Showing papers on "Heuristic published in 1996"

Acting under uncertainty: discrete Bayesian models for mobile-robot navigation

Abstract: Discrete Bayesian models have been used to model uncertainty for mobile-robot navigation, but the question of how actions should be chosen remains largely unexplored. This paper presents the optimal solution to the problem, formulated as a partially observable Markov decision process. Since solving for the optimal control policy is intractable, in general, it goes on to explore a variety of heuristic control strategies. The control strategies are compared experimentally, both in simulation and in runs on a robot.

MAC and combined heuristics: two reasons to forsake FC (and CBJ?) on hard problems

Abstract: In the last twenty years, many algorithms and heuristics were developed to find solutions in constraint networks. Their number increased to such an extent that it quickly became necessary to compare their performances in order to propose a small number of "good" methods. These comparisons often led us to consider FC or FC-CBJ associated with a "minimum domain" variable ordering heuristic as the best techniques to solve a wide variety of constraint networks. In this paper, we first try to convince once and for all the CSP community that MAC is not only more efficient than FC to solve large practical problems, but it is also really more efficient than FC on hard and large random problems. Afterwards, we introduce an original and efficient way to combine variable ordering heuristics. Finally, we conjecture that when a good variable ordering heuristic is used, CBJ becomes an expensive gadget which almost always slows down the search, even if it saves a few constraint checks.

Theory and Methodology A fast and effective heuristic for the orienteering problem

Abstract: In the orienteering problem, start and end points are specified along with other locations which have associated scores. Given a fixed amount of time, the goal is to determine a path from the start point to the end point through a subset of locations in order to maximize the total path score. In this paper, a fast and extremely effective heuristic is presented and tested on 67 problems taken from the literature and 40 new test problems. The computational results are presented in detail.

A Lagrangean-based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times

Abstract: In this paper a heuristic approach for the dynamic multilevel multiitem lotsizing problem in general product structures with multiple constrained resources and setup times is proposed. With the help of Lagrangean relaxation the capacitated multilevel multiitem lotsizing problem is decomposed into several uncapacitated single-item lotsizing problems. From the solutions of these single-item problems lower bounds on the minimum objective function value are derived. Upper bounds are generated by means of a heuristic finite scheduling procedure. The quality of the approach is tested with reference to various problem groups of differing sizes.

The constrainedness of search

Abstract: We introduce a parameter that measures the "constrainedness" of an ensemble of combinatorial problems. If problems are over-constrained, they are likely to be insoluble. If problems are under-constrained, they are likely to be soluble. This constrainedness parameter generalizes a number of parameters previously used in different NP-complete problem classes. Phase transitions in different NP classes can thus be directly compared. This parameter can also be used in a heuristic to guide search. The heuristic captures the intuition of making the most constrained choice first, since it is often useful to branch into the least constrained subproblem. Many widely disparate heuristics can be seen as minimizing constrainedness.

Genetic Algorithms for Product Design

Abstract: Product design is increasingly recognized as a critical activity that has a significant impact on the performance of firms. Consequently, when firms undertake a new existing product design redesign activity, it is important to employ techniques that will generate optimal solutions. As optimal product design using conjoint analysis data is an NP-hard problem, heuristic techniques for its solution have been proposed. This research proposes the use of and evaluates the performance of Genetic Algorithms GA, which is based on the principles of natural selection, as an alternative procedure for generating "good" i.e., close to optimal solutions for the product design problem. The paper focuses on 1 how GA can be applied to the product design problems, 2 determining the comparative performance of GA vis-i-vis the dynamic programming DP heuristic Kohli and Krishnamurti [Kohli, R., R. Krishnamurti. 1987. A heuristic approach to product design. Management Sci.3312 1523-1533.], [Kohli, R., R. Krishnamurti. 1989. Optimal product design using conjoint analysis: Computational complexity and algorithms. Eur. J. Oper. Res.40 186-195.] in generating solutions to the product design problems, 3 the sensitivity of the GA solutions to variations in parameter choices, and 4 generalizing the results of the dynamic programming heuristic to product designs involving attributes with varying number of levels and studying the impact of alternate attribute sequencing rules.

A Dynamic Subgradient-Based Branch-and-Bound Procedure for Set Covering

Abstract: We discuss a branch and bound algorithm for set covering, whose centerpiece is a new integrated upper bounding/lower bounding procedure called dynamic subgradient optimization DYNSGRAD. This new procedure, applied to a Lagrangean dual at every node of the search tree, combines the standard subgradient method with primal and dual heuristics that interact to change the Lagrange multipliers and tighten the upper and lower bounds, fix variables, and periodically restate the Lagrangean itself. Extensive computational testing is reported. As a stand-alone heuristic, DYNSGRAD performs significantly better than other procedures in terms of the quality of solutions obtainable with a certain computational effort. When incorporated into a branch-and-bound algorithm, DYNSGRAD considerably advances the state of the art in solving set covering problems.

Heuristics for the integer one-dimensional cutting stock problem: A computational study

Abstract: In this paper the problem of generating integer solutions to the standard one-dimensional cutting stock problem is treated. In particular, we study a specific class of heuristic approaches that have been proposed in the literature, and some straightforward variants. These methods are compared with respect to solution quality and computing time. Our evaluation is based on having solved 4,000 randomly generated test problems. Not only will it be shown that two methods are clearly superior to the others but also that they solve almost any instance of the standard one-dimensional cutting stock problem to an optimum.

A heuristic estimator for means-ends analysis in planning

Abstract: Means-ends analysis is a seemingly well understood search technique, which can be described, using planning terminology, as: keep adding actions that are feasible and achieve pieces of the goal. Unfortunately, it is often the case that no action is both feasible and relevant in this sense. The traditional answer is to make subgoals out of the preconditions of relevant but infeasible actions. These subgoals become part of the search state. An alternative, surprisingly good, idea is to recompute the entire subgoal hierarchy after every action. This hierarchy is represented by a greedy regression-match graph. The actions near the leaves of this graph are feasible and relevant to a sub...subgoals of the original goal. Furthermore, each subgoal is assigned an estimate of the number of actions required to achieve it. This number can be shown in practice to be a useful heuristic estimator for domains that are otherwise intractable.

Adaptive search for solving hard project scheduling problems

Abstract: In this article we propose a new heuristic solution technique for resource-constrained project scheduling problems. Basically, it is a hybrid of priority rule and random search techniques which employs two types of adaptations in order to determine the solution space. We enhance this general scheme by the use of a new priority rule and by lower bounding techniques. The method is evaluated by comparing it with other recently proposed heuristics on a widely used set of benchmark-instances. Furthermore, we show that the procedure can be usefully applied to solve different hard problems within the field of project scheduling. © 1996 John Wiley & Sons, Inc.

Heuristic-biased stochastic sampling

Abstract: This paper presents a search technique for scheduling problems, called Heuristic-Biased Stochastic Sampling (HBSS). The underlying assumption behind the HBSS approach is that strictly adhering to a search heuristic often does not yield the best solution and, therefore, exploration off the heuristic path can prove fruitful. Within the HBSS approach, the balance between heuristic adherence and exploration can be controlled according to the confidence one has in the heuristic. By varying this balance, encoded as a bias function, the HBSS approach encompasses a family of search algorithms of which greedy search and completely random search are extreme members. We present empirical results from an application of HBSS to the real-world problem of observation scheduling. These results show that with the proper bias function, it can be easy to outperform greedy search.

A new model for optimal routing and wavelength assignment in wavelength division multiplexed optical networks

Abstract: We consider the problem of routing and assignment of wavelength (RAW) in optical networks. Given a set of requests for all-optical connections (or lightpaths), the problem is to (a) find routes from the source nodes to their respective destination nodes, and (b) assign wavelengths to these routes. Since the number of wavelengths is limited, lightpaths cannot be established between every pair of access nodes. In this paper we first consider the dynamic RAW problem where lightpath requests arrive randomly with exponentially distributed call holding times. Then, the static RAW problem is considered which assumes that all the lightpaths that are to be set-up in the network are known initially. Several heuristic algorithms have already been proposed for establishing a maximum number of lightpaths out of a given set of requests. However most of these algorithms are based an the traditional model of circuit-switched networks where routing and wavelength assignment steps are decoupled. In this paper a new graph-theoretic formulation of the RAW problem, dubbed as layered-graph, has been proposed which provides an efficient tool for solving dynamic as well as static RAW problems. The layered-graph model also provides a framework for obtaining exact optimal solution for the number of requested lightpaths as well as far the throughput that a given network can support. A dynamic and two static RAW schemes are proposed which are based on the layered-graph model. Layered-graph-based RAW schemes are shown to perform better than the existing ones.

Hierarchical A *: searching abstraction hierarchies efficiently

Abstract: ion, in search, problem solving, and planning, works by replacing one state space by another (the "abstract" space) that is easier to search. The results of the search in the abstract space are used to guide search in the original space. For instance, the length of the abstract solution can be used as a heuristic for A* in searching in the original space. However, there are two obstacles to making this work efficiently. The first is a theorem (Valtorta, 1984) stating that for a large class of abstractions, "embedding abstractions," every state expanded by blind search must also be expanded by A* when its heuristic is computed in this way. The second obstacle arises because in solving a problem A* needs repeatedly to do a full search of the abstract space while computing its heuristic. This paper introduces a new abstraction-induced search technique, "Hierarchical A*," that gets around both of these difficulties: first, by drawing from a different class of abstractions, "homomorphism abstractions," and, secondly, by using novel caching techniques to avoid repeatedly expanding the same states in successive searches in the abstract space. Hierarchical A* outperforms blind search on all the search spaces studied.

An (s,Q) inventory model with remanufacturing and disposal

Abstract: textIn this paper we analyse an (s, Q) inventory model in which used products can be remanufactured to new ones. We develop two approximations for the average costs and compare their performance with that of an approximation suggested by Muckstadt and Isaac. Next we extend the model with the option to dispose returned products and present a heuristic optimisation procedure which is checked with full enumeration.

An Improved Petal Heuristic for the Vehicle Routeing Problem

Abstract: Solutions produced by the first generation of heuristics for the vehicle routeing problem are often far from optimal. Recent adaptations of local search improvement heuristics, like tabu search, produce much better solutions but require increased computing time. However there are situations where good solutions must be obtained quickly. The algorithm proposed in this paper yields solutions almost as good as those produced by tabu search adaptations, but at only a small fraction of their computing time. This heuristic can be seen as an improved version of the original petal heuristic. On 14 benchmark test problems, the proposed heuristic yields solutions whose values lie on average within 2.38% of that of the best known solutions.

Using the deterministic EOQ formula in stochastic inventory control

Abstract: This note gives an improved bound √5-2/2 ≈ 0.1180 for the relative cost increase when using the deterministic EOQ formula as a heuristic solution when demands are stochastic. We also discuss under what circumstances this bound is tight.

Finding optimal solutions to the twenty-four puzzle

Abstract: We have found the first optimal solutions to random instances of the Twenty-Four Puzzle, the 5 × 5 version of the well-known sliding-tile puzzles. Our new contribution to this problem is a more powerful admissible heuristic function. We present a general theory for the automatic discovery of such heuristics, which is based on considering multiple subgoals simultaneously. In addition, we apply a technique for pruning duplicate nodes in depth-first search using a finitestate machine. Finally, we observe that as heuristic search problems are scaled up, more powerful heuristic functions become both necessary and cost-effective.

A Genetic Algorithm for Vehicle Routing with Backhauling

Abstract: In this paper, a greedy route construction heuristic for a vehicle routing problem with backhauling is described. This heuristic inserts customers one by one into the routes using a fixed a priori ordering of customers. Then, a genetic algorithm is used to identify an ordering that produces good routes. Numerical comparisons are provided with an exact algorithm and with other heuristic approaches.