scholarly journals Symbolic Regression by Exhaustive Search: Reducing the Search Space Using Syntactical Constraints and Efficient Semantic Structure Deduplication

2020 ◽  
pp. 79-99
Author(s):  
Lukas Kammerer ◽  
Gabriel Kronberger ◽  
Bogdan Burlacu ◽  
Stephan M. Winkler ◽  
Michael Kommenda ◽  
...  
Keyword(s):  
Search Space ◽  
Symbolic Regression ◽  
Exhaustive Search ◽  
Semantic Structure

scholarly journals Cluster Analysis of a Symbolic Regression Search Space

2019 ◽  
pp. 85-102 ◽  
Author(s):  
Gabriel Kronberger ◽  
Lukas Kammerer ◽  
Bogdan Burlacu ◽  
Stephan M. Winkler ◽  
Michael Kommenda ◽  
...  
Keyword(s):  
Cluster Analysis ◽  
Search Space ◽  
Symbolic Regression

scholarly journals A Bounded Exhaustive Search Technique for Optimal Phasor Measurement Unit Placement in Power Grids

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2021
Author(s):  
Ahmad Asrul Ibrahim ◽  
Khairuddin Khalid ◽  
Hussain Shareef ◽  
Nor Azwan Mohamed Kamari
Keyword(s):  
Search Space ◽  
Exhaustive Search ◽  
Operating Conditions ◽  
Power Grids ◽  
Phasor Measurement Unit ◽  
Computational Time ◽  
Measurement Unit ◽  
Search Technique ◽  
Phasor Measurement ◽  
Pmu Placement

This paper proposes a technique to determine the possible optimal placement of the phasor measurement unit (PMU) in power grids for normal operating conditions. All possible combinations of PMU placement, including infeasible combinations, are typically considered in finding the optimal solution, which could be a massive search space. An integer search algorithm called the bounded search technique is introduced to reduce the search space in solving a minimum number of PMU allocations whilst maintaining full system observability. The proposed technique is based on connectivity and symmetry constraints that can be derived from the observability matrix. As the technique is coupled with the exhaustive technique, the technique is called the bounded exhaustive search (BES) technique. Several IEEE test systems, namely, IEEE 9-bus, IEEE 14-bus, IEEE 24-bus and IEEE 30-bus, are considered to showcase the performance of the proposed technique. An initial Monte Carlo simulation was carried out to evaluate the capability of the bounded search technique in providing a smaller feasible search space. The effectiveness of the BES technique in terms of computational time is compared with the existing exhaustive technique. Results demonstrate that the search space can be reduced tremendously, and the computational burden can be eased, when finding the optimal PMU placement in power grids.

Divide and Conquer: A Quick Scheme for Symbolic Regression

2021 ◽  
Author(s):  
Changtong Luo ◽  
Chen Chen ◽  
Zonglin Jiang
Keyword(s):  
Target Function ◽  
Search Space ◽  
Symbolic Regression ◽  
Divide And Conquer ◽  
Model Function ◽  
Quick Scheme ◽  
Special Machine ◽  
Sample Data ◽  
Accurate Expression ◽  
Regression Problems

Symbolic regression (SR), as a special machine learning method, can produce mathematical models with explicit expressions. It has received increasing attention in recent years. However, finding a concise, accurate expression is still challenging because of its huge search space. In this work, a divide and conquer (D&C) scheme is proposed. It tries to divide the search space into a number of orthogonal sub-spaces based on the separability feature inferred from the sample data (dividing process). For each sub-space, a sub-function is learned (conquering process). The target model function is then reconstructed with the sub-functions according to their separability patterns. To this end, a separability pattern detecting technique, bi-correlation test (Bi-CT), is also proposed. Note that the sub-functions could be determined by any of the existing SR methods, which makes D&C easy to use. The D&C powered SR has been tested on many symbolic regression problems, and the study shows that D&C can help SR to get the target function more quickly and reliably.

scholarly journals An adaptive parallel algorithm for finite language decomposition

2021 ◽  
Author(s):  
Tomasz Jastrzęb ◽  
Zbigniew J. Czech ◽  
Wojciech Wieczorek
Keyword(s):  
Parallel Computing ◽  
Parallel Algorithm ◽  
Search Space ◽  
Exhaustive Search ◽  
Computational Experiments ◽  
Hard Problem ◽  
Finite Language ◽  
Behavior Based

AbstractThe computationally hard problem of finite language decomposition is investigated. A finite language L is decomposable if there are two languages L1 and L2 such that L = L1L2. Otherwise, L is prime. The main contribution of the paper is an adaptive parallel algorithm for finding all decompositions L1L2 of L. The algorithm is based on an exhaustive search and incorporates several original methods for pruning the search space. Moreover, the algorithm is adaptive since it changes its behavior based on the runtime acquired data related to its performance. Comprehensive computational experiments on more than 4000 benchmark languages generated over alphabets of various sizes have been carried out. The experiments showed that by using the power of parallel computing the decompositions of languages containing more than 200000 words can be found. Decompositions of languages of that size have not been reported in the literature so far.

scholarly journals Universal Approach to Solution of Optimization Problems by Symbolic Regression

2021 ◽  
Vol 11 (11) ◽  
pp. 5081
Author(s):  
Elena Sofronova ◽  
Askhat Diveev
Keyword(s):  
Optimization Problems ◽  
Optimal Solution ◽  
Small Variation ◽  
Search Space ◽  
Search Algorithms ◽  
Symbolic Regression ◽  
Basic Solution ◽  
Potential Solution ◽  
Regression Methods ◽  
Universal Approach

Optimization problems and their solution by symbolic regression methods are considered. The search is performed on non-Euclidean space. In such spaces it is impossible to determine a distance between two potential solutions and, therefore, algorithms using arithmetic operations of multiplication and addition are not used there. The search of optimal solution is performed on the space of codes. It is proposed that the principle of small variations of basic solution be applied as a universal approach to create search algorithms. Small variations cause a neighborhood of a potential solution, and the solution is searched for within this neighborhood. The concept of inheritance property is introduced. It is shown that for non-Euclidean search space, the application of evolution and small variations of possible solutions is effective. Examples of using the principle of small variation of basic solution for different symbolic regression methods are presented.

scholarly journals Intelligent UAV Deployment for a Disaster-Resilient Wireless Network

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 6140 ◽  
Author(s):  
Hassaan Hydher ◽  
Dushantha Nalin K. Jayakody ◽  
Kasun T. Hemachandra ◽  
Tharaka Samarasinghe
Keyword(s):  
Energy Savings ◽  
Network Connectivity ◽  
Emergency Situation ◽  
Search Space ◽  
Exhaustive Search ◽  
Base Stations ◽  
Optimal Placement ◽  
Stable Marriage ◽  
Similar Amount ◽  
The Impact

Deployment of unmanned aerial vehicles (UAVs) as aerial base stations (ABSs) has been considered to be a feasible solution to provide network coverage in scenarios where the conventional terrestrial network is overloaded or inaccessible due to an emergency situation. This article studies the problem of optimal placement of the UAVs as ABSs to enable network connectivity for the users in such a scenario. The main contributions of this work include a less complex approach to optimally position the UAVs and to assign user equipment (UE) to each ABS, such that the total spectral efficiency (TSE) of the network is maximized, while maintaining a minimum QoS requirement for the UEs. The main advantage of the proposed approach is that it only requires the knowledge of UE and ABS locations and statistical channel state information. The optimal 2-dimensional (2D) positions of the ABSs and the UE assignments are found using K-means clustering and a stable marriage approach, considering the characteristics of the air-to-ground propagation channels, the impact of co-channel interference from other ABSs, and the energy constraints of the ABSs. Two approaches are proposed to find the optimal altitudes of the ABSs, using search space constrained exhaustive search and particle swarm optimization (PSO). The numerical results show that the PSO-based approach results in higher TSE compared to the exhaustive search-based approach in dense networks, consuming similar amount of energy for ABS movements. Both approaches lead up to approximately 8-fold energy savings compared to ABS placement using naive exhaustive search.

EVOLUTIONARY MOTIFS FOR THE AUTOMATED DISCOVERY OF SELF-ORGANIZING DIMER AUTOMATA

2012 ◽  
Vol 15 (08) ◽  
pp. 1250081
Author(s):  
DUSTIN ARENDT ◽  
YANG CAO
Keyword(s):  
Building Blocks ◽  
Search Space ◽  
Exhaustive Search ◽  
Self Organization ◽  
Diverse Population ◽  
Reverse Engineer ◽  
Automated Discovery ◽  
Physical Phenomena ◽  
Interesting Behavior ◽  
Fast Growth Rate

It is usually difficult to reverse engineer a simple rule that exhibits some desirable and interesting behavior. We approach this problem by searching for dimer automaton rules exhibiting a broadly defined behavior, self-organization. We expected the simple and asynchronous nature of dimer automata to hinder self-organization, but an exhaustive search quickly yielded three rules that do, in fact, exhibit properties of self-organization. Two of these rules are applicable to actual physical phenomena, motivating searching for additional, more complex rules. However, exhaustive searches scale poorly here because of the rarity of interesting rules combined with the fast growth rate of the search space. To address these challenges we developed the evolutionary motifs algorithm. This algorithm finds the building blocks of the previously found dimer automaton rules, and combines them to form new rules in an evolutionary manner. Our evolutionary algorithm was more effective than an exhaustive search, producing a diverse population of rules exhibiting self-organization.

THE UNIQUE EQUIVALENCE CLASS OF CHROMATIC RECTANGLE FREE 3-COLORINGS OF A 10 × 10 CHESSBOARD

2010 ◽  
Vol 03 (04) ◽  
pp. 715-729
Author(s):  
L. K. Waters
Keyword(s):  
Equivalence Class ◽  
Search Space ◽  
Exhaustive Search ◽  
The Other ◽  
Positive Integers

Consider an M × N chess board with each space colored one of K colors. A chromatic rectangle is a rectangular collection of spaces with all four corner spaces colored the same. An M × N : K NCR board is an M × N board for which there exists a K coloring with no chromatic rectangles. If every K coloring includes a chromatic rectangle, then that board is called an M × N : K CR board. The classification as NCR versus CR has been settled for K ∈ {1, 2, 3} and all positive integers N and M. Note that transposition, or interchanging rows, columns, or colors, will preserve the existence of chromatic rectangles within a coloring. With this in mind, two colorings of a board are called equivalent if one can be produced from the other by such manipulations. This paper establishes that all 10 × 10 : 3 NCR colorings are equivalent. The results stem from characterizations of NCR colorings. These characterizations permit devising and implementing a backtracking algorithm for finding NCR colorings within a significantly restricted search space. In the 10 × 10 : 3 case, the restricted search space is small enough to complete an exhaustive search in about an hour. Several NCR colorings for larger boards, with K > 3, are also included.

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