Intelligent Backtracking Research Articles

Implementing Backjumping by Means of Exception Handling

AbstractWe discuss how to implement backjumping (or intelligent backtracking) in Prolog by using the built-ins throw/1 and catch/3. We show that it is impossible in a general case, contrary to a claim that “backjumping is exception handling." We provide two solutions. One works for binary programs; in a general case it imposes a restriction on where backjumping may originate. The other restricts the class of backjump targets. We also discuss implementing backjumping by using backtracking and the Prolog database. Additionally, we explain the semantics of Prolog exception handling in the presence of coroutining.

Smart approach to constraint programming: intelligent backtracking using artificial intelligence

Smart approach to constraint programming: intelligent backtracking using artificial intelligence

RETRACTED ARTICLE: Constraint Programming with Intelligent Backtracking using Artificial Intelligence

Recently, Intelligent Backtracking can be defined as a method used in constrained programming to minimize search results in the resolution of combinatorial problems. The technology utilizes information from limited collections of infeasible restrictions in one search area to discourage searching in other related areas. It will substantially reduce the search space. However, the computing work needed to reduce the search area for many issues. In this research, an Artificial Intelligence-based Branch and Cut Algorithm has been proposed, which uses an intelligent tracking system based on Constraint programming. This proposed framework displays an extreme dual ray associated with an unfeasible linear program to automatically deduce minimum infeasible settings. Furthermore, it has reduced space for intelligent monitoring without paying high processing costs. The experimental results demonstrate that the realization of the proposed intellectual monitoring paradigm.

B-Theta*: an Efficient Online Coverage Algorithm for Autonomous Cleaning Robots

We propose a novel approach to deal with the online complete-coverage task of cleaning robots in unknown workspaces with arbitrarily-shaped obstacles. Our approach is based on the boustrophedon motions, the boundary-following motions, and the Theta* algorithm known as B-Theta*. Under control of B-Theta*, the robot performs a single boustrophedon motion to cover an unvisited region. While performing the boustrophedon motion, if the robot encounters an obstacle with a boundary that has not yet been covered, it switches to the boundary mode to cover portions along the obstacle boundary, and then continues the boustrophedon motion until it detects an ending point. To move to an unvisited region, the robot detects backtracking points based on its accumulated knowledge, and applies an intelligent backtracking mechanism thanks to the proposed Theta* for multi-goals in order to reach the next starting point. Complete coverage is achieved when no starting point exists for a new boustrophedon motion. Computer simulations and experiments on real workspaces show that our proposed B-Theta* is efficient for the complete-coverage task of cleaning robots.

CONSTRAINT SOVLING ENGINE BASED NURSE ROSTERING WITH INTELLIGENT BACKTRACKING

Efficient utilization of time and effort is essenti al in Personnel scheduling problems to evenly balan ce the workload among the people and attempt to satisfy th e personnel preferences. In Constraint Satisfaction Problem based scheduling problems, when a branch of the search fails the backtracking search algorithm back up to the preceding variable and try a differe nt value for it. So here the most recent decision p oint is revisited. Its run-time complexity for most nontriv ial problems is still exponential. A solution is in telligent backtracking scheme in which backtracking is done directly to the variable that caused the failure. Th is study proposes Constraint Satisfaction Problem base d Nurse Rostering using Intelligent Backtracking approach. The proposed Minimal Critical Set based I ntelligent Backtracking (MCS-IBT) algorithm incorporates Critical Set detection which is follow ed by Minimal Critical Set reduction in order to re duce the search space for nurse rostering. MCS_IBT overcomes missing good MCSs by visiting optimal number of sets. This study finds its applications in sched uling, temporal reasoning, graph problems, floor pl an design, the planning of genetic experiments and the satisfiability problems. The implemented system is tested on the real life data from the hospital and the results shown remarkable performance.

BoB: an online coverage approach for multi-robot systems

Online complete coverage is required in many applications, such as in floor cleaning, lawn mowing, mine hunting, and harvesting, and can be performed by single- or multi-robot systems. Motivated by the efficiency and robustness of multi-robot systems, this study proposes a solution to provide online complete coverage through a boustrophedon and backtracking mechanism called the BoB algorithm. This approach designs robots in the system according to a market-based approach. Without a central supervisor, the robots use only local interactions to coordinate and construct simultaneously non-overlapping regions in an incremental manner via boustrophedon motion. To achieve complete coverage, that is, the union of all covered regions in the entire accessible area of the workspace, each robot is equipped with an intelligent backtracking mechanism based on a proposed greedy A* search (GA*) to move to the closest unvisited region. The robots complete the coverage task when no more backtracking points are detected. Computer simulations show that the BoB approach is efficient in terms of the coverage rate, the length of the coverage path, and the balance of the workload distribution of robots.

BA*: an online complete coverage algorithm for cleaning robots

This paper presents a novel approach to solve the online complete coverage task of autonomous cleaning robots in unknown workspaces based on the boustrophedon motions and the A* search algorithm (BA*). In this approach, the robot performs a single boustrophedon motion to cover an unvisited region until it reaches a critical point. To continue covering the next unvisited region, the robot wisely detects backtracking points based on its accumulated knowledge, determines the best backtracking point as the starting point of the next boustrophedon motion, and applies an intelligent backtracking mechanism based on the proposed A* search with smoothed path on tiling so as to reach the starting point with the shortest collision-free path. The robot achieves complete coverage when no backtracking point is detected. Computer simulations and experiments in real workspaces prove that our proposed BA* is efficient for the complete coverage task of cleaning robots.

Reasoning from last conflict(s) in constraint programming

Constraint programming is a popular paradigm to deal with combinatorial problems in artificial intelligence. Backtracking algorithms, applied to constraint networks, are commonly used but suffer from thrashing, i.e. the fact of repeatedly exploring similar subtrees during search. An extensive literature has been devoted to prevent thrashing, often classified into look-ahead (constraint propagation and search heuristics) and look-back (intelligent backtracking and learning) approaches. In this paper, we present an original look-ahead approach that allows to guide backtrack search toward sources of conflicts and, as a side effect, to obtain a behavior similar to a backjumping technique. The principle is the following: after each conflict, the last assigned variable is selected in priority, so long as the constraint network cannot be made consistent. This allows us to find, following the current partial instantiation from the leaf to the root of the search tree, the culprit decision that prevents the last variable from being assigned. This way of reasoning can easily be grafted to many variations of backtracking algorithms and represents an original mechanism to reduce thrashing. Moreover, we show that this approach can be generalized so as to collect a (small) set of incompatible variables that are together responsible for the last conflict. Experiments over a wide range of benchmarks demonstrate the effectiveness of this approach in both constraint satisfaction and automated artificial intelligence planning.

Improving inter-block backtracking with interval Newton

Inter-block backtracking (IBB) computes all the solutions of sparse systems of nonlinear equations over the reals. This algorithm, introduced by Bliek et al. (1998) handles a system of equations previously decomposed into a set of (small) k ×k sub-systems, called blocks. Partial solutions are computed in the different blocks in a certain order and combined together to obtain the set of global solutions. When solutions inside blocks are computed with interval-based techniques, IBB can be viewed as a new interval-based algorithm for solving decomposed systems of nonlinear equations. Previous implementations used Ilog Solver and its IlcInterval library as a black box, which implied several strong limitations. New versions come from the integration of IBB with the interval-based library Ibex. IBB is now reliable (no solution is lost) while still gaining at least one order of magnitude w.r.t. solving the entire system. On a sample of benchmarks, we have compared several variants of IBB that differ in the way the contraction/filtering is performed inside blocks and is shared between blocks. We have observed that the use of interval Newton inside blocks has the most positive impact on the robustness and performance of IBB. This modifies the influence of other features, such as intelligent backtracking. Also, an incremental variant of inter-block filtering makes this feature more often fruitful.

Labelled splitting

We define a superposition calculus with explicit splitting on the basis of labelled clauses. For the first time we show a superposition calculus with an explicit non-chronological backtracking rule sound and complete. The new backtracking rule advances backtracking with branch condensing known from SPASS. An experimental evaluation of an implementation of the new rule shows that it improves considerably on the previous SPASS splitting implementation. Finally, we discuss the relationship between labelled first-order splitting and DPLL style splitting with intelligent backtracking and clause learning.

A CSP Search Algorithm with Responsibility Sets and Kernels

A CSP search algorithm, like FC or MAC, explores a search tree during its run. Every node of the search tree can be associated with a CSP created by the refined domains of unassigned variables. If the algorithm detects that the CSP associated with a node is insoluble, the node becomes a dead-end. A strategy of pruning "by analogy" states that the current node of the search tree can be discarded if the CSP associated with it is "more constrained" than a CSP associated with some dead-end node. In this paper we present a method of pruning based on the above strategy. The information about the CSPs associated with dead-end nodes is kept in the structures called responsibility sets and kernels. We term the method that uses these structures for pruning RKP, which is abbreviation of Responsibility set, Kernel, Propagation. We combine the pruning method with algorithms FC and MAC. We call the resulting solvers FC-RKP and MAC-RKP, respectively. Experimental evaluation shows that MAC-RKP outperforms MAC-CBJ on random CSPs and on random graph coloring problems. The RKP-method also has theoretical interest. We show that under certain restrictions FC-RKP simulates FC-CBJ. It follows from the fact that intelligent backtracking implicitly uses the strategy of pruning "by analogy."

PROGRAMMING PEARL: Enhancing a search algorithm to perform intelligent backtracking

This paper illustrates how a Prolog program, using chronological backtracking to find a solution in some search space, can be enhanced to perform intelligent backtracking. The enhancement crucially relies on the impurity of Prolog that allows a program to store information when a dead end is reached. To illustrate the technique, a simple search program is enhanced.

Eliminating redundant search space on backtracking for forward chaining theorem proving

This paper introduces some improvements on the intelligent backtracking strategy for forward chaining theorem proving. How to decide a minimal useful consequent atom set for a refutation derived at a node in a proof tree is discussed. In most cases, an unnecessary non-Horn clause used for forward chaining will be split only once. The increase of the search space by invoking unnecessary forward chaining clauses will be nearly linear, not exponential anymore. In this paper, the principle of the proposed method and its correctness are introduced. Moreover, some examples are provided to show that the proposed approach is powerful for forward chaining theorem proving.

Efficient Intelligent Backtracking Using Linear Programming

Intelligent backtracking is a technique used in constraint programming for reducing search in solving combinatorial feasibility problems. The technique uses information derived from small sets of infeasible constraints discovered in one part of the search space to avoid searching other, similar, regions. It is often able to reduce the size of the search space significantly. For many problems, however, the computational effort required to achieve this reduction in search space is prohibitive. We introduce an algorithm that uses intelligent backtracking inside a linear-programming based branch-and-bound framework. We show that minimal infeasible sets can immediately be deduced from the dual extreme ray associated with the infeasible linear program. This allows us to obtain the reduction in search space associated with intelligent backtracking, without paying the large computational cost. We show the implementation of our intelligent backtracking approach as a branch-and-cut algorithm, and present computational results.

INTERLEAVED BACKTRACKING IN DISTRIBUTED CONSTRAINT NETWORKS

The adaptation of software technology to distributed environments is an important challenge today. In this work we combine parallel and distributed search. By this way we add the potential speed-up of a parallel exploration in the processing of distributed problems. This paper extends DIBT, a distributed search procedure operating in distributed constraint networks.11 The extension is threefold. First, the ordered hierarchies used during backtracking are extended to remove partial orders. Second the procedure is updated to face delayed information problems upcoming in heterogeneous (We would like to thank here M. Yokoo for rising this potential problem.)Third, the search is extended to simultaneously explore independent parts of a distributed search tree. The first and third points were first presented in 1999.7 The third improvement introduces parallelism into distributed search, which brings to Interleaved Distributed Intelligent BackTracking (IDIBT). Our results show that 1) insoluble problems do not greatly degrade performance over DIBT and 2) super-linear speed-up can be achieved when the distribution of solutions is non-uniform.

Efficient generation of rotating workforce schedules

Generating high-quality schedules for a rotating workforce is a critical task in all situations where a certain staffing level must be guaranteed, such as in industrial plants or police departments. Results from ergonomics (BEST, Guidelines for shiftworkers, Bulletin of European Time Studies No. 3, European Foundation for the Improvement of Living and Working Conditions, 1991) indicate that rotating workforce schedules have a profound impact on the health and satisfaction of employees as well as on their performance at work. Moreover, rotating workforce schedules must satisfy legal requirements and should also meet the objectives of the employing organization. In this paper, our description of a solution to this problem is being stated. One of the basic design decisions was to aim at high-quality schedules for realistically sized problems obtained rather quickly, while maintaining human control. The interaction between the decision-maker and the algorithm therefore consists of four steps: (1) choosing a set of lengths of work blocks (a work block is a sequence of consecutive days of work), (2) choosing a particular sequence of blocks of work and days-off blocks amongst these that have optimal weekend characteristics, (3) enumerating possible shift sequences for the chosen work blocks subject to shift change constraints and bounds on sequences of shifts, and (4) assignment of shift sequences to work blocks while fulfilling the staffing requirements. The combination of constraint satisfaction and problem-oriented intelligent backtracking algorithms in each of the four steps allows for finding good solutions for real-world problems in acceptable time. Computational results from a benchmark example found in the literature confirmed the viability of our approach. The algorithms have been implemented in commercial shift scheduling software.

Exploiting the real power of unit propagation lookahead

Abstract Abstract One of the best SAT solvers for random 3-SAT formulae, SATZ, is based on a heuristic called unit propagation lookahead (UPL). Unfortunately, it does not perform so well on specific structured instances, especially on the ones coming from an area where a huge interest for SAT has emerged in recent years: symbolic model checking (SMC). We claim that all the power of this heuristic is not used in SATZ, and that UPL can be extended to solve some real world structured problems, where the major competitors are using intelligent backtracking or specific deduction rules. We introduce a preprocessing technique that can be applied to simplify instances containing equivalent literals. This technique is based on UPL, so it can be easily added to any solver using this heuristic. We compare our approach to the new extension of SATZ for equivalency reasoning (EqSATZ) and another approach, the Stalmarck method, which is mainly used in SMC. The author would like to thank Yacine Boufkhad for his insights about C-SAT and 2-simplify, Mamoun Filali-Amine for pointing out the Stalmark method, Chu-Min Li for his discussions about EqSATZ and his implementation of the implied literal propagation in SATZ, Laurent Simon for his SAT-Ex web site, Miroslav Velev for his remarks on the early version of the paper and the referees for their helpful comments. This research was funded by an ARC Large Grant at The University of Newcastle.

I-SATCHMO: An Improvement of SATCHMO

We introduce a method for reducing the redundant search space for SATCHMO's model generation approach by means of intelligent backtracking. During the reasoning, we mark an asserted consequent atom as “useful” whenever it has been used as an antecedent atom for forward chaining. We show that a splitting of the consequence of a non-Horn clause is unnecessary if one of its consequent atoms is found not to be “useful” at the time it is retracted from the database on backtracking, and therefore the remaining splitting over the clause's consequence can be immediately abandoned. In this way, much of the redundant search space can be eliminated. Our method is simple in principle, easy to implement in Prolog, independent of other refinements, and effective for model generation theorem proving.

Using intelligent backtracking to improve branch-and-bound methods: An application to Open-Shop problems

Only two branch-and-bound methods have been published so far for the Open-Shop problem. The best one has been proposed by Brucker et al. But some square problems from size 7 remain still unsolved with it.We present an improving technique for branch-and-bound methods applied to Brucker et al.'s algorithm for Open-Shop problems. Our technique is based on intelligent backtracking. An adaptation of a generic explanation system we have initially developed in the constraint programming scheme is used to develop that technique.We tested our approach on Open-Shop problems from the literature (benchmarks of Taillard). The search is definitely improved: on some square problems of size 10, the number of backtracks is reduced by more than 90% and we even solved an open problem of that size.

Combining satisfiability techniques from AI and OR

The recent effort to integrate techniques from the fields of artificial intelligence and operations research has been motivated in part by the fact that scientists in each group are often unacquainted with recent (and not so recent) progress in the other field. Our goal in this paper is to introduce the artificial intelligence community to pseudo-Boolean representation and cutting plane proofs, and to introduce the operations research community to restricted learning methods such as relevance-bounded learning. Complete methods for solving satisfiability problems are necessarily bounded from below by the length of the shortest proof of unsatisfiability; the fact that cutting plane proofs of unsatisfiability can be exponentially shorter than the shortest resolution proof can thus in theory lead to substantial improvements in the performance of complete satisfiability engines. Relevance-bounded learning is a method for bounding the size of a learned constraint set. It is currently the best artificial intelligence strategy for deciding which learned constraints to retain and which to discard. We believe these two elements or some analogous form of them are necessary ingredients to improving the performance of satisfiability algorithms generally. We also present a new cutting plane proof of the pigeonhole principle that is of size n2, and show how to implement some intelligent backtracking techniques using pseudo-Boolean representation.