Hyperconical Random Search

1972 ◽  
Vol 94 (1) ◽  
pp. 71-78 ◽  
Author(s):  
M. J. Wozny ◽  
G. T. Heydt
Keyword(s):  
Rate Of Convergence ◽  
Chemical Reaction ◽  
Search Algorithm ◽  
Random Search ◽  
Measured Data ◽  
Convergence Properties ◽  
Search Region

The rate of convergence of a multidimensional random search is found to improve when the search region is restricted to a directed adaptive hypercone. The convergence properties of the hyperconical search algorithm are investigated and the scheme is applied to the problem of identifying twenty-two constants of a given chemical reaction from measured data.

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 Heterogeneous Simulated Annealing Teams: An Optimizing Search Algorithm Inspired by Engineering Design Teams

2018 ◽  
Author(s):  
Christopher McComb ◽  
Jonathan Cagan ◽  
Kenneth Kotovsky
Keyword(s):  
Simulated Annealing ◽  
Engineering Design ◽  
Simulated Annealing Algorithm ◽  
Search Algorithm ◽  
Random Search ◽  
Design Teams ◽  
Design Cognition ◽  
Gradient Based ◽  
Multi Agent ◽  
Annealing Algorithms

Although insights uncovered by design cognition are often utilized to develop the methods used by human designers, using such insights to inform computational methodologies also has the potential to improve the performance of design algorithms. This paper uses insights from research on design cognition and design teams to inform a better simulated annealing search algorithm. Simulated annealing has already been established as a model of individual problem solving. This paper introduces the Heterogeneous Simulated Annealing Team (HSAT) algorithm, a multi-agent simulated annealing algorithm. Each agent controls an adaptive annealing schedule, allowing the team develop heterogeneous search strategies. Such diversity is a natural part of engineering design, and boosts performance in other multi-agent algorithms. Further, interaction between agents in HSAT is structured to mimic interaction between members of a design team. Performance is compared to several other simulated annealing algorithms, a random search algorithm, and a gradient-based algorithm. Compared to other algorithms, the team-based HSAT algorithm returns better average results with lower variance.

scholarly journals Constructing Synthetic Samples

2016 ◽  
Vol 32 (1) ◽  
pp. 113-127
Author(s):  
Hua Dong ◽  
Glen Meeden
Keyword(s):  
Optimization Problem ◽  
Search Algorithm ◽  
Random Search ◽  
The United States ◽  
Simulation Studies ◽  
Synthetic Sample ◽  
Population Means ◽  
Adaptive Random Search ◽  
Random Search Algorithm ◽  
Two Populations

Abstract We consider the problem of constructing a synthetic sample from a population of interest which cannot be sampled from but for which the population means of some of its variables are known. In addition, we assume that we have in hand samples from two similar populations. Using the known population means, we will select subsamples from the samples of the other two populations which we will then combine to construct the synthetic sample. The synthetic sample is obtained by solving an optimization problem, where the known population means, are used as constraints. The optimization is achieved through an adaptive random search algorithm. Simulation studies are presented to demonstrate the effectiveness of our approach. We observe that on average, such synthetic samples behave very much like actual samples from the population of interest. As an application we consider constructing a one-percent synthetic sample for the missing 1890 decennial sample of the United States.

scholarly journals An Optimization Framework for Wind Farm Design in Complex Terrain

2018 ◽  
Vol 8 (11) ◽  
pp. 2053 ◽  
Author(s):  
Ju Feng ◽  
Wen Shen ◽  
Ye Li
Keyword(s):  
Complex Terrain ◽  
Wind Farm ◽  
Search Algorithm ◽  
Random Search ◽  
Wind Farms ◽  
Minimal Distance ◽  
Original Design ◽  
Optimization Framework ◽  
Random Search Algorithm ◽  
Wind Resource

Designing wind farms in complex terrain is an important task, especially for countries with a large portion of complex terrain territory. To tackle this task, an optimization framework is developed in this study, which combines the solution from a wind resource assessment tool, an engineering wake model adapted for complex terrain, and an advanced wind farm layout optimization algorithm. Various realistic constraints are modelled and considered, such as the inclusive and exclusive boundaries, minimal distances between turbines, and specific requirements on wind resource and terrain conditions. The default objective function in this framework is the total net annual energy production (AEP) of the wind farm, and the Random Search algorithm is employed to solve the optimization problem. A new algorithm called Heuristic Fill is also developed in this study to find good initial layouts for optimizing wind farms in complex terrain. The ability of the framework is demonstrated in a case study based on a real wind farm with 25 turbines in complex terrain. Results show that the framework can find a better design, with 2.70% higher net AEP than the original design, while keeping the occupied area and minimal distance between turbines at the same level. Comparison with two popular algorithms (Particle Swarm Optimization and Genetic Algorithm) also shows the superiority of the Random Search algorithm.

Simulation Optimization Using Multi-Time-Scale Adaptive Random Search

2019 ◽  
Vol 36 (06) ◽  
pp. 1940014
Author(s):  
Qi Zhang ◽  
Jiaqiao Hu
Keyword(s):  
Search Algorithm ◽  
Numerical Study ◽  
Random Search ◽  
Solution Space ◽  
Population Based ◽  
Global Optimum ◽  
Adaptive Random Search ◽  
Candidate Solution ◽  
Approximation Type ◽  
Effective Use

We propose a random search algorithm for seeking the global optimum of an objective function in a simulation setting. The algorithm can be viewed as an extension of the MARS algorithm proposed in Hu and Hu (2011) for deterministic optimization, which iteratively finds improved solutions by modifying and sampling from a parameterized probability distribution over the solution space. However, unlike MARS and many other algorithms in this class, which are often population-based, our method only requires a single candidate solution to be generated at each iteration. This is primarily achieved through an effective use of past sampling information by means of embedding multiple nested stochastic approximation type of recursions into the algorithm. We prove the global convergence of the algorithm under general conditions and discuss two special simulation noise cases of interest, in which we show that only one simulation replication run is needed for each sampled solution. A preliminary numerical study is also carried out to illustrate the algorithm.

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