abstract: We formulate a class of adaptive heuristics for combinatorial optimization. Recently proposed methods such as simulated annealing, probabilistic hill climbing, and sequence heuristics, as well as classical perturbation methods are all members of this class of adaptive heuristics. We expose the issues involved in using an adaptive heuristic in general, and simulated annealing, probabilistic hill climbing, and sequence heuristics in particular. These issues are investigated experimentally.

Scheduling with multiple performance measures: the one-machine case

Abstract: Most scheduling research has considered optimizing a single performance measure criterion. In this paper we consider the problem of scheduling jobs on a single machine when the desirability of a schedule is evaluated using more than one performance measure. The procedures developed here can be used to construct trade-off curves among selected performance measures. The importance of the trade-off curve is that it provides the complete set of possibly optimal solutions for any objective function cost function involving only the selected performance measures. With this information, a manager can concentrate on selecting the most preferred schedule from the set. Algorithms are presented for the three two-criteria problems utilizing mean flow time, maximum tardiness, and number of tardy jobs and the three-criteria problem involving all of these criteria. Computational results for the four algorithms are provided. The most striking result is that the number of efficient solutions is very small in comparison to the number of permutation schedules for all three two-criteria problems and only modestly larger for the three-criteria problem. This has the managerial significance that, irrespective of the individual manager's specific trade-offs between the criteria, the number of possibly optimal schedules that need to be considered is relatively small. Several research directions on heuristic approaches, man-machine interactive approaches, computational efficiency, etc. are possible for the type of problem studied. The work reported here has the potential to stimulate research incorporating multiple performance measures in more complex scheduling models.

Probabilistic analysis of two heuristics for the 3-satisfiability problem

Abstract: An algorithm for the 3-Satisfiability problem is presented and a probabilistic analysis is performed. The analysis is based on an instance distribution which is parameterized to simulate a variety of sample characteristics. The algorithm assigns values to variables appearing in a given instance of 3-Satisfiability, one at a time, using the unit clause heuristic and a maximum occurring literal selection heuristic; at each step a variable is chosen randomly from a subset of variables which is usually large. The algorithm runs in polynomial time and it is shown that the algorithm finds a solution to a random instance of 3-Satisfiability with probability bounded from below by a constant greater than zero for a range of parameter values. The heuristics studied here can be used to select variables in a Backtrack algorithm for 3-Satisfiability. Experiments have shown that for about the same range of parameters as above the Backtrack algorithm using the heuristics finds a solution in polynomial average time.

On the Minimum Violations Ranking of a Tournament

Abstract: This paper examines the problem of rank ordering a set of players or objects on the basis of a set of pairwise comparisons arising from a tournament. The criterion for deriving this ranking is to have as few cases as possible where player i is ranked above j while i was actually defeated by j in the tournament. Such a situation is referred to as a violation. The objective, therefore, is to determine the Minimum Violations Ranking MVR. While there are situations where this ranking would be allowed to contain ties among subsets of objects, we will concern ourselves herein with linear ordering no ties. A series of examples are given where this requirement would seem to be appropriate. In order to put the MVR problem into proper perspective we introduce the concept of a distance on the set of tournaments. A set of natural axioms is presented which any such distance measure should obey, and it is proven that in the presence of these axioms a unique such measure exists. It is then shown that the MVR problem is equivalent to the minimum distance problem, which can be represented in several forms-in particular as a problem of determining the minimum feedback edge set in a graph and as a mixed integer generalized network problem. This opens up a wide scope of possible solution procedures for the MVR problem. An optimal algorithm is presented along with computational results. In addition, various heuristics are discussed including an improved heuristic referred to as the Iterated Kendall method.

A Local Improvement Heuristic for the Design of Less-than-Truckload Motor Carrier Networks

Abstract: The load planning problem for less-than-truckload motor carriers is formulated as a fixed charge network design problem where level of service constraints are represented heuristically through a set of minimum frequencies on links. If direct service is offered between two terminals, it is required to do so at a given minimum frequency, implying not only a fixed charge from adding direct service but also a link cost function that is then flat until the flow on the link exceeds the minimum frequency. A local improvement heuristic is proposed which adds and drops links to and from the network in an intelligent sequence. After each change, the routing of the freight over the network is approximately reoptimized. Empty balancing of equipment is also handled explicitly. The approach has been applied successfully to a network with over 300 terminals; numerical tests on a 140 terminal network are reported.

Heuristic classification

Abstract: A broad range of well-structured problems--embracing forms of diagnosis, catalog selection, and skeletal planning--are solved in "expert systems" by the method of heuristic classification. These programs have a characteristic inference structure that systematically relates data to a pre-enumerated set of solutions by abstraction, heuristic association, and refinement. In contrast with previous descriptions of classification reasoning, particularly in psychology, this analysis emphasizes the role of a heuristic in routine problem solving as a non-hierarchical, direct association between concepts. In contrast with other descriptions of expert systems, this analysis specifies the knowledge needed to solve a problem, independent of its representation in a particular computer language. The heuristic classification problem-solving model provides a useful framework for characterizing kinds of problems, for designing representation tools, and for understanding non-classification (constructive) problem-solving methods.

Configuration of physical distribution networks

Abstract: Distribution problems, including vehicle routing and warehouse location problems, are usually formulated by considering a finite number of possible locations for the customers, the warehouses, and vehicle stops. The question of selecting which of these points are actually used (and how) is a mixed-integer programming problem which is difficult to solve. Thus, such a discrete formulation results in a problem that has to be solved heuristically; it also entails a large data preparation effort each time a solution has to be developed in response to changing world conditions. The continuous approach used in this paper attempts to circumvent some of these drawbacks. We consider one source and its customers in a service area; customer locations are modeled by a density surface over the service area. With this information, and data about the cost of inventory and transportation, we can determine the number of transhipment points, and the frequency and routing of all the distribution vehicles. An example is given. The continuous approach does not yield a solution. It gives design guidelines, which ensure near minimum total cost. These design guidelines are based on general properties of optimal solutions (discussed at the beginning of the paper) and on the specific characteristics of the case at hand. Implementation of the guidelines to obtain a feasible configuration requires human intervention. While the continuous method involves approximations (the real world is discrete and considerably more complicated than in our model), it yields insight into the structure of logistic systems. This insight should not only help in the design process; it may well also lead to improved heuristic solution methods for discrete formulations. Hybrid methods may eventually emerge.

A Heuristic for Multiple Lot Sizing For an Order Under Variable Yield

Abstract: Consider a job shop which must completely fill a large make-to-order demand of a product where production yield is highly variable. After a production lot is completed, if the total output of satisfactory units is inadequate to satisfy the demand, then a new run (with associated setup cost) is made. When the output of good units exceeds the demand, then the excess units are scrapped (with possible salvage value). The optimal lot size minimizes the total of production, setup, holding, shortage, and scrap costs. A heuristic is developed based on the incremental cost of increasing the lot size by one unit. The computational ease and excellent cost performance of the heuristic favor its use in place of the mathematically optimal solution obtained by dynamic programming. Real world manufacturing applications and additional properties of the model are also discussed.

An efficient heuristic method for the simple assembly line balancing problem

Abstract: SUMMARY An efficient single-pass heuristic method capable of finding good solutions for the single-model deterministic line balancing problem is presented. The method involves four phases for simplifying a given problem, reducing its size and decomposing it into smaller subproblems when appropriate. The solution is then found by using combinations of various heuristic rules. The procedure is illustrated on the 70-task problem of Tonge (1960)and computational results on well-known test problems are reported.

Optimal and heuristic procedures for component log-splitting in multi-stage manufacturing systems

Abstract: Component lot-splitting considerations, in which the lot-size of a component item may cover only a fraction of its parent item's lot-size, have been ignored in the literature when determining lot-sizes of items in multi-stage manufacturing systems. In this paper, a multi-stage lot-sizing problem is formulated under a specified component lot-splitting policy for the case of noninstantaneous production of items and constant demand for the end item. Optimal and heuristic solution procedures for the formulated problem are provided, including experimental results of comparison between these procedures. It is shown that considerable cost savings can result if the component lot-splitting approach is employed under favorable conditions in multi-stage manufacturing environments. In addition, reduced inventory levels are achieved which translate into lower working capital requirements and a less cluttered shop floor. The heuristic procedure is recommended as an acceptable alternative to the optimal procedure if the number of items in the multi-stage system is large or if inventory carrying and setup/order costs cannot be accurately estimated. Further, component lot-splitting considerations may be ignored if production rates of facilities in the system are in balance. Finally, a methodology for application of the component lot-splitting policy where the end item demand is time-varying is discussed.

Optimal Lot-Sizing for Dynamic Assembly Systems

Abstract: The simple case of a dynamic assembly system with no initial stocks is investigated as a test case for some new ideas on lot-sizing for Materials Requirements Planning. The model relies on the facility location formulation of Wagner’s and Whitin’s inventory problem. An iterative procedure is proposed that derives close upper and lower bounds through cost modifications based on Benders Decomposition and level-by-level optimization. The bounding procedure is integrated into a branch and bound scheme that outperforms by at least an order of magnitude its probably best competitor, the algorithm due to Afentakis et al (1984). The bounding procedure behaves excellently well as a heuristic and relates interestingly to the well-known lot-sizing methods of Graves (1981) and Blackburn and Milien (1982).

A unified theory of heuristic evaluation functions and its application to learning

Abstract: We present a characterization of heuristic evaluation functions which unifies their treatment in single-agent problems and two-person games. The central result is that a useful heuristic function is one which determines the outcome of a search and is invariant along a solution path. This local characterization of heuristics can be used to predict die effectiveness of given heuristics and to automatically learn useful heuristic functions for problems. In one experiment, a set of relative weights for the different chess pieces was automatically learned.

A comparative analysis of static and dynamic load balancing strategies

Abstract: The problem of uniformly distributing the load of a parallel program over a multiprocessor system was considered. A program was analyzed whose structure permits the computation of the optimal static solution. Then four strategies for load balancing were described and their performance compared. The strategies are: (1) the optimal static assignment algorithm which is guaranteed to yield the best static solution, (2) the static binary dissection method which is very fast but suboptimal, (3) the greedy algorithm, a static fully polynomial time approximation scheme, which estimates the optimal solution to arbitrary accuracy, and (4) the predictive dynamic load balancing heuristic which uses information on the precedence relationships within the program and outperforms any of the static methods. It is also shown that the overhead incurred by the dynamic heuristic is reduced considerably if it is started off with a static assignment provided by either of the three strategies.

A Decision Support System for Assigning Classes to Rooms

Abstract: A large 0-1 integer program is approximately solved by a very fast heuristic as part of a decision support system for assigning classes to rooms at the University of California at Berkeley. The system has been implemented and has been in regular use since the fall of 1983.

An Interactive Heuristic Approach for Multi-Objective Integer-Programming Problems

Abstract: An interactive approach to solve the multi-objective integer-programming problem heuristically is described. The approach consists of two main parts. The first is an algorithm to guide the search for a set of weights to the objective functions which would produce the solution most preferred by the decision-maker given a linear utility function. The search area is successively decreased through an interaction process, with the decision-maker using a selection and contraction method. During each stage of this algorithm, a number of single integer-programming problems are solved heuristically. The motivation for this approach, along with some computational experimentation, is provided.

Multi-Stage Lot-Sizing for General Production Systems

Abstract: In this paper the multi-stage lot-sizing problem for general production structures is considered. General production structures are characterized by the fact that each stage may have several predecessor or successor stages. The objective is to minimize total costs which consist of a fixed charge per lot at each stage and linear holding costs. Time varying demand for final products is assumed to be known and has to be satisfied. A simple heuristic procedure is presented consisting of two phases. In the first phase a “basic policy” is determined which derives reorder times under the assumption of demand being constant. These reorder intervals are then in a second phase used to solve the time varying problem. In doing so a first possibility is to realize a cyclic policy simply according to the “basic policy”. A second possibility of taking into account non-stationarity is to take adjusted cost parameters and apply single-stage inventory models. A simulation study shows that considerable cost improvements can be realized using this heuristic.

A new heuristic for determining fleet size and composition

Abstract: In the fleet size and composition vehicle routing problem (FSCVRP), one decides upon the composition of a possibly heterogeneous fleet of vehicles so as to minimize the sum of fixed vehicle acquisition costs and routing costs for customer deliveries. In this note, we build upon a previously-described lower bound procedure for the FSCVRP in order to present a new heuristic. Computational results to date have been encouraging.