Showing papers on "Heuristic published in 2004"

Revenue Management Under a General Discrete Choice Model of Consumer Behavior

Abstract: Customer choice behavior, such as buy-up and buy-down, is an important phenomenon in a wide range of revenue management contexts. Yet most revenue management methodologies ignore this phenomenon - or at best approximate it in a heuristic way. In this paper, we provide an exact and quite general analysis of this problem. Specifically, we analyze a single-leg reserve management problem in which the buyers' choice behavior is modeled explicitly. The choice model is very general, simply specifying the probability of purchase for each fare product as a function of the set of fare products offered. The control problem is to decide which subset of fare products to offer at each point in time. We show that the optimal policy for this problem has a quite simple form. Namely, it consists of identifying an ordered family of "efficient" subsets S 1 ,..., S m , and at each point in time opening one of these sets S k , where the optimal index k is increasing in the remaining capacity x and decreasing in the remaining time. That is, the more capacity (or less time) available, the further the optimal set is along this sequence. We also show that the optimal policy is a nested allocation policy if and only if the sequence of efficient sets is nested, that is S 1 ? S 2 ?... ? S m . Moreover, we give a characterization of when nesting by fare order is optimal. We also develop an estimation procedure for this setting based on the expectation-maximization (EM) method that jointly estimates arrival rates and choice model parameters when no-purchase outcomes are unobservable. Numerical results are given to illustrate both the model and estimation procedure.

A New Placement Heuristic for the Orthogonal Stock-Cutting Problem

Abstract: This paper presents a new best-fit heuristic for the two-dimensional rectangular stock-cutting problem and demonstrates its effectiveness by comparing it against other published approaches. A placement algorithm usually takes a list of shapes, sorted by some property such as increasing height or decreasing area, and then applies a placement rule to each of these shapes in turn. The proposed method is not restricted to the first shape encountered but may dynamically search the list for better candidate shapes for placement. We suggest an efficient implementation of our heuristic and show that it compares favourably to other heuristic and metaheuristic approaches from the literature in terms of both solution quality and execution time. We also present data for new problem instances to encourage further research and greater comparison between this and future methods.

A hybrid heuristic for DAG scheduling on heterogeneous systems

Abstract: Summary form only given. This paper is motivated by the observation that different methods to compute the weights of nodes and edges when scheduling DAGs onto heterogeneous machines may lead to significant variations in the generated schedule. To minimize such variations, we present a novel heuristic for DAG scheduling, which is based upon solving a series of independent task scheduling problems. A novel heuristic for the latter problem is also included. Both heuristics compare favourably with other related heuristics.

Incorporating inventory control decisions into a strategic distribution network design model with stochastic demand

Abstract: In this paper, we propose a simultaneous approach to incorporate inventory control decisions––such as economic order quantity and safety stock decisions––into typical facility location models, which are used to solve the distribution network design problem. A simultaneous model is developed considering a stochastic demand, modeling also the risk pooling phenomenon. We present a non-linear-mixed-integer model and a heuristic solution approach, based on Lagrangian relaxation and the sub-gradient method. In a numerical application, we found that the potential cost reduction, compared to the traditional approach, increases when the holding costs and/or the variability of demand are higher.

New and improved approaches for shared-path protection in WDM mesh networks

Abstract: This paper investigates the problem of dynamic survivable lightpath provisioning in optical mesh networks employing wavelength-division multiplexing (WDM). In particular, we focus on shared-path protection because it is resource efficient due to the fact that backup paths can share wavelength links when their corresponding working paths are mutually diverse. Our main contributions are as follows. 1) First, we prove that the problem of finding an eligible pair of working and backup paths for a new lightpath request requiring shared-path protection under the current network state is NP-complete. 2) Then, we develop a heuristic, called CAFES, to compute a feasible solution with high probability. 3) Finally, we design another heuristic, called OPT, to optimize resource consumption for a given solution. The merits of our approaches are that they capture the essence of shared-path protection and approach to optimal solutions without enumerating paths. We evaluate the effectiveness of our heuristics and the results are found to be promising.

The Effort Heuristic

Abstract: The research presented here suggests that effort is used as a heuristic for quality. Participants rating a poem (Experiment 1), a painting (Experiment 2), or a suit of armor (Experiment 3) provided higher ratings of quality, value, and liking for the work the more time and effort they thought it took to produce. Experiment 3 showed that the use of the effort heuristic, as with all heuristics, is moderated by ambiguity: Participants were more influenced by effort when the quality of the object being evaluated was difficult to ascertain. Discussion centers on the implications of the effort heuristic for everyday judgment and decision-making.

A planning heuristic based on causal graph analysis

Abstract: In recent years, heuristic search methods for classical planning have achieved remarkable results. Their most successful representative, the FF algorithm, performs well over a wide spectrum of planning domains and still sets the state of the art for STRIPS planning. However, there are some planning domains in which algorithms like FF and HSP perform poorly because their relaxation method of ignoring the "delete lists" of STRIPS operators loses too much vital information. Planning domains which have many dead ends in the search space are especially problematic in this regard. In some domains, dead ends are readily found by the human observer yet remain undetected by all propositional planning systems we are aware of. We believe that this is partly because the STRIPS representation obscures the important causal structure of the domain, which is evident to humans. In this paper, we propose translating STRIPS problems to a planning formalism with multi-valued state variables in order to expose this underlying causal structure. Moreover, we show how this structure can be exploited by an algorithm for detecting dead ends in the search space and by a planning heuristic based on hierarchical problem decomposition. Our experiments show excellent overall performance on the benchmarks from the international planning competitions.

Particle swarm optimization algorithm for single machine total weighted tardiness problem

Abstract: In This work we present a particle swarm optimization algorithm to solve the single machine total weighted tardiness problem. A heuristic rule, the smallest position value (SPV) rule, is developed to enable the continuous particle swarm optimization algorithm to be applied to all classes of sequencing problems, which are NP-hard in the literature. A simple but very efficient local search method is embedded in the particle swarm optimization algorithm. The computational results show that the particle swarm algorithm is able to find the optimal and best-known solutions on all instances of widely used benchmarks from the OR library.

Breadth-first heuristic search

Abstract: Recent work shows that the memory requirements of best-first heuristic search can be reduced substantially by using a divide-and-conquer method of solution reconstruction. We show that memory requirements can be reduced even further by using a breadth-first instead of a best-first search strategy. We describe optimal and approximate breadth-first heuristic search algorithms that use divide-and-conquer solution reconstruction. Computational results show that they outperform other optimal and approximate heuristic search algorithms in solving domain-independent planning problems.

Ant colony optimization and local search for bin packing and cutting stock problems

Abstract: The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimization problems. Exact solution methods can only be used for very small instances, so for real-world problems, we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In the work presented here, we used an ant colony optimization (ACO) approach to solve both Bin Packing and Cutting Stock Problems. We present a pure ACO approach, as well as an ACO approach augmented with a simple but very effective local search algorithm. It is shown that the pure ACO approach can compete with existing evolutionary methods, whereas the hybrid approach can outperform the best-known hybrid evolutionary solution methods for certain problem classes. The hybrid ACO approach is also shown to require different parameter values from the pure ACO approach and to give a more robust performance across different problems with a single set of parameter values. The local search algorithm is also run with random restarts and shown to perform significantly worse than when combined with ACO.

Approximate Solutions for Partially Observable Stochastic Games with Common Payoffs

Abstract: Partially observable decentralized decision making in robot teams is fundamentally different from decision making in fully observable problems. Team members cannot simply apply single-agent solution techniques in parallel. Instead, we must turn to game theoretic frameworks to correctly model the problem. While partially observable stochastic games (POSGs) provide a solution model for decentralized robot teams, this model quickly becomes intractable. We propose an algorithm that approximates POSGs as a series of smaller, related Bayesian games, using heuristics such as QMDP to provide the future discounted value of actions. This algorithm trades off limited look-ahead in uncertainty for computational feasibility, and results in policies that are locally optimal with respect to the selected heuristic. Empirical results are provided for both a simple problem for which the full POSG can also be constructed, as well as more complex, robot-inspired, problems.

An overview of heuristic solution methods

Abstract: Besides those analysts who are already familiar with a number of heuristic methods, this paper should also be of interest to those analysts and managers who, although not yet aware of specific heuristic approaches, are quite comfortable with the use of mathematical modelling as an aid to decision making. It is concerned with obtaining usable solutions to well-defined mathematical representations of real-world problem situations. Heuristic procedures are defined and reasons for their importance are listed. A wide variety of heuristic methods, including several metaheuristics, are described. In each case, references for further details, including applications, are provided. There is also considerable discussion related to performance evaluation.

Conformant Planning via Heuristic Forward Search: A New Approach

Abstract: Conformant planning is the task of generating plans given uncertainty about the initial state and action effects, and without any sensing capabilities during plan execution. The plan should be successful regardless of which particular initial world we start from. It is well known that conformant planning can be transformed into a search problem in belief space, the space whose elements are sets of possible worlds. We introduce a new representation of that search space, replacing the need to store sets of possible worlds with a need to reason about the effects of action sequences. The reasoning is done by deciding solvability of CNFs that capture the action sequence's semantics. Based on this approach, we extend the classical heuristic planning system FF to the conformant setting. The key to this extension is the introduction of approximative CNF reasoning in FF's heuristic function. Our experimental evaluation shows Conformant-FF to be superior to the state-of-the-art conformant planners MBP, KACMBP, and GPT in a variety of benchmark domains.

Using Clustering Techniques to Improve the Performance of a Multi-objective Particle Swarm Optimizer

Abstract: In this paper, we present an extension of the heuristic called “particle swarm optimization” (PSO) that is able to deal with multiobjective optimization problems. Our approach uses the concept of Pareto dominance to determine the flight direction of a particle and is based on the idea of having a set of sub-swarms instead of single particles. In each sub-swarm, a PSO algorithm is executed and, at some point, the different sub-swarms exchange information. Our proposed approach is validated using several test functions taken from the evolutionary multiobjective optimization literature. Our results indicate that the approach is highly competitive with respect to algorithms representative of the state-of-the-art in evolutionary multiobjective optimization.

Choosing search heuristics by non-stationary reinforcement learning

Abstract: Search decisions are often made using heuristic methods because real-world applications can rarely be tackled without any heuristics. In many cases, multiple heuristics can potentially be chosen, and it is not clear a priori which would perform best. In this article, we propose a procedure that learns, during the search process, how to select promising heuristics. The learning is based on weight adaptation and can even switch between different heuristics during search. Different variants of the approach are evaluated within a constraint-programming environment.

Solving Examination Timetabling Problems through Adaption of Heuristic Orderings

Abstract: Heuristic ordering based methods, very similar to those used for graph colouring problems, have long been applied successfully to the examination timetabling problem. Despite the success of these methods on real life problems, even with limited computing resources, the approach has the fundamental flaw that it is only as effective as the heuristic that is used. We present a method that adapts to suit a particular problem instance “on the fly.” This method provides an alternative to existing forms of ‘backtracking,’ which are often required to cope with the possible unsuitability of a heuristic. We present a range of experiments on benchmark problems to test and evaluate the approach. In comparison to other published approaches to solving this problem, the adaptive method is more general, significantly quicker and easier to implement and produces results that are at least comparable (if not better) than the current state of the art. We also demonstrate the level of generality of this approach by starting it with the inverse of a known good heuristic, a null ordering and random orderings, showing that the adaptive method can transform a bad heuristic ordering into a good one.

Monte-carlo go developments

Abstract: We describe two Go programs, Olga and Oleg, developed by a Monte-Carlo approach that is simpler than Bruegmann’s (1993) approach. Our method is based on Abramson (1990). We performed experiments, to assess ideas on (1) progressive pruning, (2) all moves as first heuristic, (3) temperature, (4) simulated annealing, and (5) depth-two tree search within the Monte-Carlo framework. Progressive pruning and the all moves as first heuristic are good speed-up enhancements that do not deteriorate the level of the program too much. Then, using a constant temperature is an adequate and simple heuristic that is about as good as simulated annealing. The depth-two heuristic gives deceptive results at the moment. The results of our Monte-Carlo programs against knowledge-based programs on 9x9 boards are promising. Finally, the ever-increasing power of computers lead us to think that Monte-Carlo approaches are worth considering for computer Go in the future.

A lookahead strategy for heuristic search planning

Abstract: Relaxed plans are used in the heuristic search planner FF for computing a numerical heuristic and extracting helpful actions. We present a novel way for extracting information from the relaxed plan and for dealing with helpful actions, by considering the high quality of the relaxed plans in numerous domains. For each evaluated state, we employ actions from these plans in order to find the beginning of a valid plan that can lead to a reachable state. We use this lookahead strategy in a complete best-first search algorithm, modified in order to take into account helpful actions. In numerous planning domains, the performance of heuristic search planning and the size of the problems that can be handled have been drastically improved.

Travel Time Estimation and Order Barching in a 2-Block Warehouse

Abstract: textThe order batching problem (OBP) is the problem of determining the number of orders to be picked together in one picking tour. Although various objectives may arise in practice, minimizing the average throughput time of a random order is a common concern. In this paper, we consider the OBP for a 2-block rectangular warehouse with the assumptions that orders arrive according to a Poisson process and the method used for routing the order-pickers is the well-known S-shape heuristic. We first elaborate on the first and second moment of the order-picker's travel time. Then we use these moments to estimate the average throughput time of a random order. This enables us to estimate the optimal picking batch size. Results from simulation show that the method provides a high accuracy level. Furthermore, the method is rather simple and can be easily applied in practice.