Showing papers on "Heuristic (computer science) published in 1991"

A Computational Study of the Job-Shop Scheduling Problem

Abstract: The job-shop scheduling problem is a notoriously difficult problem in combinatorial optimization. Although even modest sized instances remain computationally intractable, a number of important algorithmic advances have been made in recent years by J. Adams, E. Balas and D. Zawack; J. Carlier and E. Pinson; B. J. Lageweg, J. K. Lenstra and A. H. G. Rinnooy Kan; and others. Making use of a number of these advances, we have designed and implemented a new heuristic procedure for finding schedules, a cutting-plane method for obtaining lower bounds, and a combinatorial branch and bound algorithm. Our optimization procedure, combining the heuristic method and the combinatorial branch and bound algorithm, solved the well-known 10×10 problem of J. F. Muth and G. L. Thomson in under 7 minutes of computation time on a Sun Sparcstation 1. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Ant System: An Autocatalytic Optimizing Process

Abstract: A combination of distributed computation, positive feedback and constructive greedy heuristic is proposed as a new approach to stochastic optimization and problem solving. Positive feedback accounts for rapid discovery of very good solutions, distributed computation avoids premature convergence, and greedy heuristic helps the procedure to find acceptable solutions in the early stages of the search process. An application of the proposed methodology to the classical travelling salesman problem shows that the system can rapidly provide very good, if not optimal, solutions. We report on many simulation results and discuss the working of the algorithm. Some hints about how this approach can be applied to a variety of optimization problems are also given.

Dynamic traffic assignment for urban road networks

Abstract: This paper presents a nonlinear programming formulation of the dynamic user-equilibrium assignment problem (DUE) for urban road networks with multiple trip origins and destinations. DUE is a temporal generalization of the static user-equilibrium assignment problem (SUE) with additional constraints to insure temporally continuous paths of flow. In DUE, the full assignment period of several hours is discretized into shorter time intervals of 10–15 minutes each for which trip departure matrices are assumed to be known. This formulation of DUE includes SUE as a special case in which there is only one time interval for the full assignment period. The assumption of steady-state flows allows SUE to have all linear constraints, but DUE requires nonlinear flow continuity constraints. Whereas SUE is typically solved by methods of linear combinations, these methods create temporally discontinuous flows if applied to DUE. A dynamic traffic assignment heuristic (DTA) is presented that generates approximate solutions to DUE in an efficient manner for large networks. DTA is not a convergent solution algorithm for DUE, but was designed instead to produce assignments that approximate the DUE optimality conditions. An overview of alternative dynamic assignment approaches is given, including the limitations of other optimization and simulation approaches. Test results presented in this paper show that DTA generates both static and dynamic assignments that approximately satisfy the user-equilibrium conditions of these problems.

An AI-based approach for transit route system planning and design

Abstract: We present an AI-based solution approach to the transit network design problem (TNDP). Past approaches fall into three categories: optimization formulations of idealized situations, heuristic approaches, or practical guidelines and ad hoc procedures reflecting the professional judgement and practical experience of transit planners. We discuss the sources of complexity of the TNDP as well as the shortcomings of the previous approaches. This discussion motivates the need for AI search techniques that implement the existing designer's knowledge and expertise to achieve better solutions efficiently. Then we propose a hybrid solution approach that incorporates the knowledge and expertise of transit network planners and implements efficient search techniques using AI tools, algorithmic procedures developed by others, and modules for tools implemented in conventional languages. The three major components of the solution approach are presented, namely, the lisp-implemented route generation design algorithm (RGA), the analysis procedure TRUST (Transit Route Analysis), and the route improvement algorithm (RIA). An example illustration is included.

Optimal Groundwater Management: 1. Simulated Annealing

Abstract: Simulated annealing is introduced and applied to the optimization of groundwater management problems cast in combinatorial form. This heuristic, probabilistic optimization method seeks minima in analogy with the annealing of solids and is effective on large-scale problems. No continuity requirements are imposed on objective (cost) functions. Constraints may be added to the cost function via penalties, imposed by designation of the solution domain, or imbedded in submodels (e.g., mass balance in aquifer flow simulators) used to evaluate costs. The location of global optima may be theoretically guaranteed, but computational limitations lead to searches for nearly optimal solutions in practice. Like other optimization methods, most of the computational effort is expended in flow and transport simulators. Practical algorithmic guidance that leads to enormous computational savings and sometimes makes simulated annealing competitive with gradient-type optimization methods is provided. The method is illustrated by example applications to idealized problems of groundwater flow and selection of remediation strategy, including optimization with multiple groundwater control technologies. They demonstrate the flexibility of the method and indicate its potential for solving groundwater management problems. The application of simulated annealing to water resources problems is new and its development is immature, so further performance improvements can be expected.

New heuristic algorithms for efficient hierarchical path planning

Abstract: The authors consider one of the most popular approaches to path planning: hierarchical approximate cell decomposition. This approach consists of constructing successive decompositions of the robot's configuration space into rectangloid cells and searching the connectivity graph built at each level of decomposition for a path. Despite its conceptual simplicity, an efficient implementation of this approach raises many delicate questions that have not yet been addressed. The major contributions this work are (1) a novel approach to cell decomposition based on constraint reformulation and (2) a new algorithm for hierarchical search with a mechanism for recording failure conditions. These algorithms have been implemented in a path planner, and experiments with this planner have been carried out on various examples. These experiments show that the proposed planner is significantly (approximately 10 times) faster than previous planners based on the same general approach. >

Exact algorithms for output encoding, state assignment, and four-level Boolean minimization

Abstract: A novel minimization procedure of prime implicant generation and covering that operates on symbolic outputs, rather than binary-valued outputs, is proposed for solving the output encoding problem. An exact solution to this minimization problem is also an exact solution to the encoding problem. While this covering problem is more complex than the classic unate covering problem, a single logic minimization step replaces O(N-factorial) minimizations. The input encoding problem can be exactly solved using multiple-valued Boolean minimization. An exact algorithm is presented for state assignment by generalizing the proposed output encoding approach to the multiple-valued input case. Four-level Boolean minimization entails finding a cascaded pair of two-level logic functions that implement another logic function, such that the sum of the product terms in the two cascaded functions or truth tables is minimum. Four-level Boolean minimization can be formulated as an encoding problem and solved exactly using the proposed algorithms. Preliminary experimental results are presented which indicate that this approach is significantly more efficient than exhaustive search. Computationally efficient heuristic approaches based on the exact algorithms are proposed for output encoding, state assignment, and four-level Boolean minimization. >

MENTOR: an algorithm for mesh network topological optimization and routing

Abstract: The problem of obtaining a minimum cost topology for a mesh network given matrices specifying the cost of links between all pairs of nodes and the internode requirements is considered. A heuristic algorithm which works in terms of general network design principles and uses utilization as a figure of merit is presented. The procedure is applicable to a wide variety of networks, especially to the problem of obtaining starting topologies for other network design procedures. The algorithm's computational complexity is shown to be of order N/sup 2/, a significant improvement over currently used algorithms and fast enough to be embedded in the inner loop of other more general design procedures, e.g., node selection procedures. Computational experience is presented which shows that the procedure is fast and simple and yields solutions of a quality competitive with other much slower procedures. >

Algorithms for the multi-resource generalized assignment problem

Abstract: The multi-resource generalized assignment problem is encountered when a set of tasks have to be assigned to a set of agents in a way that permits assignment of multiple tasks to an agent subject to the availability of a set of multiple resources consumed by that agent. This problem differs from the generalized assignment problem in that an agent consumes not just one but a variety of resources in performing the tasks assigned to him. This paper develops effective solution procedures for the multi-resource generalized assignment problem. Various relaxations of the problem are studied and theoretical relations among these relaxations are pointed out. Rules for reducing problem size are discussed and are shown to be effective through computational experiments. Heuristic solution procedures and an efficient branch and bound procedure are developed. Results of computational experiments testing these procedures are reported.

Fast shape from shading

Abstract: Extracting surface orientation and surface depth from a shaded image is one of the classic problems in computer vision. Many previous algorithms either violate integrability, i.e., the surface normals do not correspond to a feasible surface, or use regularization, which biases the solution away from the true answer. A recent iterative algorithm proposed by Horn overcomes both of these limitations but converges slowly. This paper uses a new algorithm, hierarchical basis conjugate gradient descent, to provide a faster solution to the shape from shading problem. This approach is similar to the multigrid techniques that have previously been used to speed convergence, but it does not require heuristic approximations to the true irradiance equation. The paper compares the accuracy and the convergence rates of the new techniques to previous algorithms.

A Multi-criteria Decision Support System for R&D Project Selection

Abstract: This paper describes the development of a decision support system for the selection of a portfolio of R&D projects, which was carried out for a large electricity utility corporation. The DSS was constructed round a reference point approach for the underlying multi-criteria decision problem. The application of this approach did require a less usual form of scalarizing function as well as a heuristic algorithm for solving a non-linear knapsack problem. Practical aspects of the implementation of the multi-criteria approach in a DSS operating on a PC are also discussed.

On multicast path finding algorithms

Abstract: Three multicast path-finding algorithms for networks with directed links are designed and implemented: an optimal algorithm based on the dynamic programming technique, a heuristic algorithm with the assumption that all vertices have the multicast capability, and a heuristic algorithm for networks where some vertices do not have the multicast capability. Computation results show that the heuristic algorithms can find multicast paths whose costs are close to optimal and can operate with reasonable response time for large networks. Applications of these path-finding algorithms to set up multipoint connections for broadband multimedia multiparty services are discussed. >

A multiphase approach to the period routing problem

Abstract: In this article, we present a multiphase approach to the period routing problem. The period routing problem involves the design of effective vehicle routes that satisfy customer service frequencies over a specified planning horizon. The first phase of analysis consists of a generalized network approximation to achieve an efficient initial solution. The second phase involves an interchange heuristic that reduces distribution costs by solving a surrogate traveling salesman problem. The third phase consists of an interchange heuristic that further reduces the distribution costs by addressing the actual vehicle routes of the period routing problem. A fourth phase utilizes a 0–1 integer model to attempt further improvements. Computational results on test problems indicate that the multiphase approach yields improvements over previous best solutions.

Determinate literals in inductive logic programming

Abstract: A recent system, FOIL, constructs Horn clause programs from numerous examples. Computational efficiency is achieved by using greedy search guided by an information-based heuristic. Greedy search tends to be myopic but determinate terms, an adaptation of an idea introduced by another new system (GOLEM), has been found to provide many of the benefits of lookahead without substantial increases in computation. This paper sketches key ideas from FOIL and GOLEM and discusses the use of determinate literals in a greedy search context. The efficacy of this approach is illustrated on the task of learning the quicksort procedure and other small but non-trivial list-manipulation functions.

Practical path planning among movable obstacles

Abstract: Path planning among movable obstacles is a practical problem that is in need of a solution. An efficient heuristic algorithm is presented that uses a generate-and-test paradigm: a good candidate path is hypothesized by a global planner and subsequently verified by a local planner. In the process of formalizing the problem, a technique for modeling object interactions through contact is presented. The algorithm has been tested on a variety of examples, and was able to generate solutions within 10 s on a 17-MIPS Sun Sparc workstation. >

A 3-OPT based simulated annealing algorithm for vehicle routing problems

Abstract: Simulated Annealing is combined with the 3-opt heuristic to solve the vehicle routing problem. The results are encouraging; two examples out of three large size problems gave results as good as the best known 3-opt solution. Preliminary results with the heuristic algorithm are presented.

Heuristic operating policies for reservoir system simulation

Abstract: Reservoir system simulation models are widely used to determine a system's firm water yield, average yield, or hydropower capacity. Most such models use heuristic guidelines to define the system's operating policy. Alternatively, optimization can be used within the simulation to identify a reasonable operating strategy. In this paper a theoretical justification is provided for several heuristic operating guidelines, including the widely used space rule. The guidelines are expressed as a mathematical objective function and combined with constraints on system operation to yield one-period optimization submodels that can be used to determine releases within a simulation. Use of these one-period optimization models improved the simulated operation of the Central Valley Project in California over the critical period of record and provided reasonable policies for other hydrologic scenarios.

Algorithms for routing in a linear lightwave network

Abstract: Routing algorithms are proposed for setting up calls on a circuit-switched basis in linear lightwave networks (LLN), i.e., networks composed only of linear components, including controllable power combiners and dividers, and possibly linear (non-regenerative) optical amplifiers. The overall problem is decomposed into three subproblems: (1) physical path allocation, (2) checking for violations of the special optical constraints on the allocated physical path, and (3) channel assignment. Only point to point connections are considered. The physical path allocation technique uses the K-shortest path algorithm and tries to minimize the number of sources potentially interfering with each other, as a result of the incoming call. A channel assignment heuristic that tends to spread out calls evenly among the available channels works better than one that tries to maximize channel reuse. >

Heuristics for the 0–1 min-knapsack problem

Abstract: textThe 0-1 min-knapsack problem consists in finding a subset of items such that the sum of their sizes is larger than or equal to a given constant and the sum of their costs is minimized. We first study a greedy-type heuristic having a worst-case bound of 2. This heuristic is then refined to obtain a new one with a worst-case bound of 3/2.

Grouping methods for printed circuit board assembly

Abstract: We present exact mathematical programming formulation and a fast heuristic method for grouping a set of Printed Circuit Boards (PCB). The assembly machines are configured for each group, thus saving set-up time, which is very long relative to process time. We extend previous work by allowing groups which contains common components of partial boards. An industrial case illustrates the proposed heuristic grouping method.

Convergent algorithm for dynamic traffic assignment

Abstract: A link flow formulation and a convergent solution algorithm for the dynamic user equilibrium (DUE) traffic assignment problem for road networks with multiple trip origins and destinations are presented. The link flow formulation does not implicitly assume complete enumeration of all origin-destination paths as does the equivalent path flow formulation. DUE is a temporal generalization of the static user equilibrium (SUE) assignment problem with additional constraints to ensure temporally continuous paths of flow. Whereas SUE can be solved by methods of linear combinations, these methods can create temporally discontinuous flows if applied to DUE. This convergent dynamic algorithm (CDA) uses the Frank-Wolfe method of linear combinations to find successive solutions to DUE while holding node time intervals fixed from each origin. In DUE, the full assignment period of several hours is discretized into shorter time intervals of 10 to 15 min each, for which trip departure matrices are assumed to be known. The performance of CDA is compared with that of a heuristic solution procedure called DTA. CDA can be applied to solving DUE on large networks, and the examples presented show that CDA consistently converges to solutions that closely satisfy the DUE optimality conditions. With computational advances such as parallel computing, CDA can be run in near real-time on large-scale networks and used with in-vehicle route advisory systems for traffic management during evacuations and special events.

Successive Linear Approximation Procedure for Generalized Fixed-Charge Transportation Problems

Abstract: In this paper, we develop a new heuristic procedure for solving a generalization of the fixed-charge transportation problem in which there are resource losses in addition to the fixed charges. The losses may be evaporation losses when the commodity is a liquid, heat losses in an electrical distribution network, or deterioration losses in distribution networks involving perishable commodities such as, for example, food items. The proposed procedure consists of solving a sequence of pro-rated problems. It is different from heuristic procedures that have been developed for solving the standard fixed charge transportation problem, in that it is not based on extreme point enumeration. We experiment with problems involving up to 2100 arcs with fixed charges and resource losses. The results show that the proposed approach is viable for solving medium-to-large sized problems.

Stowage Container Planning: A Model for Getting an Optimal Solution

Abstract: In this paper a mathematical programming model for the container stowage problem is shown; the binary decision variables determine, for each port, the container unloading and loading sequence. In fact, the solution indicates successively which container will be handled, and from or to which cell in the ship. Unless for some constraint linearisations (related to ship safety parameters), the proposed model finds, from the theoretical point of view, an optimal global solution for the stowage problem. Nevertheless, this combinatorial problem is NP-HARD and cannot be solved for commercial ship sizes in reasonable processing time using the available computer software and hardware. The basic features of this model were used for the development of an implicit enumeration procedure for solving the container stowage problem. In spite of the computational complexity of this approach, some heuristic rules are proposed to explore the combinatorial tree in an intelligent way and produce good, if not optimal, solutions for the problem in a reasonable processing time.

Fast search algorithms for the n-queens problem

Abstract: The n-queens problem is to place n queens on an n*n chessboard so that no two queens attack each other. The authors present two new algorithms, called queen search 2 (QS2) and queen search 3 (QS3). QS2 and QS3 are probabilistic local search algorithms, based on a gradient-based heuristic. These algorithms, running in almost linear time, are capable of finding a solution for extremely large n-queens problems. For example, QS3 can find a solution for 500000 queens in approximately 1.5 min. >

Facility dispersion problems: Heuristics and special cases

Abstract: Facility dispersion problem deals with the location of facilities on a network so as to maximize some function of the distances between facilities. We consider the problem under two different optimality criteria, namely maximizing the minimum distance (MAX-MIN) between any pair of facilities and maximizing the average distance (MAX-AVG) between any pair of facilities. Under either criterion, the problem is known to be NP-hard, even when the distances satisfy the triangle inequality. We consider the question of obtaining near-optimal solutions. For the MAX-MIN criterion, we show that if the distances do not satisfy the triangle inequality, there is no polynomial time relative approximation algorithm unless P=NP. When the distances do satisfy the triangle inequality, we present an efficient heuristic which provides a performance guarantee of 2, thus improving the performance guarantee of 3 proven in [Wh91]. We also prove that obtaining a performance guarantee of less than 2 is NP-hard. For the MAX-AVG criterion, we present a heuristic which provides a performance guarantee of 4, provided that the distances satisfy the triangle inequality. For the 1-dimensional dispersion problem, we provide polynomial time algorithms for obtaining optimal solutions under both MAX-MIN and MAX-AVG criteria. Using the latter algorithm, we obtain a heuristic which provides a performance guarantee of 4(\(\sqrt 2 - 1\)) ≈ 1.657 for the 2-dimensional dispersion problem under the MAX-AVG criterion.

A class of methods for solving large, convex quadratic programs subject to box constraints

Abstract: In this paper we analyze conjugate gradient-type algorithms for solving convex quadratic programs subject only to box constraints (i.e., lower and upper bounds on the variables). Programs of this type, which we denote by BQP, play an important role in many optimization models and algorithms. We propose a new class of finite algorithms based on a nonfinite heuristic for solving a large, sparse BQP. The numerical results suggest that these algorithms are competitive with Dembo and Tulowitzski's (1983) CRGP algorithm in general, and perform better than CRGP for problems that have a low percentage of free variables at optimality, and for problems with only nonnegativity constraints.

An algorithm for the manufacturing equipment selection problem

Abstract: This paper provides a unified framework in which product and process demands can be related to manufacturing system requirements. A nonlinear cost minimization model is developed that can be used by facility planners to guide the analyses underlying the equipment selection problem. The approach extends current work by accounting for machine flexibility. The objective is to determine how many of each machine type to purchase, as well as what fraction of the time each piece of equipment will be configured for a particular type of operation. The resultant problem is solved with a depth-first branch and bound routine that employs a greedy set covering heuristic to find good feasible solutions. This permits early fathoming and greatly contributes to the efficiency of the algorithm. A small example is presented to highlight the computations. This is followed by a discussion of me results for a series of test problems designed to evaluate overall algorithmic performance. We show mat 16 process, 25 machi...