scholarly journals Pure Random Orthogonal Search (PROS): A Plain and Elegant Parameterless Algorithm for Global Optimization

2021 ◽  
Vol 11 (11) ◽  
pp. 5053
Author(s):  
Vagelis Plevris ◽  
Nikolaos P. Bakas ◽  
German Solorzano
Keyword(s):  
Convergence Rates ◽  
Random Search ◽  
Optimal Solution ◽  
Decision Variable ◽  
Candidate Solution ◽  
Simple Alternative ◽  
Orthogonal Search ◽  
Optimization Search ◽  
Pure Random Search ◽  
Metaheuristic Optimization Algorithms

A new, fast, elegant, and simple stochastic optimization search method is proposed, which exhibits surprisingly good performance and robustness considering its simplicity. We name the algorithm pure random orthogonal search (PROS). The method does not use any assumptions, does not have any parameters to adjust, and uses basic calculations to evolve a single candidate solution. The idea is that a single decision variable is randomly changed at every iteration and the candidate solution is updated only when an improvement is observed; therefore, moving orthogonally towards the optimal solution. Due to its simplicity, PROS can be easily implemented with basic programming skills and any non-expert in optimization can use it to solve problems and start exploring the fascinating optimization world. In the present work, PROS is explained in detail and is used to optimize 12 multi-dimensional test functions with various levels of complexity. The performance is compared with the pure random search strategy and other three well-established algorithms: genetic algorithms (GA), particle swarm optimization (PSO), and differential evolution (DE). The results indicate that, despite its simplicity, the proposed PROS method exhibits very good performance with fast convergence rates and quick execution time. The method can serve as a simple alternative to established and more complex optimizers. Additionally, it could also be used as a benchmark for other metaheuristic optimization algorithms as one of the simplest, yet powerful, optimizers. The algorithm is provided with its full source code in MATLAB for anybody interested to use, test or explore.

Numerical Optimization of the Thermoelectric Cooling Devices

2005 ◽  
Author(s):  
B. Abramzon
Keyword(s):  
Electric Current ◽  
Optimum Design ◽  
Random Search ◽  
Thermal Conductance ◽  
Physical Parameters ◽  
Thermoelectric Cooling ◽  
Thermoelectric Coolers ◽  
Independent Variables ◽  
Cooling Devices ◽  
Optimization Search

The present study proposes the unified numerical approach to the problem of optimum design of the thermoelectric devices for cooling electronic components. The method is illustrated with several examples which are based on the standard mathematical model of a single-stage thermoelectric cooler with constant material properties. The model takes into account the thermal resistances from the hot and cold sides of the TEC. Values of the main physical parameters governing the TEC performance (Zeebeck coefficient, electrical resistance and thermal conductance) are derived from the manufacturer catalog data on the maximum achievable temperature difference, and the corresponding electric current and voltage. The independent variables for the optimization search are the number of the thermoelectric coolers, the electric current and the cold side temperature of the TEC. The additional independent variables in other cases are the number of thermoelectric couples and the height-to area ratio of the thermoelectric pellet. The objective for the optimization search is the maximum of the total cooling rate or maximum of COP. In the present study, the problems of optimum design of thermoelectric cooling devices are solved using the so-called Multistart Adaptive Random Search (MARS) method [16].

Numerical Optimization of the Thermoelectric Cooling Devices

2006 ◽  
Vol 129 (3) ◽  
pp. 339-347 ◽  
Author(s):  
Boris Abramzon
Keyword(s):  
Electric Current ◽  
Optimization Problems ◽  
Random Search ◽  
Thermal Conductance ◽  
Numerical Approach ◽  
Physical Parameters ◽  
Optimization Approach ◽  
Independent Variables ◽  
Adaptive Random Search ◽  
Optimization Search

The present study proposes a unified numerical approach to the problem of optimum design of the thermoelectric devices for cooling electronic components. The standard mathematical model of a single-stage thermoelectric cooler (TEC) with constant material properties is employed. The model takes into account the thermal resistances from the hot and cold sides of the TEC. Values of the main physical parameters governing the TEC performance (Seebeck coefficient, electrical resistance, and thermal conductance) are derived from the manufacturer catalog data on the maximum achievable temperature difference, and the corresponding electric current and voltage. The optimization approach is illustrated with several examples for different design objective functions, variables, and constraints. The objective for the optimization search is the maximization of the total cooling rate or the performance coefficient of the cooling device. The independent variables for the optimization search are as follows: The number of the thermoelectric modules, the electric current, and the cold side temperature of the TEC. Additional independent variables in other cases include the number of thermoelectric couples and the area-to-height ratio of the thermoelectric pellet. In the present study, the optimization problems are solved numerically using the so-called multistart adaptive random search method.

Supply Chain Coordination Under Service Level Constraint and Controllable Lead Time

2016 ◽  
Vol 7 (2) ◽  
pp. 84-106 ◽  
Author(s):  
Prashant Jindal ◽  
Anjana Solanki
Keyword(s):  
Supply Chain ◽  
Cost Reduction ◽  
Lead Time ◽  
Cost Allocation ◽  
Optimal Solution ◽  
Service Level ◽  
Decision Variable ◽  
Allocation Model ◽  
Controllable Lead Time ◽  
Ordering Cost Reduction

This paper investigates the coordination issue in a decentralized supply chain having a vendor and a buyer for a defective product. The authors develop two inventory models with controllable lead time under service level constraint. The first one is propose under decentralized mode based on the Stackelberg model, the other one is propose under centralized mode of the integrated supply chain. Ordering cost reduction is also including as a decision variable along with shipping quantity, lead time and number of shipments. Computational findings using the software Matlab 7.0 are provided to find the optimal solution. The results of numerical examples show that centralized mode is better than that of decentralized mode, and to induce both vendor and buyer for coordination, proposed cost allocation model is effective. The authors also numerically investigate the effects of backorder parameter on the optimal solutions. Benefit of ordering cost reduction in both models is also provided.

scholarly journals Routing for Hazardous Materials Transportation in Urban Areas

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1091 ◽  
Author(s):  
Zhang ◽  
Feng ◽  
Yang ◽  
Ding
Keyword(s):  
Urban Areas ◽  
Optimal Solution ◽  
Hazardous Materials ◽  
Work Load ◽  
Decision Variable ◽  
Daily Production ◽  
Hazardous Materials Transportation ◽  
Decision Variables ◽  
Hazmat Transportation ◽  
Local Risk

Hazardous materials (HAZMAT) are important for daily production in cities, which usually have a high population. To avoid the threat to public safety and security, the routes for HAZMAT transportation should be planned legitimately by mitigating the maximum risk to population centers. For the objective of min-max local risk in urban areas, this study has newly proposed an optimization model where the service of a link for HAZMAT transportation was taken as the key decision variable. Correspondingly, the symmetric problem of min-max optimization takes significant meanings. Moreover, in consideration of the work load of solving the model under a lot of decision variables, a heuristic algorithm was developed to obtain an optimal solution. Thereafter, a case study was made to test the proposed model and algorithm, and the results were compared with those generated by deterministic solving approaches. In addition, this research is able to be an effective reference for authorities on the management of HAZMAT transportation in urban areas.

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.

scholarly journals Black-box combinatorial optimization using models with integer-valued minima

2020 ◽  
Author(s):  
Laurens Bliek ◽  
Sicco Verwer ◽  
Mathijs de Weerdt
Keyword(s):  
Optimization Algorithm ◽  
Surrogate Model ◽  
Optimization Problems ◽  
Random Search ◽  
Continuous Optimization ◽  
Optimal Solution ◽  
Black Box ◽  
Combinatorial Problems ◽  
Bayesian Optimization ◽  
Bayesian Optimization Algorithm

Abstract When a black-box optimization objective can only be evaluated with costly or noisy measurements, most standard optimization algorithms are unsuited to find the optimal solution. Specialized algorithms that deal with exactly this situation make use of surrogate models. These models are usually continuous and smooth, which is beneficial for continuous optimization problems, but not necessarily for combinatorial problems. However, by choosing the basis functions of the surrogate model in a certain way, we show that it can be guaranteed that the optimal solution of the surrogate model is integer. This approach outperforms random search, simulated annealing and a Bayesian optimization algorithm on the problem of finding robust routes for a noise-perturbed traveling salesman benchmark problem, with similar performance as another Bayesian optimization algorithm, and outperforms all compared algorithms on a convex binary optimization problem with a large number of variables.

Approximate Implementations of Pure Random Search in the Presence of Noise

2005 ◽  
Vol 31 (4) ◽  
pp. 601-612 ◽  
Author(s):  
David L. J. Alexander ◽  
David W. Bulger ◽  
James M. Calvin ◽  
H. Edwin. Romeijn ◽  
Ryan L. Sherriff
Keyword(s):  
Random Search ◽  
Pure Random Search

scholarly journals Using random search and brute force algorithm in factoring the RSA modulus

2018 ◽  
Vol 2 (1) ◽  
pp. 45-52
Author(s):  
Mohammad Andri Budiman ◽  
Dian Rachmawati
Keyword(s):  
Numerical Optimization ◽  
Random Search ◽  
Prime Numbers ◽  
Brute Force ◽  
Rsa Cryptosystem ◽  
Candidate Solution ◽  
Python Programming Language ◽  
Primality Test ◽  
Factorization Algorithms ◽  
Python Programming

Abstract. The security of the RSA cryptosystem is directly proportional to the size of its modulus, n. The modulus n is a multiplication of two very large prime numbers, notated as p and q. Since modulus n is public, a cryptanalyst can use factorization algorithms such as Euler’s and Pollard’s algorithms to derive the private keys, p and q. Brute force is an algorithm that searches a solution to a problem by generating all the possible candidate solutions and testing those candidates one by one in order to get the most relevant solution. Random search is a numerical optimization algorithm that starts its search by generating one candidate solution randomly and iteratively compares it with other random candidate solution in order to get the most suitable solution. This work aims to compare the performance of brute force algorithm and random search in factoring the RSA modulus into its two prime factors by experimental means in Python programming language. The primality test is done by Fermat algorithm and the sieve of Eratosthenes.

scholarly journals Adaptive Opposition Slime Mould Algorithm

2021 ◽  
Author(s):  
Manoj Kumar Naik ◽  
Rutuparna Panda ◽  
Ajith Abraham
Keyword(s):  
Random Search ◽  
Optimal Solution ◽  
Optimization Methods ◽  
Function Optimization ◽  
Rank Test ◽  
Test Functions ◽  
Slime Mould ◽  
Opposition Based Learning ◽  
Suggested Technique ◽  
Better Than

Abstract Recently, the slime mould algorithm (SMA) has become popular in function optimization, because it effectively uses exploration and exploitation to reach an optimal solution or near-optimal solution. However, the SMA uses two random search agents from the whole population to decide the future displacement and direction from the best search agents, which limits its exploitation and exploration. To solve this problem, we investigate an adaptive approach to decide whether opposition based learning (OBL) will be used or not. Sometimes the OBL is used to further increase the exploration. In addition, it maximizes the exploitation by replacing one random search agent with the best one in the position updating. The suggested technique is called an adaptive opposition slime mould algorithm (AOSMA). The qualitative and quantitative analysis of AOSMA is reported using 29 test functions consisting of 23 classical test functions and 6 recently used composition functions from the IEEE CEC 2014 test suite. The results are compared with state-of-the-art optimization methods. Results presented in this paper show that AOSMA’s performance is better than other optimization algorithms. The AOSMA is evaluated using Wilcoxon’s rank-sum test. It also ranked one in Friedman’s mean rank test. The proposed AOSMA algorithm would be useful for function optimization to solve real-world engineering problems.

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