scholarly journals A Symmetry-Breaking Node Equivalence for Pruning the Search Space in Backtracking Algorithms

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1300
Author(s):  
Uroš Čibej ◽  
Luka Fürst ◽  
Jurij Mihelič
Keyword(s):  
Symmetry Breaking ◽  
Optimization Problem ◽  
Heuristic Method ◽  
Search Space ◽  
Search Tree ◽  
Backtracking Search ◽  
Complete Problems ◽  
Np Complete ◽  
Complexity Hierarchy ◽  
General Graphs

We introduce a new equivalence on graphs, defined by its symmetry-breaking capability. We first present a framework for various backtracking search algorithms, in which the equivalence is used to prune the search tree. Subsequently, we define the equivalence and an optimization problem with the goal of finding an equivalence partition with the highest pruning potential. We also position the optimization problem into the computational-complexity hierarchy. In particular, we show that the verifier lies between P and NP -complete problems. Striving for a practical usability of the approach, we devise a heuristic method for general graphs and optimal algorithms for trees and cycles.

scholarly journals Symmetry-Breaking for Airflow Control Optimization of an Oscillating-Water-Column System

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 895 ◽  
Author(s):  
Fares M’zoughi ◽  
Izaskun Garrido ◽  
Aitor J. Garrido
Keyword(s):  
Symmetry Breaking ◽  
Water Column ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Search Time ◽  
Pso Algorithm ◽  
Search Space ◽  
Oscillating Water Column ◽  
Column System ◽  
Control Optimization

Global optimization problems are mostly solved using search methods. Therefore, decreasing the search space can increase the efficiency of their solving. A widely exploited technique to reduce the search space is symmetry-breaking, which helps impose constraints on breaking existing symmetries. The present article deals with the airflow control optimization problem in an oscillating-water-column using the Particle Swarm Optimization (PSO). In an effort to ameliorate the efficiency of the PSO search, a symmetry-breaking technique has been implemented. The results of optimization showed that shrinking the search space helped to reduce the search time and ameliorate the efficiency of the PSO algorithm.

scholarly journals A Hyper-Heuristic Approach for Efficient Resource Scheduling in Grid

2008 ◽  
Vol 3 (3) ◽  
pp. 249 ◽  
Author(s):  
S. Mary Saira Bhanu ◽  
N.P. Gopalan
Keyword(s):  
Optimization Problem ◽  
Optimal Schedule ◽  
Search Space ◽  
Time Varying ◽  
Problem Domain ◽  
Dynamic Nature ◽  
Grid Environment ◽  
Efficient Resource ◽  
Np Hard Problem ◽  
Np Complete

Efficient execution of computations in grid can require mapping of tasks to processors whose performance is both irregular and time varying because of dynamic nature. The task of mapping jobs to the available computing nodes or scheduling of the jobs on the grid is a NP complete problem. The NP-hard problem is often solved using heuristics techniques. Heuristic and metaheuristic approaches tend to be knowledge rich, requiring substantial expertise in both the problem domain and appropriate heuristics techniques. To alleviate this problem the concept of Hyperheuristic was introduced. They operate on the search space of heuristics instead of candidate solutions and can be applied to any optimization problem. This paper emphasizes the use of Hyper-heuristics built on top of hybridized Metaheuristics to efficiently and effectively schedule jobs onto available resources in a grid environment thus resulting in an optimal schedule with minimum makespan.

scholarly journals Influence of Variables Encoding and Symmetry Breaking on the Performance of Optimization Modulo Theories Tools Applied to Cloud Resource Selection

10.29007/zwdh ◽  
2018 ◽  
Author(s):  
Madalina Erascu ◽  
Flavia Micota ◽  
Daniela Zaharie
Keyword(s):  
Symmetry Breaking ◽  
Resource Selection ◽  
Optimization Problem ◽  
Virtual Machines ◽  
State Of The Art ◽  
Search Space ◽  
Resource Provisioning ◽  
Conflict Graph ◽  
Cloud Resource ◽  
Optimization Modulo Theories

The problem of Cloud resource provisioning for component-based applications is very important. It consists in the allocation of virtual machines (VMs) from various Cloud Providers (CPs), to a set of applications such that the constraints induced by the inter- actions between components and by the components hardware/software requirements are satisfied and the performance objectives are optimized (e.g. costs are minimized). It can be formulated as a constrained optimization problem and tackled by state-of-the-art optimization modulo theories (OMT) tools. The performance of the OMT tools is highly dependent on the way the problem is formalized as this determines the size of the search space. In the case when the number of VMs offers is large, a naive encoding which does not exploit the symmetries of the underlying problem leads to a huge search space making the optimization problem intractable. We overcame this issue by reducing the search space by using: (1) a heuristic which exploits the particularities of the application by detect- ing cliques in the conflict graph of the application components fixing all components of the clique with the largest number of component instances, and (2) a lex-leader method for breaking variable symmetry where the canonical solution fulfills an order based on either the number of components deployed on VMs, or on the VMs price. As the result, the running time of the optimization problem improves considerably and the optimization problem scales up to hundreds of VM offers. We also observed that by combining the heuristic with the lex-leader method we obtained better computational results than by using them separately, suggesting the fact that symmetry breaking constraints have the advantage of interacting well with the search heuristic being used.

scholarly journals The Complexity of Integer Bound Propagation

2011 ◽  
Vol 40 ◽  
pp. 657-676 ◽  
Author(s):  
L. Bordeaux ◽  
G. Katsirelos ◽  
N. Narodytska ◽  
M. Y. Vardi
Keyword(s):  
Numerical Range ◽  
Search Space ◽  
Search Tree ◽  
Linear Constraints ◽  
Polynomial Algorithms ◽  
Worst Case ◽  
Programming Tools ◽  
The Common ◽  
Np Complete ◽  
Branch And Prune

Bound propagation is an important Artificial Intelligence technique used in Constraint Programming tools to deal with numerical constraints. It is typically embedded within a search procedure (”branch and prune”) and used at every node of the search tree to narrow down the search space, so it is critical that it be fast. The procedure invokes constraint propagators until a common fixpoint is reached, but the known algorithms for this have a pseudo-polynomial worst-case time complexity: they are fast indeed when the variables have a small numerical range, but they have the well-known problem of being prohibitively slow when these ranges are large. An important question is therefore whether strongly-polynomial algorithms exist that compute the common bound consistent fixpoint of a set of constraints. This paper answers this question. In particular we show that this fixpoint computation is in fact NP-complete, even when restricted to binary linear constraints.

scholarly journals Secure the IoT Networks as Epidemic Containment Game

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 156
Author(s):  
Juntao Zhu ◽  
Hong Ding ◽  
Yuchen Tao ◽  
Zhen Wang ◽  
Lanping Yu
Keyword(s):  
Heuristic Algorithms ◽  
Heuristic Method ◽  
Exact Algorithms ◽  
Epidemic Threshold ◽  
Solution Quality ◽  
Sis Model ◽  
Linear Programming Formulation ◽  
Iot Devices ◽  
General Graphs ◽  
The Internet Of Things

The spread of a computer virus among the Internet of Things (IoT) devices can be modeled as an Epidemic Containment (EC) game, where each owner decides the strategy, e.g., installing anti-virus software, to maximize his utility against the susceptible-infected-susceptible (SIS) model of the epidemics on graphs. The EC game’s canonical solution concepts are the Minimum/Maximum Nash Equilibria (MinNE/MaxNE). However, computing the exact MinNE/MaxNE is NP-hard, and only several heuristic algorithms are proposed to approximate the MinNE/MaxNE. To calculate the exact MinNE/MaxNE, we provide a thorough analysis of some special graphs and propose scalable and exact algorithms for general graphs. Especially, our contributions are four-fold. First, we analytically give the MinNE/MaxNE for EC on special graphs based on spectral radius. Second, we provide an integer linear programming formulation (ILP) to determine MinNE/MaxNE for the general graphs with the small epidemic threshold. Third, we propose a branch-and-bound (BnB) framework to compute the exact MinNE/MaxNE in the general graphs with several heuristic methods to branch the variables. Fourth, we adopt NetShiled (NetS) method to approximate the MinNE to improve the scalability. Extensive experiments demonstrate that our BnB algorithm can outperform the naive enumeration method in scalability, and the NetS can improve the scalability significantly and outperform the previous heuristic method in solution quality.

Application of formal languages in polynomial transformations of instances between NP-complete problems

2013 ◽  
Vol 14 (8) ◽  
pp. 623-633
Author(s):  
Jorge A. Ruiz-Vanoye ◽  
Joaquín Pérez-Ortega ◽  
Rodolfo A. Pazos Rangel ◽  
Ocotlán Díaz-Parra ◽  
Héctor J. Fraire-Huacuja ◽  
...  
Keyword(s):  
Formal Languages ◽  
Complete Problems ◽  
Polynomial Transformations ◽  
Np Complete

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.

scholarly journals EcoRacer: Game-Based Optimal Electric Vehicle Design and Driver Control Using Human Players

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Yi Ren ◽  
Alparslan Emrah Bayrak ◽  
Panos Y. Papalambros
Keyword(s):  
Optimization Problem ◽  
Solution Space ◽  
Efficient Global Optimization ◽  
Vehicle Design ◽  
Control Problems ◽  
Short Term ◽  
Algorithm Efficiency ◽  
Np Complete ◽  
And Control

We compare the performance of human players against that of the efficient global optimization (EGO) algorithm for an NP-complete powertrain design and control problem. Specifically, we cast this optimization problem as an online competition and received 2391 game plays by 124 anonymous players during the first month from launch. We found that while only a small portion of human players can outperform the algorithm in the long term, players tend to formulate good heuristics early on that can be used to constrain the solution space. Such constraining of the search enhances algorithm efficiency, even for different game settings. These findings indicate that human-assisted computational searches are promising in solving comprehensible yet computationally hard optimal design and control problems, when human players can outperform the algorithm in a short term.

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