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 Control Synthesis as Machine Learning Control by Symbolic Regression Methods

2021 ◽  
Vol 11 (12) ◽  
pp. 5468
Author(s):  
Elizaveta Shmalko ◽  
Askhat Diveev
Keyword(s):  
Machine Learning ◽  
Genetic Programming ◽  
Mathematical Formulation ◽  
Small Variation ◽  
Learning Control ◽  
Symbolic Regression ◽  
Control Technique ◽  
Control Synthesis ◽  
Basic Solution ◽  
Regression Methods

The problem of control synthesis is considered as machine learning control. The paper proposes a mathematical formulation of machine learning control, discusses approaches of supervised and unsupervised learning by symbolic regression methods. The principle of small variation of the basic solution is presented to set up the neighbourhood of the search and to increase search efficiency of symbolic regression methods. Different symbolic regression methods such as genetic programming, network operator, Cartesian and binary genetic programming are presented in details. It is shown on the computational example the possibilities of symbolic regression methods as unsupervised machine learning control technique to the solution of MLC problem of control synthesis for obtaining the stabilization system for a mobile robot.

scholarly journals Comparative Analysis of Low Discrepancy Sequence-Based Initialization Approaches Using Population-Based Algorithms for Solving the Global Optimization Problems

2021 ◽  
Vol 11 (16) ◽  
pp. 7591
Author(s):  
Waqas Haider Bangyal ◽  
Kashif Nisar ◽  
Ag. Asri Bin Ag. Ibrahim ◽  
Muhammad Reazul Haque ◽  
Joel J. P. C. Rodrigues ◽  
...  
Keyword(s):  
Random Distribution ◽  
Random Number ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Search Space ◽  
Metaheuristic Algorithms ◽  
Test Problems ◽  
Uniform Random Number ◽  
Low Discrepancy Sequences ◽  
The Family

Metaheuristic algorithms have been widely used to solve diverse kinds of optimization problems. For an optimization problem, population initialization plays a significant role in metaheuristic algorithms. These algorithms can influence the convergence to find an efficient optimal solution. Mainly, for recognizing the importance of diversity, several researchers have worked on the performance for the improvement of metaheuristic algorithms. Population initialization is a vital factor in metaheuristic algorithms such as PSO and DE. Instead of applying the random distribution for the initialization of the population, quasirandom sequences are more useful for the improvement the diversity and convergence factors. This study presents three new low-discrepancy sequences named WELL sequence, Knuth sequence, and Torus sequence to initialize the population in the search space. This paper also gives a comprehensive survey of the various PSO and DE initialization approaches based on the family of quasirandom sequences such as Sobol sequence, Halton sequence, and uniform random distribution. The proposed methods for PSO (TO-PSO, KN-PSO, and WE-PSO) and DE (DE-TO, DE-WE, and DE-KN) have been examined for well-known benchmark test problems and training of the artificial neural network. The finding of our techniques shows promising performance using the family of low-discrepancy sequences over uniform random numbers. For a fair comparison, the approaches using low-discrepancy sequences for PSO and DE are compared with the other family of low-discrepancy sequences and uniform random number and depict the superior results. The experimental results show that the low-discrepancy sequences-based initialization performed exceptionally better than a uniform random number. Moreover, the outcome of our work presents a foresight on how the proposed technique profoundly impacts convergence and diversity. It is anticipated that this low-discrepancy sequence comparative simulation survey would be helpful for studying the metaheuristic algorithm in detail for the researcher.

scholarly journals SOLVING INTEGER PROGRAMMING PROBLEMS BY USING POPULATION-BASED BEETLE ANTENNAE SEARCH ALGORITHM

2021 ◽  
Vol 9 (3-4) ◽  
pp. 89-99
Author(s):  
Ivona Brajević ◽  
Miodrag Brzaković ◽  
Goran Jocić
Keyword(s):  
Integer Programming ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Search Space ◽  
Population Based ◽  
Local Optimum ◽  
Integer Programming Problems ◽  
Metaheuristic Techniques

Beetle antennae search (BAS) algorithm is a newly proposed single-solution based metaheuristic technique inspired by the beetle preying process. Although BAS algorithm has shown good search abilities, it can be easily trapped into local optimum when it is used to solve hard optimization problems. With the intention to overcome this drawback, this paper presents a population-based beetle antennae search (PBAS) algorithm for solving integer programming problems.  This method employs the population's capability to search diverse regions of the search space to provide better guarantee for finding the optimal solution. The PBAS method was tested on nine integer programming problems and one mechanical design problem. The proposed algorithm was compared to other state-of-the-art metaheuristic techniques. The comparisons show that the proposed PBAS algorithm produces better results for majority of tested problems.  

Numerical Optimization Using the Heart Algorithm

2018 ◽  
Vol 9 (2) ◽  
pp. 33-37
Author(s):  
Abdolreza Hatamlou
Keyword(s):  
Numerical Optimization ◽  
Optimization Problems ◽  
Heart Function ◽  
Circulatory System ◽  
Optimal Solution ◽  
Search Space ◽  
Human Beings ◽  
Unconstrained Optimization Problems ◽  
And Performance ◽  
The Given

In this article the authors investigate the application of the heart algorithm for solving unconstraint numerical optimization problems. Heart algorithms are a novel optimization algorithm which mimics the heart function and circulatory system procedure in the human beings. It starts with a number of candidate solutions for the given problem and utilizes the contraction and expansion actions to move the candidates in the search space for finding optimal solution. The applicability and performance of the heart algorithm for solving unconstrained optimization problems has been tested using several benchmark functions. Experimental results show its potential and superiority.

Genetic Algorithms with Immigrants Scheme for Dynamic Optimization Problems

2013 ◽  
Vol 333-335 ◽  
pp. 1379-1383
Author(s):  
Yan Wu ◽  
Xiao Xiong Liu
Keyword(s):  
Genetic Algorithms ◽  
Dynamic Optimization ◽  
Optimization Problems ◽  
Main Idea ◽  
Optimal Solution ◽  
Search Space ◽  
Dynamic Environments ◽  
Dynamic Optimization Problems ◽  
New Space ◽  
Over Time

In dynamic environments, it is difficult to track a changing optimal solution over time. Over the years, many approaches have been proposed to solve the problem with genetic algorithms. In this paper a new space-based immigrant scheme for genetic algorithms is proposed to solve dynamic optimization problems. In this scheme, the search space is divided into two subspaces using the elite of the previous generation and the range of variables. Then the immigrants are generated from both the subspaces and inserted into current population. The main idea of the approach is to increase the diversity more evenly and dispersed. Finally an experimental study on dynamic sphere function was carried out to compare the performance of several genetic algorithms. The experimental results show that the proposed algorithm is effective for the function with moving optimum and can adapt the dynamic environments rapidly.

scholarly journals Solving integer programming problems by using population-based beetle antennae search algorithm

2021 ◽  
Vol 9 (3-4) ◽  
pp. 89-99
Author(s):  
Ivona Brajević ◽  
Miodrag Brzaković ◽  
Goran Jocić
Keyword(s):  
Integer Programming ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Search Space ◽  
Population Based ◽  
Local Optimum ◽  
Integer Programming Problems ◽  
Metaheuristic Techniques

Beetle antennae search (BAS) algorithm is a newly proposed single-solution based metaheuristic technique inspired by the beetle preying process. Although BAS algorithm has shown good search abilities, it can be easily trapped into local optimum when it is used to solve hard optimization problems. With the intention to overcome this drawback, this paper presents a population-based beetle antennae search (PBAS) algorithm for solving integer programming problems. This method employs the population's capability to search diverse regions of the search space to provide better guarantee for finding the optimal solution. The PBAS method was tested on nine integer programming problems and one mechanical design problem. The proposed algorithm was compared to other state-of-the-art metaheuristic techniques. The comparisons show that the proposed PBAS algorithm produces better results for majority of tested problems.

scholarly journals Designation of Candidate Solutions in Differential Evolution Based on Bandit Algorithm and its Evaluation

2019 ◽  
Vol 23 (4) ◽  
pp. 758-766
Author(s):  
Masaya Sakakibara ◽  
◽  
Akira Notsu ◽  
Seiki Ubukata ◽  
Katsuhiro Honda
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Random Search ◽  
Optimal Solution ◽  
Search Space ◽  
Optimization Method ◽  
Local Solution ◽  
Search Speed ◽  
Mathematical Programming Problems

We propose UCT-Grid Area Search (UCT-GAS), which is an efficient optimization method that roughly estimates specific values in areas, and consider exploration and exploitation in optimization problems. This approach divides the search space and imagines it to be a multi-armed bandit, which enables us to use bandit algorithms to solve mathematical programming problems. Although the search speed is fast than other search algorithm like differential evolution, it might converge to a local solution. In this study, we improve this algorithm by replacing its random search part with differential evolution after several searches. Comparative experiments confirmed the search ability of the optimal solution, and our method benefits by showing that it avoids falling into a local solution and that its search speed is fast.

scholarly journals Optimizing Constraint Solving via Dynamic Programming

2019 ◽  
Author(s):  
Shu Lin ◽  
Na Meng ◽  
Wenxin Li
Keyword(s):  
Dynamic Programming ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Search Space ◽  
Constraint Solving ◽  
Constraint Optimization ◽  
Objective Functions ◽  
Constraint Solver ◽  
Constraint Optimization Problems ◽  
Finite Domains

Constraint optimization problems (COP) on finite domains are typically solved via search. Many problems (e.g., 0-1 knapsack) involve redundant search, making a general constraint solver revisit the same subproblems again and again. Existing approaches use caching, symmetry breaking, subproblem dominance, or search with decomposition to prune the search space of constraint problems. In this paper we present a different approach--DPSolver--which uses dynamic programming (DP) to efficiently solve certain types of constraint optimization problems (COPs). Given a COP modeled with MiniZinc, DPSolver first analyzes the model to decide whether the problem is efficiently solvable with DP. If so, DPSolver refactors the constraints and objective functions to model the problem as a DP problem. Finally, DPSolver feeds the refactored model to Gecode--a widely used constraint solver--for the optimal solution. Our evaluation shows that DPSolver significantly improves the performance of constraint solving.

scholarly journals Search Space Reduction for Genetic Algorithms Applied to Drainage Network Optimization Problems

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2008
Author(s):  
Leonardo Bayas-Jiménez ◽  
F. Javier Martínez-Solano ◽  
Pedro L. Iglesias-Rey ◽  
Daniel Mora-Meliá
Keyword(s):  
Genetic Algorithms ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Search Space ◽  
Computational Effort ◽  
Joint Work ◽  
Large Space ◽  
Space Reduction ◽  
Drainage Networks ◽  
Search Space Reduction

In recent years, a significant increase in the number of extreme rains around the world has been observed, which has caused an overpressure of urban drainage networks. The lack of capacity to evacuate this excess water generates the need to rehabilitate drainage systems. There are different rehabilitation methodologies that have proven their validity; one of the most used is the heuristic approach. Within this approach, the use of genetic algorithms has stood out for its robustness and effectiveness. However, the problem to be overcome by this approach is the large space of solutions that algorithms must explore, affecting their efficiency. This work presents a method of search space reduction applied to the rehabilitation of drainage networks. The method is based on reducing the initially large search space to a smaller one that contains the optimal solution. Through iterative processes, the search space is gradually reduced to define the final region. The rehabilitation methodology contemplates the optimization of networks using the joint work of the installation of storm tanks, replacement of pipes, and implementation of hydraulic control elements. The optimization model presented uses a pseudo genetic algorithm connected to the SWMM model through a toolkit. Optimization problems consider a large number of decision variables, and could require a huge computational effort. For this reason, this work focuses on identifying the most promising region of the search space to contain the optimal solution and to improve the efficiency of the process. Finally, this method is applied in real networks to show its validity.

scholarly journals Theoretical Analysis of Local Search and Simple Evolutionary Algorithms for the Generalized Travelling Salesperson Problem

2019 ◽  
Vol 27 (3) ◽  
pp. 525-558
Author(s):  
Mojgan Pourhassan ◽  
Frank Neumann
Keyword(s):  
Evolutionary Algorithms ◽  
Local Search ◽  
Polynomial Time ◽  
Theoretical Perspective ◽  
Optimal Solution ◽  
Search Space ◽  
Search Algorithms ◽  
Variable Neighbourhood Search ◽  
Local Search Algorithms ◽  
Travelling Salesperson Problem

The generalized travelling salesperson problem is an important NP-hard combinatorial optimization problem for which metaheuristics, such as local search and evolutionary algorithms, have been used very successfully. Two hierarchical approaches with different neighbourhood structures, namely a cluster-based approach and a node-based approach, have been proposed by Hu and Raidl ( 2008 ) for solving this problem. In this article, local search algorithms and simple evolutionary algorithms based on these approaches are investigated from a theoretical perspective. For local search algorithms, we point out the complementary abilities of the two approaches by presenting instances where they mutually outperform each other. Afterwards, we introduce an instance which is hard for both approaches when initialized on a particular point of the search space, but where a variable neighbourhood search combining them finds the optimal solution in polynomial time. Then we turn our attention to analysing the behaviour of simple evolutionary algorithms that use these approaches. We show that the node-based approach solves the hard instance of the cluster-based approach presented in Corus et al. ( 2016 ) in polynomial time. Furthermore, we prove an exponential lower bound on the optimization time of the node-based approach for a class of Euclidean instances.

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