scholarly journals Adiabatic optimization without local minima

2015 ◽  
Vol 15 (3&4) ◽  
pp. 181-199
Author(s):  
Michael Jarret ◽  
Stephen P. Jordan
Keyword(s):  
Ground State ◽  
Global Minimum ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Basic Question ◽  
Local Energy ◽  
Ground State Wavefunction ◽  
Eigenvalue Gap ◽  
Adiabatic Optimization ◽  
Exponentially Small

Several previous works have investigated the circumstances under which quantum adiabatic optimization algorithms can tunnel out of local energy minima that trap simulated annealing or other classical local search algorithms. Here we investigate the even more basic question of whether adiabatic optimization algorithms always succeed in polynomial time for trivial optimization problems in which there are no local energy minima other than the global minimum. Surprisingly, we find a counterexample in which the potential is a single basin on a graph, but the eigenvalue gap is exponentially small as a function of the number of vertices. In this counterexample, the ground state wavefunction consists of two ``lobes'' separated by a region of exponentially small amplitude. Conversely, we prove if the ground state wavefunction is single-peaked then the eigenvalue gap scales at worst as one over the square of the number of vertices.

Comparison of Meta-heuristic Algorithms on Benchmark Functions

2019 ◽  
Vol 2 (3) ◽  
pp. 508-517
Author(s):  
FerdaNur Arıcı ◽  
Ersin Kaya
Keyword(s):  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Optimization Algorithms ◽  
Gravitational Search Algorithm ◽  
Differential Evolution Algorithm ◽  
Population Based ◽  
Time Interval ◽  
Bee Colony ◽  
Different Characteristics

Optimization is a process to search the most suitable solution for a problem within an acceptable time interval. The algorithms that solve the optimization problems are called as optimization algorithms. In the literature, there are many optimization algorithms with different characteristics. The optimization algorithms can exhibit different behaviors depending on the size, characteristics and complexity of the optimization problem. In this study, six well-known population based optimization algorithms (artificial algae algorithm - AAA, artificial bee colony algorithm - ABC, differential evolution algorithm - DE, genetic algorithm - GA, gravitational search algorithm - GSA and particle swarm optimization - PSO) were used. These six algorithms were performed on the CEC’17 test functions. According to the experimental results, the algorithms were compared and performances of the algorithms were evaluated.

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 A New “Good and Bad Groups-Based Optimizer” for Solving Various Optimization Problems

2021 ◽  
Vol 11 (10) ◽  
pp. 4382
Author(s):  
Ali Sadeghi ◽  
Sajjad Amiri Doumari ◽  
Mohammad Dehghani ◽  
Zeinab Montazeri ◽  
Pavel Trojovský ◽  
...  
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Fitness Function ◽  
Optimization Algorithms ◽  
Gravitational Search Algorithm ◽  
Gray Wolf ◽  
Good Group ◽  
Good Ability ◽  
Whale Optimization

Optimization is the science that presents a solution among the available solutions considering an optimization problem’s limitations. Optimization algorithms have been introduced as efficient tools for solving optimization problems. These algorithms are designed based on various natural phenomena, behavior, the lifestyle of living beings, physical laws, rules of games, etc. In this paper, a new optimization algorithm called the good and bad groups-based optimizer (GBGBO) is introduced to solve various optimization problems. In GBGBO, population members update under the influence of two groups named the good group and the bad group. The good group consists of a certain number of the population members with better fitness function than other members and the bad group consists of a number of the population members with worse fitness function than other members of the population. GBGBO is mathematically modeled and its performance in solving optimization problems was tested on a set of twenty-three different objective functions. In addition, for further analysis, the results obtained from the proposed algorithm were compared with eight optimization algorithms: genetic algorithm (GA), particle swarm optimization (PSO), gravitational search algorithm (GSA), teaching–learning-based optimization (TLBO), gray wolf optimizer (GWO), and the whale optimization algorithm (WOA), tunicate swarm algorithm (TSA), and marine predators algorithm (MPA). The results show that the proposed GBGBO algorithm has a good ability to solve various optimization problems and is more competitive than other similar algorithms.

scholarly journals GMBO: Group Mean-Based Optimizer for Solving Various Optimization Problems

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1190
Author(s):  
Mohammad Dehghani ◽  
Zeinab Montazeri ◽  
Štěpán Hubálovský
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Random Search ◽  
Optimization Algorithms ◽  
Gravitational Search Algorithm ◽  
Main Idea ◽  
Population Based ◽  
Grey Wolf Optimizer ◽  
Whale Optimization

There are many optimization problems in the different disciplines of science that must be solved using the appropriate method. Population-based optimization algorithms are one of the most efficient ways to solve various optimization problems. Population-based optimization algorithms are able to provide appropriate solutions to optimization problems based on a random search of the problem-solving space without the need for gradient and derivative information. In this paper, a new optimization algorithm called the Group Mean-Based Optimizer (GMBO) is presented; it can be applied to solve optimization problems in various fields of science. The main idea in designing the GMBO is to use more effectively the information of different members of the algorithm population based on two selected groups, with the titles of the good group and the bad group. Two new composite members are obtained by averaging each of these groups, which are used to update the population members. The various stages of the GMBO are described and mathematically modeled with the aim of being used to solve optimization problems. The performance of the GMBO in providing a suitable quasi-optimal solution on a set of 23 standard objective functions of different types of unimodal, high-dimensional multimodal, and fixed-dimensional multimodal is evaluated. In addition, the optimization results obtained from the proposed GMBO were compared with eight other widely used optimization algorithms, including the Marine Predators Algorithm (MPA), the Tunicate Swarm Algorithm (TSA), the Whale Optimization Algorithm (WOA), the Grey Wolf Optimizer (GWO), Teaching–Learning-Based Optimization (TLBO), the Gravitational Search Algorithm (GSA), Particle Swarm Optimization (PSO), and the Genetic Algorithm (GA). The optimization results indicated the acceptable performance of the proposed GMBO, and, based on the analysis and comparison of the results, it was determined that the GMBO is superior and much more competitive than the other eight algorithms.

scholarly journals GBUO: “The Good, the Bad, and the Ugly” Optimizer

2021 ◽  
Vol 11 (5) ◽  
pp. 2042
Author(s):  
Hadi Givi ◽  
Mohammad Dehghani ◽  
Zeinab Montazeri ◽  
Ruben Morales-Menendez ◽  
Ricardo A. Ramirez-Mendoza ◽  
...  
Keyword(s):  
High Dimension ◽  
Essential Role ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Stochastic Search ◽  
Objective Functions ◽  
Science And Engineering ◽  
Fixed Dimension ◽  
Dimension Functions ◽  
Simulation Results

Optimization problems in various fields of science and engineering should be solved using appropriate methods. Stochastic search-based optimization algorithms are a widely used approach for solving optimization problems. In this paper, a new optimization algorithm called “the good, the bad, and the ugly” optimizer (GBUO) is introduced, based on the effect of three members of the population on the population updates. In the proposed GBUO, the algorithm population moves towards the good member and avoids the bad member. In the proposed algorithm, a new member called ugly member is also introduced, which plays an essential role in updating the population. In a challenging move, the ugly member leads the population to situations contrary to society’s movement. GBUO is mathematically modeled, and its equations are presented. GBUO is implemented on a set of twenty-three standard objective functions to evaluate the proposed optimizer’s performance for solving optimization problems. The mentioned standard objective functions can be classified into three groups: unimodal, multimodal with high-dimension, and multimodal with fixed dimension functions. There was a further analysis carried-out for eight well-known optimization algorithms. The simulation results show that the proposed algorithm has a good performance in solving different optimization problems models and is superior to the mentioned optimization algorithms.

scholarly journals Comparative Study of Optimization Algorithms for The Optimal Reservoir Operation

2018 ◽  
Vol 246 ◽  
pp. 01003
Author(s):  
Xinyuan Liu ◽  
Yonghui Zhu ◽  
Lingyun Li ◽  
Lu Chen
Keyword(s):  
Reservoir Operation ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Complex Problem ◽  
Optimization Techniques ◽  
Decision Variables ◽  
Handling Methods ◽  
Optimality Algorithm ◽  
Parameter Values

Apart from traditional optimization techniques, e.g. progressive optimality algorithm (POA), modern intelligence algorithms, like genetic algorithms, differential evolution have been widely used to solve optimization problems. This paper deals with comparative analysis of POA, GA and DE and their applications in a reservoir operation problem. The results show that both GA and DES are feasible to reservoir operation optimization, but they display different features. GA and DE have many parameters and are difficult in determination of these parameter values. For simple problems with mall number of decision variables, GA and DE are better than POA when adopting appropriate parameter values and constraint handling methods. But for complex problem with large number of variables, POA combined with simplex method are much superior to GA and DE in time-assuming and quality of optimal solutions. This study helps to select proper optimization algorithms and parameter values in reservoir operation.

scholarly journals Parallelization of computational algorithms for optimization problems with high time consumption

2018 ◽  
Vol 157 ◽  
pp. 02054 ◽  
Author(s):  
Milan Vaško ◽  
Marián Handrik ◽  
Alžbeta Sapietová ◽  
Jana Handriková
Keyword(s):  
Computational Models ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Fe Analysis ◽  
Function Evaluation ◽  
Computational Algorithms ◽  
Distributed Computing Systems ◽  
Computing Systems ◽  
Time Consumption ◽  
Design Variables

The paper presents an analysis of the use of optimization algorithms in parallel solutions and distributed computing systems. The primary goal is to use evolutionary algorithms and their implementation into parallel calculations. Parallelization of computational algorithms is suitable for the following cases - computational models with a large number of design variables or cases where the objective function evaluation is time consuming (FE analysis). As the software platform for application of distributed optimization algorithms is using MATLAB and BOINC software package.

DFT and TD-DFT study of the enol and thiol tautomers of 3-thioxopropanal in the ground and first singlet excited states

2017 ◽  
Vol 16 (04) ◽  
pp. 1750034 ◽  
Author(s):  
Kolsoom Shayan ◽  
Alireza Nowroozi
Keyword(s):  
Excited States ◽  
Ground State ◽  
Global Minimum ◽  
Substitution Effects ◽  
Structure Stability ◽  
Stable Form ◽  
Orbital Parameters ◽  
Td Dft ◽  
Intramolecular Hydrogen ◽  
Linear Correlations

In the first part of this paper, a comprehensive theoretical study of molecular structure, stability, intramolecular hydrogen bond (IMHB) and [Formula: see text]-electron delocalization ([Formula: see text]-ED) of the enol and thiol tautomers of 3-thioxopropanal (TPA) in the ground state is performed. In this regard, all of the plausible conformations of TPA at M06-2X/6-311[Formula: see text]G(d,p) are optimized and a variety of theoretical levels are employed to identify the global minimum. Our calculations show that E1 is the most stable form that is in contrast to the results of Gonzalez et al. [J Phys Chem 101: 9710, 1997]. In order to elucidate this duality, the IMHB and [Formula: see text]-ED of chelated forms (E1 and T1) have been extensively investigated. So, it is found that both of the IMHB analysis and [Formula: see text]-ED concepts emphasize on the E1, as the global minimum. In the second part of this study, a set of simple electron-withdrawing and electron-donating substituents such as CN, F, Cl, CH3 and NH2 have been considered to evaluate their effects on the IMHB of the first singlet excited state of E1 and T1 at TD-DFT/6–311[Formula: see text]G(d,p) level of theory. According to our analysis, it was found that the IMHB strength of the excited states are much weaker than the ground states. Surprisingly, the IMHB of thiol derivatives is stronger than the enol ones in contrast to the ground state. Furthermore, the substitution effects in the ground and excited states are significantly different. Finally, various linear correlations between the IMHB energies with geometrical, topological and molecular orbital parameters are obtained.

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