Backtrack Search Algorithm Research Articles

Solution of the Multi-Objective Optimal Power Flow Problem Using Oppositional-Based Algorithm

An efficient optimal power flow (OPF) algorithm allows the finest setting of the plant by solving multi-objective optimization problem to minimise the overall operating cost. This paper proposes the quasi oppositional backtrack search algorithm (QOBSA) for optimal setting of OPF control variables. The QOBSA is stochastic algorithm which gives committed and robust results compared to the traditional methods. This technique has been implemented to test the control parameters for the IEEE 30-bus with single and multi-objective functions like the minimization of fuel cost, minimization of total voltage deviation (TVD), voltage stability enhancement, emission reduction, and multi-fuel cost minimization. The result provides better voltage profile at every bus based on L-index which in turn greatly reduces the burden on load buses. The QOBSA code has been developed in the MATLAB platform and tested with the help of IEEE 30-bus and the outcomes have been compared with ongoing literature.

Chaotic slime mould optimization algorithm for optimal load-shedding in distribution system

• Introduces Chaotic Slime Mould Algorithm (CSMA) as an optimal load shedding scheme of islanded DG integrated systems. • A fitness function comprising of maximum amount of remaining load and voltage stability margin (VSM) is adopted. • IEEE 33 bus and IEEE 69 bus distribution systems are used to assess the algorithm’s efficacy. • The proposed CSMA algorithm is compared with Slime mould algorithm (SMA) and Backtrack search algorithm (BSA). In addition, non-parametric statistical analysis have been conducted to adequately compare the algorithms. • In terms of fitness value, time consumption, and convergence characteristics, CSMA outperforms both BSA and SMA. In addition, CSMA ensures a better voltage profile and provides a solution with the least amount of load to be shed. The critical challenge for an efficient islanding operation of a distribution system having Distributed Generation (DG) is preserving the frequency and voltage stability. Contemporary load shedding schemes are inefficient and do not adequately assess the optimum amount of load to shed which results in either excessive or inadequate load shedding. Hence, this paper presents an optimal load shedding technique using Chaotic Slime Mould Algorithm (CSMA) with sinusoidal map in order to achieve greater efficiency. A constrained function with static voltage stability margin (VSM) index and total remaining load after load shedding was applied to accomplish the evaluation. A total of three islanding scenarios of IEEE 33 bus and IEEE 69 bus radial distribution systems were used as test systems to assess the efficacy of the proposed load shedding approach using MATLAB software. To identify performance enhancements, the developed method was compared to Backtrack Search Algorithm (BSA) and the original SMA. According to the results, CSMA outperforms both BSA and SMA in terms of remaining load and voltage stability margin index values in all the test systems.

Optimization of wind solar and battery hybrid renewable system using backtrack search algorithm

<p>Penetration of renewable sources to the grid is always a problem for electrical engineers, apart from reliability and efficiency, cost optimization is also a big concern among them. Wind, solar and battery hybrid combinations (WSB-HPS) are also very common among hybrid systems, but this WSBHPS combines wind and solar energy power generation reduces the charge and discharge time of the battery. Therefore, this system improves the reliability of the power supply by fully utilizing the wind and solar power generation and improves the charging and discharging state of the battery and hence reduces the whole cost as the investment in battery is reduced. backtrack search algorithm (BSA) is the highly efficient and powerful algorithm to solve combinatorial optimization problems. In this paper an attempt is made to optimize the hybrid combination using BSA in the matrix laboratory (MATLAB) environment and comparable study is made using HOMER. A complete optimised data is generated for a particular area in Manipur and reduced cost is suggested.</p>

Permutation group algorithms based on directed graphs

We introduce a new framework for solving an important class of computational problems involving finite permutation groups, which includes calculating set stabilisers, intersections of subgroups, and isomorphisms of combinatorial structures. Our techniques are inspired by and generalise ‘partition backtrack’, which is the current state-of-the-art algorithm introduced by Jeffrey Leon in 1991. But, instead of ordered partitions, we use labelled directed graphs to organise our backtrack search algorithms, which allows for a richer representation of many problems while often resulting in smaller search spaces. In this article we present the theory underpinning our framework, we describe our algorithms, and we show the results of some experiments. An implementation of our algorithms is available as free software in the GraphBacktracking package for GAP.

Partial (Neighbourhood) Singleton Arc Consistency for Constraint Satisfaction Problems

Algorithms based on singleton arc consistency (SAC) show considerable promise for improving backtrack search algorithms for constraint satisfaction problems (CSPs). The drawback is that even the most efficient of them is still comparatively expensive. Even when limited to preprocessing, they give overall improvement only when problems are quite difficult to solve with more typical procedures such as maintained arc consistency (MAC). The present work examines a form of partial SAC and neighbourhood SAC (NSAC) in which a subset of the variables in a CSP are chosen to be made SAC-consistent or neighbourhood-SAC-consistent. Such consistencies, despite their partial character, are still well-characterized in that algorithms have unique fixpoints. Heuristic strategies for choosing an effective subset of variables are described and tested, the best being choice by highest degree and a more complex strategy of choosing by constraint weight after random probing. Experimental results justify the claim that these methods can be nearly as effective as the corresponding full version of the algorithm in terms of values discarded or problems proven unsatisfiable, while significantly reducing the effort required to achieve this.

Conditional Preference Networks with User's Genuine Decisions

AbstractUser's choices involve habitual behavior and genuine decision. Habitual behavior is often expressed using preferences. In a multiattribute case, the Conditional Preference Network (CP‐net) is a graphical model to represent user's conditional ceteris paribus (all else being equal) preference statements. Indeed, the CP‐net induces a strict partial order over the outcomes. By contrast, we argue that genuine decisions are environmentally influenced and introduce the notion of “comfort” to represent this type of choices. In this article, we propose an extension of the CP‐net model that we call the CP‐net with Comfort (CPC‐net) to represent a user's comfort with preferences. Given that preference and comfort might be two conflicting objectives, we define the Pareto optimality of outcomes when achieving outcome optimization with respect to a given CPC‐net. Then, we propose a backtrack search algorithm to find the Pareto optimal outcomes. On the other hand, two outcomes can stand in one of six possible relations with respect to a CPC‐net. The exact relation can be obtained by performing dominance testing in the corresponding CP‐net and comparing the numeric comforts.

Variable ordering and constraint propagation for constrained CP-nets

A Conditional Preferences network (CP-net) is a known graphical model for representing qualitative preferences. In many real world applications we are often required to manage both constraints and preferences in an efficient way. The goal here is to select one or more scenarios that are feasible according to the constraints while maximizing a given utility function. This problem has been modelled as a CP-net where some variables share a set of constraints. This latter framework is called a Constrained CP-net. Solving the constrained CP-net has been proposed in the past using a variant of the branch and bound algorithm called Search CP. In this paper, we experimentally study the effect of variable ordering heuristics and constraint propagation when solving a constrained CP-net using a backtrack search algorithm. More precisely, we investigate several look ahead strategies as well as the most constrained heuristic for variable ordering during search. The results of the experiments conducted on random Constrained CP-net instances generated through the RB model, clearly show a significant improvement when adopting these techniques for specific graph structures as well as the case where a large number of variables are sharing constraints.

Enumeration of Strength Three Orthogonal Arrays and Their Implementation in Parameter Design

This paper describes the construction and enumeration of mixed orthogonal arrays (MOA) to produce optimal experimental designs. A MOA is a multiset whose rows are the different combinations of factor levels, discrete values of the variable under study, having very well defined features such as symmetry and strength three (all main interactions are taken in consideration). The applied methodology blends the fields of combinatorics and group theory by applying the ideas of orbits, stabilizers and isomorphisms to array generation and enumeration. Integer linear programming was used in order to exploit the symmetry property of the arrays under study. The backtrack search algorithm was used to find suitable arrays in the underlying space of possible solutions. To test the performance of the MOAs, an engineered system was used as a case study within the stage of parameter design. The analysis showed how the MOAs were capable of meeting the fundamental engineering design axioms and principles, creating optimal experimental designs within the desired context.

Accelerating backtrack search with a best-first-search strategy

Abstract Backtrack-style exhaustive search algorithms for NP-hard problems tend to have large variance in their runtime. This is because “fortunate” branching decisions can lead to finding a solution quickly, whereas “unfortunate” decisions in another run can lead the algorithm to a region of the search space with no solutions. In the literature, frequent restarting has been suggested as a means to overcome this problem. In this paper, we propose a more sophisticated approach: a best-firstsearch heuristic to quickly move between parts of the search space, always concentrating on the most promising region. We describe how this idea can be efficiently incorporated into a backtrack search algorithm, without sacrificing optimality. Moreover, we demonstrate empirically that, for hard solvable problem instances, the new approach provides significantly higher speed-up than frequent restarting.

Space-efficient parallel algorithms for combinatorial search problems

We present space-efficient parallel strategies for two fundamental combinatorial search problems, namely, backtrack search and branch-and-bound, both involving the visit of an n-node tree of height h under the assumption that a node can be accessed only through its father or its children. For both problems we propose efficient algorithms that run on a p-processor distributed-memory machine. For backtrack search, we give a deterministic algorithm running in O(n/p+hlogp) time, and a Las Vegas algorithm requiring optimal O(n/p+h) time, with high probability. Building on the backtrack search algorithm, we also derive a Las Vegas algorithm for branch-and-bound which runs in O((n/p+hlogplogn)hlog2n) time, with high probability. A remarkable feature of our algorithms is the use of only constant space per processor, which constitutes a significant improvement upon previous algorithms whose space requirements per processor depend on the (possibly huge) tree to be explored.

The constraints satisfaction problem approach in the design of an architectural functional layout

A design support system with a new strategy for finding the optimal functional configurations of rooms for architectural layouts is presented. A set of configurations satisfying given constraints is generated and ranked according to multiple objectives. The method can be applied to problems in architectural practice, urban or graphic design—wherever allocation of related geometrical elements of known shape is optimized. Although the methodology is shown using simplified examples—a single story residential building with two apartments each having two rooms—the results resemble realistic functional layouts. One example of a practical size problem of a layout of three apartments with a total of 20 rooms is demonstrated, where the generated solution can be used as a base for a realistic architectural blueprint. The discretization of design space is discussed, followed by application of a backtrack search algorithm used for generating a set of potentially ‘good’ room configurations. Next the solutions are classified by a machine learning method (FFN) as ‘proper’ or ‘improper’ according to the internal communication criteria. Examples of interactive ranking of the ‘proper’ configurations according to multiple criteria and choosing ‘the best’ ones are presented. The proposed framework is general and universal—the criteria, parameters and weights can be individually defined by a user and the search algorithm can be adjusted to a specific problem.

Efficient Constraint Propagation for Graph Coloring

Abstract In this paper, we investigate constraint propagation, a mechanism that is run at each basic step of a backtrack search algorithm such as the popular MAC. From a statistical analysis of some relevant features concerning propagation on a large set of graph coloring instances, we show that it is possible to make reasonable predictions about the capability of constraint propagation to detect inconsistency. Using this observation in order to control propagation effort, we show its practical effectiveness.

Backtracking-based load balancing

High-productivity languages for parallel computing become more important as parallel environments including multicores become more common. Cilk is such a language. It provides good load balancing for many applications including irregular ones; that is, it keeps all workers busy by creating plenty of "logical" threads and adopting the oldest-first work stealing strategy. This paper proposes a "logical thread"-free framework called Tascell , which achieves a higher performance and supports a wider range of parallel environments including clusters without loss of productivity. A Tascell worker spawns a "real" task only when requested by another idle worker. The worker performs the spawning by temporarily "backtracking" and restoring its oldest task-spawnable state. Our approach eliminates the cost of spawning/managing logical threads. It also promotes the reuse of workspaces and improves the locality of reference since it does not need to prepare a workspace for each concurrently runnable logical thread. Furthermore, Tascell enables elegant and highly-efficient backtrack search algorithms with delayed workspace copying. For instance, our 16-queens problem solver is 1.86 times faster than Cilk on a system with two dual-core processors. Our approach also enables a single program to run in both shared and distributed memory environments with reasonable efficiency and scalability.

Tracking Unsatisfiable Subformulas from Reduced Refutation Proof

Explaining the causes of infeasibility of Boolean formulas has many practical applications in various fields. A small unsatisfiable subformula provides a succinct explanation of infeasibility and is valuable for applications. In recent years finding unsatisfiable subformulas has been addressed frequently by research works, mostly based on the SAT solvers with DPLL backtrack-search algorithm. However little attention has been concentrated on extraction of unsatisfiable subformulas using incomplete methods. In this paper, we present the definitions of refutation proof and refutation parsing graph, and then propose a resolution based local search algorithm to track unsatisfiable subformulas according to the reduced refutation proof of a formula. This approach directly constructs the resolution sequences for proving unsatisfiability with a local search procedure, and then recursively derives unsatisfiable subformulas from the resolve traces. We report and analyze the experimental results on well-known and randomly generated benchmarks.

Random backtracking in backtrack search algorithms for satisfiability

This paper proposes the utilization of randomized backtracking within complete backtrack search algorithms for propositional satisfiability (SAT). In recent years, randomization has become pervasive in SAT algorithms. Incomplete algorithms for SAT, for example the ones based on local search, often resort to randomization. Complete algorithms also resort to randomization. These include state-of-the-art backtrack search SAT algorithms that often randomize variable selection heuristics. Moreover, it is plain that the introduction of randomization in other components of backtrack search SAT algorithms can potentially yield new competitive search strategies. As a result, we propose a stochastic backtrack search algorithm for SAT, that randomizes both the variable selection and the backtrack steps of the algorithm. In addition, we relate randomized backtracking with a more general form of backtracking, referred to as unrestricted backtracking. Finally, experimental results for different organizations of randomized backtracking are described and compared, providing empirical evidence that the new search algorithm for SAT is a very competitive approach for solving hard real-world instances.

Heuristic-Based Backtracking Relaxation for Propositional Satisfiability

In recent years backtrack search algorithms for propositional satisfiability (SAT) have been the subject of dramatic improvements. These improvements allowed SAT solvers to successfully solve instances with thousands or tens of thousands of variables. However, many new challenging problem instances are still too hard for current SAT solvers. As a result, further improvements to SAT technology are expected to have key consequences in solving hard real-world instances. This paper introduces a new idea: choosing the backtrack variable using a heuristic approach with the goal of diversifying the regions of the space that are explored during the search. The proposed heuristics are inspired by the heuristics proposed in recent years for the decision branching step of SAT solvers, namely, VSIDS and its improvements. Completeness conditions are established, which guarantee completeness for the new algorithm, as well as for any other incomplete backtracking algorithm. Experimental results on hundreds of instances derived from real-world problems show that the new technique is able to speed SAT solvers, while aborting fewer instances. These results clearly motivate the integration of heuristic backtracking in SAT solvers.

EvIA - Evidential Interval Algebra and Heuristic Backtrack-Free Algorithm

The Interval Algebra (IA) framework for temporal reasoning encodes indefinite knowledge in terms of disjunctions of relations. Many problems arising in practice can have evidences from past or from other external sources to indicate that some relations in a disjunction may be more probable than others. IA framework is inadequate to encode this information. The aim of the present study is two fold. First, to extend IA framework by associating numeric weights to the relations for capturing additional information and provide a reasoning methodology for the extended framework. Second, to apply the extended framework for developing a heuristic algorithm which finds a solution of the conventional IA network problem without backtrack. We make use of well-known evidential reasoning techniques to develop the new framework, Evidential Interval Algebra (EvIA). EvIA is an augmentation of interval algebra with evidential techniques. The constraint, constraint operators namely converse, composition and intersection, and path consistency algorithm of interval algebra are overlayed by evidential function and evidential operations to get enhanced expressiveness and efficient reasoning capability. The efficiency of the EvIA framework is demonstrated in the form of a heuristic which finds a solution of the interval algebra network without backtrack. Experimental results of the heuristic algorithm reveal that the algorithm is sound and for some specific types of the problems, the success of finding a solution is more than 90 percent. The results also show that the algorithm is efficient in terms of runtime when compared with a backtrack search algorithm.

Enumeration of balanced ternary designs

A ( V, B; ρ 1, ρ 2, R; K,Λ) balanced ternary design is a pair ( V , B ) , where V is a V-set of points and B is a collection of B K-multisubsets of V called blocks, such that each point appears R times in the blocks and no block contains a point with multiplicity greater than two. Each point must appear in ρ 1 blocks with multiplicity one and in ρ 2 blocks with multiplicity two. Additionally, every pair of distinct points must appear exactly Λ times in the blocks of the design. A backtrack search algorithm with isomorph rejection is described and employed to enumerate the balanced ternary designs with V⩽10, B⩽30, and R⩽15 for all but 12 of the 155 possible design classes with these parameters.

An Overview of Backtrack Search Satisfiability Algorithms

Propositional Satisfiability (SAT) is often used as the underlying model for a significant number of applications in Artificial Intelligence as well as in other fields of Computer Science and Engineering. Algorithmic solutions for SAT include, among others, local search, backtrack search and algebraic manipulation. In recent years, several different organizations of local search and backtrack search algorithms for SAT have been proposed, in many cases allowing larger problem instances to be solved in different application domains. While local search algorithms have been shown to be particularly useful for random instances of SAT, recent backtrack search algorithms have been used for solving large instances of SAT from real-world applications. In this paper we provide an overview of backtrack search SAT algorithms. We describe and illustrate a number of techniques that have been empirically shown to be highly effective in pruning the amount of search on significant and representative classes of problem instances. In particular, we review strategies for non-chronological backtracking, procedures for clause recording and for the identification of necessary variable assignments, and mechanisms for the structural simplification of instances of SAT.

Run-time performance optimization of an FPGA-based deduction engine for SAT solvers

FPGAs are a promising technology for accelerating SAT solvers. Besides their high density, fine granularity, and massive parallelism, FPGAs provide the opportunity for run-time customization of the hardware based on the given SAT instance. In this article, a parallel deduction engine is proposed for backtrack search algorithms. The performance of the deduction engine is critical to the overall performance of the algorithm because, for any moderate SAT instance, millions of implications are derived. We propose a novel approach in which p , the amount of parallelization of the engine, is fine-tuned during problem solving in order to optimize performance. Not only the hardware is initially customized based on the input instance, but it is also dynamically modified in terms of p based on the knowledge gained during solving the SAT instance. Compared with conventional deduction engines that correspond to p = 1, we demonstrate speedups in the range of 2.87 to 5.44 for several SAT instances.