scholarly journals A Hybrid Soft Computing Approach for Subset Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Broderick Crawford ◽  
Ricardo Soto ◽  
Eric Monfroy ◽  
Carlos Castro ◽  
Wenceslao Palma ◽  
...  
Keyword(s):  
Optimization Problems ◽  
Hybrid Approach ◽  
Search Space ◽  
Constraint Satisfaction Problems ◽  
Combinatorial Problems ◽  
Set Partitioning ◽  
Set Covering ◽  
Packing And Covering ◽  
Arc Consistency ◽  
Hybrid Solver

Subset problems (set partitioning, packing, and covering) are formal models for many practical optimization problems. A set partitioning problem determines how the items in one set (S) can be partitioned into smaller subsets. All items inSmust be contained in one and only one partition. Related problems are set packing (all items must be contained in zero or one partitions) and set covering (all items must be contained in at least one partition). Here, we present a hybrid solver based on ant colony optimization (ACO) combined with arc consistency for solving this kind of problems. ACO is a swarm intelligence metaheuristic inspired on ants behavior when they search for food. It allows to solve complex combinatorial problems for which traditional mathematical techniques may fail. By other side, in constraint programming, the solving process of Constraint Satisfaction Problems can dramatically reduce the search space by means of arc consistency enforcing constraint consistencies either prior to or during search. Our hybrid approach was tested with set covering and set partitioning dataset benchmarks. It was observed that the performance of ACO had been improved embedding this filtering technique in its constructive phase.

scholarly journals A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems

2011 ◽  
Vol 21 (4) ◽  
pp. 733-744 ◽  
Author(s):  
Marlene Arangú ◽  
Miguel Salido
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Real Life ◽  
Search Space ◽  
Constraint Satisfaction Problems ◽  
Fine Grained ◽  
Arc Consistency ◽  
Life Problems ◽  
Programming Techniques ◽  
Np Complete

A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems Constraint programming is a powerful software technology for solving numerous real-life problems. Many of these problems can be modeled as Constraint Satisfaction Problems (CSPs) and solved using constraint programming techniques. However, solving a CSP is NP-complete so filtering techniques to reduce the search space are still necessary. Arc-consistency algorithms are widely used to prune the search space. The concept of arc-consistency is bidirectional, i.e., it must be ensured in both directions of the constraint (direct and inverse constraints). Two of the most well-known and frequently used arc-consistency algorithms for filtering CSPs are AC3 and AC4. These algorithms repeatedly carry out revisions and require support checks for identifying and deleting all unsupported values from the domains. Nevertheless, many revisions are ineffective, i.e., they cannot delete any value and consume a lot of checks and time. In this paper, we present AC4-OP, an optimized version of AC4 that manages the binary and non-normalized constraints in only one direction, storing the inverse founded supports for their later evaluation. Thus, it reduces the propagation phase avoiding unnecessary or ineffective checking. The use of AC4-OP reduces the number of constraint checks by 50% while pruning the same search space as AC4. The evaluation section shows the improvement of AC4-OP over AC4, AC6 and AC7 in random and non-normalized instances.

A New Differential Evolution Based Metaheuristic for Discrete Optimization

2012 ◽  
pp. 104-119 ◽  
Author(s):  
Ricardo Sérgio Prado ◽  
Rodrigo César Pedrosa Silva ◽  
Frederico Gadelha Guimarães ◽  
Oriane M. Neto
Keyword(s):  
Combinatorial Optimization ◽  
Differential Evolution ◽  
Discrete Optimization ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Search Space ◽  
Combinatorial Problems ◽  
Search Mechanism ◽  
The Difference ◽  
Discrete Domains

The Differential Evolution (DE) algorithm is an important and powerful evolutionary optimizer in the context of continuous numerical optimization. Recently, some authors have proposed adaptations of its differential mutation mechanism to deal with combinatorial optimization, in particular permutation-based integer combinatorial problems. In this paper, the authors propose a novel and general DE-based metaheuristic that preserves its interesting search mechanism for discrete domains by defining the difference between two candidate solutions as a list of movements in the search space. In this way, the authors produce a more meaningful and general differential mutation for the context of combinatorial optimization problems. The movements in the list can then be applied to other candidate solutions in the population as required by the differential mutation operator. This paper presents results on instances of the Travelling Salesman Problem (TSP) and the N-Queen Problem (NQP) that suggest the adequacy of the proposed approach for adapting the differential mutation to discrete optimization.

PREPROCESSING QUANTIFIED CONSTRAINT SATISFACTION PROBLEMS WITH VALUE REORDERING AND DIRECTIONAL ARC AND PATH CONSISTENCY

2008 ◽  
Vol 17 (02) ◽  
pp. 321-337 ◽  
Author(s):  
KOSTAS STERGIOU
Keyword(s):  
Constraint Satisfaction ◽  
Early Stage ◽  
Constraint Satisfaction Problem ◽  
Constraint Satisfaction Problems ◽  
Combinatorial Problems ◽  
Arc Consistency ◽  
Solution Methods ◽  
Speed Up ◽  
Phase Transition Region ◽  
The Impact

The Quantified Constraint Satisfaction Problem (QCSP) is an extension of the CSP that can be used to model combinatorial problems containing contingency or uncertainty. It allows for universally quantified variables that can model uncertain actions and events, such as the unknown weather for a future party, or an opponent's next move in a game. Although interest in QCSPs is increasing in recent years, the development of techniques for handling QCSPs is still at an early stage. For example, although it is well known that local consistencies are of primary importance in CSPs, only arc consistency has been extended to quantified problems. In this paper we contribute towards the development of solution methods for QCSPs in two ways. First, by extending directional arc and path consistency, two popular local consistencies in constraint satisfaction, to the quantified case and proposing an algorithm that achieves these consistencies. Second, by showing how value ordering heuristics can be utilized to speed up computation in QCSPs. We study the impact of preprocessing QCSPs with value reordering and directional quantified arc and path consistency by running experiments on randomly generated problems. Results show that our preprocessing methods can significantly speed up the QCSP solving process, especially on hard instances from the phase transition region.

Methods for Parallelizing Constraint Propagation through the Use of Strong Local Consistencies

2018 ◽  
Vol 27 (04) ◽  
pp. 1860002 ◽  
Author(s):  
Minas Dasygenis ◽  
Kostas Stergiou
Keyword(s):  
Search Space ◽  
Constraint Propagation ◽  
Search Tree ◽  
Search Algorithms ◽  
Combinatorial Problems ◽  
Search Process ◽  
Worst Case ◽  
Arc Consistency ◽  
Local Propagation ◽  
Propagation Methods

Constraint programming (CP) is a powerful paradigm for various types of hard combinatorial problems. Constraint propagation techniques, such as arc consistency (AC), are used within solvers to prune inconsistent values from the domains of the variables and narrow down the search space. Local consistencies stronger than AC have the potential to prune the search space even more, but they are not widely used because they incur a high run time penalty in cases where they are unsuccessful. All constraint propagation techniques are sequential by nature, and thus they cannot be scaled up to modern multicore machines. For this reason, research on parallelizing constraint propagation is very limited. Contributing towards this direction, we exploit the parallelization possibilities of modern CPUs in tandem with strong local propagation methods in a novel way. Instead of trying to parallelize constraint propagation algorithms, we propose two search algorithms that apply different propagation methods in parallel. Both algorithms consist of a master search process, which is a typical CP solver, and a number of slave processes, with each one implementing a strong propagation method. The first algorithm runs the different propagators synchronously at each node of the search tree explored in the master process, while the second one can run them asynchronously at different nodes of the search tree. Preliminary experimental results on well-established benchmarks display the promise of our research by illustrating that our algorithms have execution times equal to those of serial solvers, in the worst case, while being faster in most cases.

Efficient Singleton Consistency by Combining Forward Checking and Bound Consistency

2014 ◽  
Vol 23 (04) ◽  
pp. 1460017
Author(s):  
Jinsong Guo ◽  
Hongbo Li ◽  
Zhanshan Li ◽  
Yonggang Zhang ◽  
Xianghua Jia
Keyword(s):  
Constraint Satisfaction ◽  
Search Algorithm ◽  
Computational Cost ◽  
Search Space ◽  
Search Algorithms ◽  
Constraint Satisfaction Problems ◽  
Local Consistency ◽  
Arc Consistency ◽  
Strong Bound

Maintaining local consistencies can improve the efficiencies of the search algorithms solving constraint satisfaction problems (CSPs). Comparing with arc consistency which is the most widely used local consistency, stronger local consistencies can make the search space smaller while they require higher computational cost. In this paper, we make an attempt on the compromise between the pruning ability and the computational cost. A new local consistency called singleton strong bound consistency (SSBC) and its light version, light SSBC, are proposed. The search algorithm maintaining light SSBC can outperform MAC on a considerable number of problems.

scholarly journals A Novel Hybrid Self-Adaptive Bat Algorithm

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Iztok Fister ◽  
Simon Fong ◽  
Janez Brest ◽  
Iztok Fister
Keyword(s):  
Optimization Problems ◽  
Bat Algorithm ◽  
Search Space ◽  
Combinatorial Problems ◽  
Control Parameters ◽  
Search Heuristics ◽  
Self Adaptation ◽  
Nature Inspired Algorithms ◽  
Extensive Family ◽  
Self Adaptive

Nature-inspired algorithms attract many researchers worldwide for solving the hardest optimization problems. One of the newest members of this extensive family is the bat algorithm. To date, many variants of this algorithm have emerged for solving continuous as well as combinatorial problems. One of the more promising variants, a self-adaptive bat algorithm, has recently been proposed that enables a self-adaptation of its control parameters. In this paper, we have hybridized this algorithm using different DE strategies and applied these as a local search heuristics for improving the current best solution directing the swarm of a solution towards the better regions within a search space. The results of exhaustive experiments were promising and have encouraged us to invest more efforts into developing in this direction.

A New Differential Evolution Based Metaheuristic for Discrete Optimization

2010 ◽  
Vol 1 (2) ◽  
pp. 15-32 ◽  
Author(s):  
Ricardo Sérgio Prado ◽  
Rodrigo César Pedrosa Silva ◽  
Frederico Gadelha Guimarães ◽  
Oriane Magela Neto
Keyword(s):  
Combinatorial Optimization ◽  
Differential Evolution ◽  
Discrete Optimization ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Search Space ◽  
Combinatorial Problems ◽  
Combinatorial Optimization Problems ◽  
De Algorithm ◽  
The Difference

The Differential Evolution (DE) algorithm is an important and powerful evolutionary optimizer in the context of continuous numerical optimization. Recently, some authors have proposed adaptations of its differential mutation mechanism to deal with combinatorial optimization, in particular permutation-based integer combinatorial problems. In this paper, the authors propose a novel and general DE-based metaheuristic that preserves its interesting search mechanism for discrete domains by defining the difference between two candidate solutions as a list of movements in the search space. In this way, the authors produce a more meaningful and general differential mutation for the context of combinatorial optimization problems. The movements in the list can then be applied to other candidate solutions in the population as required by the differential mutation operator. This paper presents results on instances of the Travelling Salesman Problem (TSP) and the N-Queen Problem (NQP) that suggest the adequacy of the proposed approach for adapting the differential mutation to discrete optimization.

GUIDING CONSTRUCTIVE SEARCH WITH STATISTICAL INSTANCE-BASE LEARNING

2002 ◽  
Vol 11 (02) ◽  
pp. 247-266 ◽  
Author(s):  
ORESTIS TELELIS ◽  
PANAGIOTIS STAMATOPOULOS
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Statistical Information ◽  
Combinatorial Problems ◽  
Set Partitioning ◽  
Greedy Heuristics ◽  
High Quality ◽  
Search Spaces ◽  
Combinatorial Optimization Problems ◽  
Real World Applications

Several real world applications involve solving combinatorial optimization problems. Commonly, existing heuristic approaches are designed to address specific difficulties of the underlying problem and are applicable only within its framework. We suspect, however, that search spaces of combinatorial problems are rich in intuitive statistical and numerical information, which could be exploited heuristically in a generic manner, towards achievement of optimized solutions. Our work presents such a heuristic methodology, which can be adequately configured for several types of optimization problems. Experimental results are discussed, concerning two widely used problem models, namely the Set Partitioning and the Kanpsack problems. It is shown that, by gathering statistical information upon previously found solutions to the problems, the heuristic is able to incrementally adapt its behaviour and reach high quality solutions, exceeding the ones obtained by commonly used greedy heuristics.

Automatic Mining of Quantitative Association Rules with Gravitational Search Algorithm

2017 ◽  
Vol 27 (03) ◽  
pp. 343-372 ◽  
Author(s):  
Umit Can ◽  
Bilal Alatas
Keyword(s):  
Association Rules ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Fitness Function ◽  
Optimization Algorithms ◽  
Gravitational Search Algorithm ◽  
Search Space ◽  
Search Method ◽  
Quantitative Association Rules ◽  
Gravitational Search

The classical optimization algorithms are not efficient in solving complex search and optimization problems. Thus, some heuristic optimization algorithms have been proposed. In this paper, exploration of association rules within numerical databases with Gravitational Search Algorithm (GSA) has been firstly performed. GSA has been designed as search method for quantitative association rules from the databases which can be regarded as search space. Furthermore, determining the minimum values of confidence and support for every database which is a hard job has been eliminated by GSA. Apart from this, the fitness function used for GSA is very flexible. According to the interested problem, some parameters can be removed from or added to the fitness function. The range values of the attributes have been automatically adjusted during the time of mining of the rules. That is why there is not any requirements for the pre-processing of the data. Attributes interaction problem has also been eliminated with the designed GSA. GSA has been tested with four real databases and promising results have been obtained. GSA seems an effective search method for complex numerical sequential patterns mining, numerical classification rules mining, and clustering rules mining tasks of data mining.

scholarly journals Solving knapsack problems using a binary gaining sharing knowledge-based optimization algorithm

2021 ◽  
Author(s):  
Prachi Agrawal ◽  
Talari Ganesh ◽  
Ali Wagdy Mohamed
Keyword(s):  
Life Span ◽  
Population Size ◽  
Linear Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Search Space ◽  
Knapsack Problems ◽  
Local Optima ◽  
Knowledge Based ◽  
Two Stages

AbstractThis article proposes a novel binary version of recently developed Gaining Sharing knowledge-based optimization algorithm (GSK) to solve binary optimization problems. GSK algorithm is based on the concept of how humans acquire and share knowledge during their life span. A binary version of GSK named novel binary Gaining Sharing knowledge-based optimization algorithm (NBGSK) depends on mainly two binary stages: binary junior gaining sharing stage and binary senior gaining sharing stage with knowledge factor 1. These two stages enable NBGSK for exploring and exploitation of the search space efficiently and effectively to solve problems in binary space. Moreover, to enhance the performance of NBGSK and prevent the solutions from trapping into local optima, NBGSK with population size reduction (PR-NBGSK) is introduced. It decreases the population size gradually with a linear function. The proposed NBGSK and PR-NBGSK applied to set of knapsack instances with small and large dimensions, which shows that NBGSK and PR-NBGSK are more efficient and effective in terms of convergence, robustness, and accuracy.

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