Showing papers on "Incremental heuristic search published in 1999"

Landscapes, operators and heuristic search

Abstract: Heuristic search methods have been increasingly applied to combinatorial optimizationproblems. While a specific problem defines a unique search space, different “landscapes”are created by the different heuristic search operators used to search it. In this paper, asimple example will be used to illustrate the fact that the landscape structure changes withthe operator; indeed, it often depends even on the way the operators are applied. Recentattention has focused on trying to better understand the nature of these “landscapes”. Recentwork by Boese et al. [2] has shown that instances of the TSP are often characterised by a“big valley” structure in the case of a 2‐opt exchange operator, and a particular distancemetric. In this paper, their work is developed by investigating the question of how landscapeschange under different search operators in the case of the n/m/P/Cmax flowshop problem.Six operators and four distance metrics are defined, and the resulting landscapes examined.The work is further extended by proposing a statistical randomisation test to provide anumerical assessment of the landscape. Other conclusions relate to the existence of ultra‐metricity,and to the usefulness or otherwise of hybrid neighbourhood operators.

Search Procedures and Parallelism in Constraint Programming

Abstract: In this paper, we present a major improvement in the search procedures in constraint programming. First, we integrate various search procedures from AI and OR. Second, we parallelize the search on shared-memory computers. Third, we add an object-oriented extensible control language to implement complex complete and incomplete search procedures. The result is a powerful set of tools which offers both brute force search using simple search procedures and parallelism, and finely tuned search procedures using that expressive control language. With this, we were able both to solve difficult and open problems using complete search procedures, and to quickly produce good results using incomplete search procedures.

Reactive grasp and tabu search based heuristics for the single source capacitated plant location problem

Abstract: This paper considers the Single Source Capacitated Plant Location Problem (SSCPLP). SSCPLP is a discrete location problem. It allows capacities on the plants to be opened and constrains each client to be served by a single open plant. The following algorithms are proposed: A Reactive GRASP heuristic; a Tabu Search heuristic; and two different hybrid approaches that combine elements of the GRASP and the Tabu Search methodologies. The elements of the proposed heuristics are presented. The Reactive GRASP algorithm is a self-tuning heuristic in which the calibration process is replaced by an automated criterion for selecting the parameter value. The Tabu Search heuristic provides the framework for the first of the hybrid approaches. It consists of two phases. The GRASP methodology is used for the first one, which can be viewed as a strong diversification mechanism. The second one consists of an intensification phase. The second hybrid algorithm follows the framework of the Reactive GRASP heuristic. It...

A parallel algorithm for the vehicle routing problem with time window constraints

Abstract: In this paper, we describe a new parallel tabu search heuristic for the vehicle routingproblem with time window constraints (VRPTW). The neighborhood structure we proposeis based on simple customer shifts and allows us to consider infeasible interim‐solutions.Similarly to the column generation approach used in exact algorithms, all routes generatedby the tabu search heuristic are collected in a pool. To obtain a new initial solution forthe tabu search heuristic, a fast set covering heuristic is periodically applied to the routes inthe pool. The parallel heuristic has been implemented on a Multiple‐Instruction Multiple‐Datacomputer architecture with eight nodes. Computational results for Solomon's benchmarkproblems demonstrate that our parallel heuristic can produce high‐quality solutions.

State of the art in parallel search techniques for discrete optimization problems

Abstract: Discrete optimization problems arise in a variety of domains, such as VLSI design, transportation, scheduling and management, and design optimization. Very often, these problems are solved using state space search techniques. Due to the high computational requirements and inherent parallel nature of search techniques, there has been a great deal of interest in the development of parallel search methods since the dawn of parallel computing. Significant advances have been made in the use of powerful heuristics and parallel processing to solve large-scale discrete optimization problems. Problem instances that were considered computationally intractable only a few years ago are routinely solved currently on server-class symmetric multiprocessors and small workstation clusters. Parallel game-playing programs are challenging the best human minds at games like chess. In this paper, we describe the state of the art in parallel algorithms used for solving discrete optimization problems. We address heuristic and nonheuristic techniques for searching graphs as well as trees, and speed-up anomalies in parallel search that are caused by the inherent speculative nature of search techniques.

A Set-Partitioning-Based Heuristic for the Vehicle Routing Problem

Abstract: We develop a generic tabu search heuristic for solving the well-known vehicle routing problem. This algorithm explores the advantages of simple local search and improvement heuristics as well as a complex meta-heuristic. The solutions generated by these heuristics are selected and assembled by a set-partitioning model to produce superior solutions. Computational experience on standard benchmark problems is discussed and comparisons with other up-to-date heuristic methods are provided.

Synthesizing a predatory search strategy for VLSI layouts

Abstract: When searching for prey, many predator species exhibit a remarkable behavior: after prey capture, the predators promptly engage in "area-restricted search", probing for consecutive captures nearby. Biologists have been surprised with the efficiency and adaptability of this search strategy to a great number of habitats and prey distributions. We propose to synthesize a similar search strategy for the massively multimodal problems of combinatorial optimization. The predatory search strategy restricts the search to a small area after each new improving solution is found. Subsequent improvements are often found during area-restricted search. Results of this approach to gate matrix layout, an important problem arising in very large scale integrated (VLSI) architectures, are presented. Compared to established methods over a set of benchmark circuits, predatory search is able to either match or outperform the best-known layouts. Additional remarks address the relation of predatory search to the "big-valley" hypothesis and to the field of artificial life.

Optimizing a Ring-Based Private Line Telecommunication Network Using Tabu Search

Abstract: One of the private line network design problems in the telecommunications industry is to interconnect a set of customer locations through a ring of end offices so as to minimize the total tariff cost and provide reliability. We develop a Tabu Search method for the problem that incorporates long term memory, probabilistic move selections, hierarchical move evaluation, candidate list strategies and an elite solution recovery strategy. Computational results for test data show that the Tabu Search heuristic finds optimal solutions for all test problems that can be solved exactly by a branch-and-cut algorithm, while running about three orders of magnitude faster than the exact algorithm. In addition, for larger size problems that cannot be solved exactly, the tabu search algorithm outperforms the best local search heuristic currently available. The performance gap favoring Tabu Search increases significantly for more difficult problem instances.

Solving Employee Timetabling Problems by Generalized Local Search

Abstract: Employee timetabling is the operation of assigning employees to tasks in a set of shifts during a fixed period of time, typically a week.We present a general definition of employee timetabling problems (ETPs) that captures many real world problem formulations and includes complex constraints.We investigate the use of several local search techniques for solving ETPs. In particular, we propose a generalization of local search that makes use of a novel search space that includes also partial assignments. We describe the distinguishing features of this generalized local search that allows it to navigate the search space effectively. We show that, on large and difficult instances of real world ETPs, where systematic search fails, local search methods perform well and solve the hardest instances. According to our experimental results on various local search techniques, generalized local search is the best method for solving large ETP instances.

Multi-level Cooperative Search: A New Paradigm for Combinatorial Optimization and an Application to Graph Partitioning

Abstract: Cooperative search is a parallelization strategy for search algorithms where parallelism is obtained by concurrently executing several search programs. The solution space is implicitly decomposed according to the search strategy of each program. The programs cooperate by exchanging information on previously explored regions of the solution space. In this paper we propose a new design for cooperative search algorithms which is also a new parallel problem solving paradigm for combinatorial optimization problems. Our new design is based on an innovative approach to decompose the solution space which is inspired from the modeling of cooperative algorithms based on dynamical systems theory. Our design also gives a new purpose to the sharing of information among cooperating tasks based on principles borrowed from scatter search evolutionary algorithms. We have applied this paradigm to the graph partitioning problem. We describe the parallel implementation of this algorithm on a cluster of workstations and compare our results with other well known graph partitioning methods.

GRT: A Domain Independent Heuristic for STRIPS Worlds Based on Greedy Regression Tables

Abstract: This paper presents Greedy Regression Tables (GRT), a new domain independent heuristic for STRIPS worlds. The heuristic can be used to guide the search process of any state-space planner, estimating the distance between each intermediate state and the goals. At the beginning of the problem solving process a table is created, the records of which contain the ground facts of the domain, among with estimates for their distances from the goals. Additionally, the records contain information about interactions that occur while trying to achieve different ground facts simultaneously. During the search process, the heuristic, using this table, extracts quite accurate estimates for the distances between intermediate states and the goals. A simple best-first search planner that uses this heuristic has been implemented in C++ and has been tested on several “classical” problem instances taken from the bibliography and on some new taken from the AIPS-98 planning competition. Our planner has proved to be faster in all of the cases, finding also in most (but not all) of the cases shorter solutions.

On cooperation between evolutionary algorithms and other search paradigms

Abstract: We present a multi-agent based approach for achieving cooperation between search systems employing different search paradigms. The search agents periodically interrupt their search, select interesting information from their states that is transmitted to the other agents, filter the information sent to them with respect to their own demands, integrate the remaining information into their search, and then continue the search. There are different kinds of information to be exchanged and the selection is both success- and demand-driven. We demonstrate the usefulness of this approach by coupling a search system based on a genetic algorithm and a branch-and-bound based system for job-shop-scheduling. Our experiments show that the cooperation results in finding better solutions within a given time limit and in finding solutions comparable to those generated by the best system working alone in less time. The speed-up factors for some examples even exceed the number of agents (computers) used.

Fast planning through greedy action graphs

Abstract: Domain-independent planning is a notoriously hard search problem. Several systematic search techniques have been proposed in the context of various formalisms. However, despite their theoretical completeness, in practice these algorithms are incomplete because for many problems the search space is too large to be (even partially) explored.In this paper we propose a new search method in the context of Blum and Furst's planning graph approach, which is based on local search. Local search techniques are incomplete, but in practice they can efficiently solve problems that are unsolvable for current systematic search methods. We introduce three heuristics to guide the local search (Walkplan, Tabuplan and T-Walkplan), and we propose two methods for combining local and systematic search.Our techniques are implemented in a system called GPG, which can be used for both plan-generation and plan-adaptation tasks. Experimental results show that GPG can efficiently solve problems that are very hard for current planners based on planning graphs.

Designing a tabu search algorithm for the two-stage flow shop problem with secondary criterion

Abstract: This paper discusses the process of desigining a tabu search-based heuristic for the two-stage flow shop problem with makespan minimization as the primary criterion and the minimization of total flow time as the secondary criterion. A factorial experiment is designed to analyse thoroughly the effects of four different factors, i.e. the initial solution, type of move, size of neighbourhood and the list size, on the performance of the tabu search-based heuristic. Using the techniques of evolution curves, and response tables and response graphs, coupled with the Taguchi method, the best combination of the factors for the tabu search-based heuristic is identified, and the effectiveness of the heuristic algorithm in finding an optimal solution is evaluated by comparing its performance with the best known heuristic to solve this problem.

Domain-dependent single-agent search enhancements

Abstract: AI research has developed an extensive collection of methods to solve state-space problems. Using the challenging domain of Sokoban, this paper studies the effect of search enhancements on program performance. We show that the current state of the art in AT generally requires a large programming and research effort into domain-dependent: methods to solve even moderately complex problems in such difficult domains. The application of domain-specific knowledge to exploit properties of the search space can result in large reductions in the size of the search tree, often several orders of magnitude per search enhancement. Understanding the effect of these enhancements on the search leads to a new taxonomy of search enhancements, and a new framework for developing single-agent search applications. This is used to illustrate the large gap between what is portrayed in the literature versus what is needed in practice.

Texture measurements as a basis for heuristic commitment techniques in constraint-directed scheduling

Abstract: The central thesis of this dissertation is that an understanding of the structure of a problem leads to high-quality heuristic problem solving performance in constraint-directed scheduling. Our methods for gaining an understanding of problem structure focus on texture measurements: algorithms that implement dynamic analyses of each search state. Texture measurements distill structural information from the constraint graph representation of a search state which is then used as a basis for heuristic decision-making. To enable the rigorous empirical investigation of the above thesis in the context of real-world scheduling problems, we define the ODO framework for constraint-directed search. The framework allows us to implement scheduling algorithms and their components, and to compare them both from the perspective of static similarities and on the basis of empirical performance. In this dissertation, we extend the scope of scheduling problems that can be addressed, in general, by constraint-directed techniques. Specifically, we develop the concept of a generalized measure of constraint criticality that enables the construction of dynamic, opportunistic heuristic commitment techniques. Based on an analysis of the requirements of a measure of constraint criticality, we suggest the probability of breakage of a constraint as such a measure. The investigation of our thesis focuses on three classes of scheduling problems: job shop scheduling, scheduling with inventory, and scheduling with alternative activities. In each of these problem classes we empirically demonstrate that, as a problem becomes more complex, knowledge of its structure has a dominant role in guiding heuristic search to a solution.

The Brélaz Heuristic and Optimal Static Orderings

Abstract: The order in which the variables are assigned can have an enormous impact on the time taken by a backtracking search algorithm to solve a constraint satisfaction problem (CSP) The Brelaz heuristic is a dynamic variable ordering heuristic which has been shown to give good results for some classes of binary CSPs when the constraint graph is not complete Its advantage over the simpler smallest-domain heuristic is that it uses information about the constraint graph This paper uses theoretical work by Nudel to assess the performance of the Brelaz heuristic Nudel’s work gives the expected number of nodes at each level of the search tree when using the forward checking algorithm to find all solutions to a CSP, given a specified order of the variables From this, optimal static orderings are found for a sample of small binary CSPs The optimal orderings are used to learn rules for a static ordering heuristic, which are converted into modifications to the Brelaz heuristic The improved heuristic is shown to halve the mean search cost of solving sparse random binary CSPs with 50 variables, at the phase transition However, our modifications, and the Brelaz heuristic itself, are mainly in the form of improved tie-breakers for the smallest-domain heuristic, which the results suggest is still the basis of good heuristics for this class of problem

Implementing Encapsulated Search for a Lazy Functional Logic Language

Abstract: A distinguishing feature of logic and functional logic languages is their ability to perform computations with partial data and to search for solutions of a goal. Having a built-in search strategy is convenient but not always sufficient. For many practical applications the built-in search strategy (usually depth-first search via global backtracking) is not well suited. Also the non-deterministic instantiation of unbound logic variables conflicts with the monadic I/O concept, which requires a single-threaded use of the world.

Mini-bucket heuristics for improved search

Abstract: The paper is a second in a series of two papers evaluating the power of a new scheme that generates search heuristics mechanically. The heuristics are extracted from an approximation scheme called mini-bucket elimination that was recently introduced. The first paper introduced the idea and evaluated it within Branch-and-Bound search. In the current paper the idea is further extended and evaluated within Best-First search. The resulting algorithms are compared on coding and medical diagnosis problems, using varying strength of the mini-bucket heuristics. Our results demonstrate an effective search scheme that permits controlled tradeoff between preprocessing (for heuristic generation) and search. Best-first search is shown to outperform Branch-and-Bound, when sup plied with good heuristics, and sufficient memory space.

Resource allocation analysis of the stochastic diffusion search

Abstract: The Stochastic Diffusion Search (SDS) was developed as a solution to the best-fit search problem. Thus, as a special case it is capable of solving the transform invariant pattern recognition problem. SDS is efficient and, although inherently probabilistic, produces very reliable solutions in widely ranging search conditions. However, to date a systematic formal investigation of its properties has not been carried out. This thesis addresses this problem. The thesis reports results pertaining to the global convergence of SDS as well as characterising its time complexity. However, the main emphasis of the work, reports on the resource allocation aspect of the Stochastic Diffusion Search operations. The thesis introduces a novel model of the algorithm, generalising an Ehrenfest Urn Model from statistical physics. This approach makes it possible to obtain a thorough characterisation of the response of the algorithm in terms of the parameters describing the search conditions in case of a unique best-fit pattern in the search space. This model is further generalised in order to account for different search conditions: two solutions in the search space and search for a unique solution in a noisy search space. Also an approximate solution in the case of two alternative solutions is proposed and compared with predictions of the extended Ehrenfest Urn model. The analysis performed enabled a quantitative characterisation of the Stochastic Diffusion Search in terms of exploration and exploitation of the search space. It appeared that SDS is biased towards the latter mode of operation. This novel perspective on the Stochastic Diffusion Search lead to an investigation of extensions of the standard SDS, which would strike a different balance between these two modes of search space processing. Thus, two novel algorithms were derived from the standard Stochastic Diffusion Search, ‘context-free’ and ‘context-sensitive’ SDS, and their properties were analysed with respect to resource allocation. It appeared that they shared some of the desired features of their predecessor but also possessed some properties not present in the classic SDS. The theory developed in the thesis was illustrated throughout with carefully chosen simulations of a best-fit search for a string pattern, a simple but representative domain, enabling careful control of search conditions.

Decomposition search: a combinatorial games approach to game tree search, with applications to solving go endgames

Abstract: We develop a new method called decomposition search for computing minimax solutions to games that can be partitioned into independent subgames. The method does not use traditional minimax search algorithms such as alpha-beta, but relies on concepts from combinatorial game theory to do locally restricted searches. This divide-and-conquer approach allows the exact solution of much larger problems than is possible with alpha-beta. We show an application of decomposition search to the game of Go, which has been traditionally regarded as beyond the range of exact search-based solution methods. Our experiments with solving endgames show that alpha-beta searches already become impractical in positions with about 15 remaining moves. However, an endgame solver based on decomposition search can solve a much larger class of endgame problems with solution lengths exceeding 60 moves.

Directions in planning: understanding the flow of time in planning

Abstract: Since the notion of general purpose planning became one of the touchstones of artificial intelligence, surprisingly little improvement has been made in the efficiency of planning algorithms. Efficient high-speed search is essential to most planning algorithms proposed to date: this can only be achieved if the search algorithms used are based on a solid understanding of the search space. The concept of search directionality—searching temporally or causally forward or backward—has been quite important to designers of planning algorithms. Nonetheless, this concept appears to be poorly understood. Through a series of constructions and experiments, it is shown here that successful planners must be capable of both forward chaining and backward chaining behavior, and that understanding directionality issues in planning is a necessary precursor to the construction of efficient planners. This work begins by discussing some of the underpinnings of directionality in planning: the physical, psychological, and computational temporal arrows that directionally orient planning problems. A previously unappreciated property of directionality in planning is then described, namely that the direction of planning problems is not a fundamental property of the standard formalism. Planning problems can be reversed, allowing a planner to search in the opposite of its normal direction without a change in planning algorithm. Next, a novel technique is described for determining the directional behavior of existing planners, and experimental results using an implementation of this technique are reported. This analysis of planner direction can be used to better understand the search strategy used in modern planning algorithms such as satisfiability-based planning. Finally, some consequences and extensions of the results are given. Together, these results shed new light on the construction of planning algorithms using high-speed search, and thus move us closer to making planning practical for real problems. DEPARTMENT OF COMPUTER AND INFORMATION SCIENCE UNIVERSITY OF OREGON Copyright 1999 Bart Massey This Technical Report is a reformatted version of the author’s Doctoral Dissertation, completed June 1999. Examining committee: Dr. Matthew Ginsberg, Co-chair Dr. Amr Sabry, Co-chair Dr. Christopher Wilson Dr. John Orbell