scholarly journals Heuristic approach applied to the optimum stratification problem

2021 ◽  
Author(s):  
José André Brito ◽  
Leonardo de Lima ◽  
Pedro Henrique González ◽  
Breno Oliveira ◽  
Nelson Maculan
Keyword(s):  
Variable Neighborhood Search ◽  
Optimal Solution ◽  
Optimization Method ◽  
Neighborhood Search ◽  
Optimal Solutions ◽  
Enumeration Algorithm ◽  
Global Optimal Solution ◽  
Optimal Sample ◽  
Precision Level ◽  
Global Optimal

The problem of finding an optimal sample stratification has been extensively studied in the literature. In this paper, we propose a heuristic optimization method for solving the univariate optimum stratification problem aiming at minimizing the sample size for a given precision level. The method is based on the variable neighborhood search metaheuristic, which was combined with an exact method. Numerical experiments were performed over a dataset of 24 instances, and the results of the proposed algorithm were compared with two very well-known methods from the literature. Our results outperformed $94\%$ of  the considered cases. In addition, we developed an enumeration algorithm to find the global optimal solution in some populations and scenarios, which enabled us to validate our metaheuristic method. Furthermore, we find that our algorithm obtained the global optimal solutions for the vast majority of the cases.

The Optimization Design of Wind Turbine Gearbox Based on Improved Genetic Algorithm and Feasibility Analysis

2014 ◽  
Vol 889-890 ◽  
pp. 107-112
Author(s):  
Ji Ming Tian ◽  
Xin Tan
Keyword(s):  
Genetic Algorithm ◽  
Wind Turbine ◽  
Optimization Design ◽  
Optimal Solution ◽  
Optimization Method ◽  
Strength Analysis ◽  
Improved Genetic Algorithm ◽  
Global Optimal Solution ◽  
Wind Turbine Gearbox ◽  
Global Optimal

The design of the gearbox must ensure the simplest structure and the lightest weight under the premise of meeting the reliability and life expectancy. According to the requirement of wind turbine, an improved method combined dynamic penalty function with pseudo-parallel genetic algorithm is used to optimize gearbox. It takes the minimum volumes as object functions. It is showed that the ability to search the global optimal solution of improved genetic algorithm and less number of iterations. The global optimal solution is worked out quickly. The size parameters are optimized, as much as the driving stability and efficiency. To verify the feasibility of improved genetic algorithm, ring gear of the gearbox is analyzed. Static strength analysis shows that the optimization method is reasonable and effective.

scholarly journals The algorithm development based on the immune search for solving unclear problems to detect the optical flow with minimal cost

2021 ◽  
Vol 258 ◽  
pp. 06052
Author(s):  
Olga Purchina ◽  
Anna Poluyan ◽  
Dmitry Fugarov
Keyword(s):  
Multiple Solutions ◽  
Optimal Solution ◽  
Evolutionary Search ◽  
Minimal Cost ◽  
Optimal Solutions ◽  
Artificial Immune ◽  
Global Optimal Solution ◽  
Immune Algorithms ◽  
Global Optimal ◽  
Artificial Immune Algorithms

The main aim of the research is the development of effective methods and algorithms based on the hybrid principles functioning of the immune system and evolutionary search to determine a global optimal solution to optimisation problems. Artificial immune algorithms are characterised as diverse ones, extremely reliable and implicitly parallel. The integration of modified evolutionary algorithms and immune algorithms is proposed to be used for the solution of above problem. There is no exact method for the efficient solving unclear optimisation problems within the polynomial time. However, by determining close to optimal solutions within the reasonable time, the hybrid immune algorithm (HIA) is capable to offer multiple solutions, which provide compromise between several goals. Quite few researches have been focused on the optimisation of more than one goal and even fewer used to have distinctly considered diversity of solutions that plays fundamental role in good performance of any evolutionary calculation method.

scholarly journals A Linearization to the Sum of Linear Ratios Programming Problem

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1004
Author(s):  
Mojtaba Borza ◽  
Azmin Sham Rambely
Keyword(s):  
Programming Problem ◽  
Computational Cost ◽  
Iterative Algorithms ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Global Optimal Solution ◽  
Straightforward Method ◽  
Global Optimal ◽  
High Computational Cost ◽  
Real World Problems

Optimizing the sum of linear fractional functions over a set of linear inequalities (S-LFP) has been considered by many researchers due to the fact that there are a number of real-world problems which are modelled mathematically as S-LFP problems. Solving the S-LFP is not easy in practice since the problem may have several local optimal solutions which makes the structure complex. To our knowledge, existing methods dealing with S-LFP are iterative algorithms that are based on branch and bound algorithms. Using these methods requires high computational cost and time. In this paper, we present a non-iterative and straightforward method with less computational expenses to deal with S-LFP. In the method, a new S-LFP is constructed based on the membership functions of the objectives multiplied by suitable weights. This new problem is then changed into a linear programming problem (LPP) using variable transformations. It was proven that the optimal solution of the LPP becomes the global optimal solution for the S-LFP. Numerical examples are given to illustrate the method.

A novel adaptive butterfly optimization algorithm

2018 ◽  
Vol 07 (04) ◽  
pp. 1850026 ◽  
Author(s):  
Bhupinder Singh ◽  
Priyanka Anand
Keyword(s):  
Optimization Algorithm ◽  
Sensory Modality ◽  
Optimal Solution ◽  
Bench Mark ◽  
Optimal Solutions ◽  
Global Optimal Solution ◽  
Simulation Process ◽  
Bee Colony ◽  
Global Optimal ◽  
Loss Of Diversity

Butterfly optimization algorithm (BOA) is an interesting bio-inspired algorithm that uses a nature inspired simulation model, based on the food foraging behavior of butterflies. A common problem with BOA is that in early stages of simulation process, it may converge to sub-optimal solutions due to the loss of diversity in its population. The sensory modality is the critical parameter which is responsible for searching new solutions in the nearby regions. In this work, an adaptive butterfly optimization algorithm is proposed in which a novel phenomenon of changing the sensory modality of BOA is employed during the optimization process in order to achieve better results in comparison to traditional BOA. The proposed Adaptive butterfly optimization algorithm (ABOA) is tested against seventeen standard bench mark functions. Its performance is then compared against existing standard optimization algorithms, namely artificial bee colony, firefly algorithm and standard butterfly optimization algorithm. The results indicate that the proposed adaptive BOA with improved parameter calculation mechanism produces superior results in terms of convergence and achievement of the global optimal solution efficiently.

Hybrid Multi-Population and Adaptive Search Range Strategy With Particle Swarm Optimization for Multimodal Optimization

2021 ◽  
Vol 12 (4) ◽  
pp. 146-168
Author(s):  
Shiqi Wang ◽  
Zepeng Shen ◽  
Yao Peng
Keyword(s):  
Particle Swarm Optimization ◽  
Optimal Solution ◽  
Search Space ◽  
Multimodal Optimization ◽  
Adaptive Search ◽  
Optimal Solutions ◽  
Search Range ◽  
Global Optimal Solution ◽  
Swarm Optimization ◽  
Global Optimal

This paper proposes an algorithm named hybrid multi-population and adaptive search range strategy with particle swarm optimization (ARPSO) for solving multimodal optimization problems. The main idea of the algorithm is to divide the global search space into multiple sub-populations searching in parallel and independently. For diversity increasing, each sub-population will continuously change the search area adaptively according to whether there are local optimal solutions in its search space and the position of the global optimal solution, and in each iteration, the optimal solution in this area will be reserved. For the purpose of accelerating convergence, at the global and local levels, when the global optimal solution or local optimal solution is found, the global search space and local search space will shrink toward the optimal solution. Experiments show that ARPSO has unique advantages for solving multi-dimensional problems, especially problems with only one global optimal solution but multiple local optimal solutions.

scholarly journals Global Simultaneous Optimization of Oil, Hysteretic and Inertial Dampers Using Real-Valued Genetic Algorithm and Local Search

2021 ◽  
Vol 7 ◽  
Author(s):  
Ryohei Uemura ◽  
Hiroki Akehashi ◽  
Kohei Fujita ◽  
Izuru Takewaki
Keyword(s):  
Genetic Algorithm ◽  
Local Search ◽  
Optimal Solution ◽  
Optimization Method ◽  
Simultaneous Optimization ◽  
Global Optimality ◽  
Building Structures ◽  
Global Optimal Solution ◽  
Maximum Acceleration ◽  
Global Optimal

A method for global simultaneous optimization of oil, hysteretic and inertial dampers is proposed for building structures using a real-valued genetic algorithm and local search. Oil dampers has the property that they can reduce both displacement and acceleration without significant change of natural frequencies and hysteretic dampers possess the characteristic that they can absorb energy efficiently and reduce displacement effectively in compensation for the increase of acceleration. On the other hand, inertial dampers can change (prolong) the natural periods with negative stiffness and reduce the effective input and the maximum acceleration in compensation for the increase of deformation. By using the proposed simultaneous optimization method, structural designers can select the best choice of these three dampers from the viewpoints of cost and performance indices (displacement, acceleration). For attaining the global optimal solution which cannot be attained by the conventional sensitivity-based approach, a method including a real-valued genetic algorithm and local search is devised. In the first stage, a real-valued genetic algorithm is used for searching an approximate global optimal solution. Then a local search procedure is activated for enhancing the optimal character of the solutions by reducing the total quantity of three types of dampers. It is demonstrated that a better design from the viewpoint of global optimality can be obtained by the proposed method and the preference of damper selection strongly depends on the design target (displacement, acceleration). Finally, a multi-objective optimization for the minimum deformation and acceleration is investigated.

scholarly journals On Locally and Globally Optimal Solutions in Scalar Variational Control Problems

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 829 ◽  
Author(s):  
Savin Treanţă
Keyword(s):  
Control Problem ◽  
Optimal Solution ◽  
Control Problems ◽  
Optimal Solutions ◽  
Global Optimal Solution ◽  
New Class ◽  
Minimal Criterion ◽  
Local Optimal Solution ◽  
Global Optimal ◽  
Curvilinear Integral

In this paper, optimality conditions are studied for a new class of PDE and PDI-constrained scalar variational control problems governed by path-independent curvilinear integral functionals. More precisely, we formulate and prove a minimal criterion for a local optimal solution of the considered PDE and PDI-constrained variational control problem to be its global optimal solution. The effectiveness of the main result is validated by a two-dimensional non-convex scalar variational control problem.

Soil Nailing Optimization Design Based on Improved Response Surface

2013 ◽  
Vol 671-674 ◽  
pp. 126-132
Author(s):  
Qiu Wang ◽  
Zhi Gang Song ◽  
Qing Xu
Keyword(s):  
Response Surface ◽  
Optimization Design ◽  
Uniform Design ◽  
Optimal Solution ◽  
Optimization Method ◽  
Gradient Algorithm ◽  
Soil Nailing ◽  
Global Optimal Solution ◽  
Global Optimal ◽  
Computationally Intensive

Gradient algorithm is difficult to obtain explicit analytic function of the optimization model, at the same time heuristic algorithm is computationally intensive with low speed and less efficient in soil nailing optimization. To overcome these problems, a new optimization method based on improved response surface (IRS) which constructed by uniform design (UD) and non-parametric regression (NR), is proposed. The soil nailing optimization is adopted by the combination of explicit analytic model based on IRS and composing program. The optimization process is explained and a soil nailing is optimized to verify the feasibility of the proposed method. The optimum results show that the introduction of UD and NR to construct the IRS calculate fast, do not need solving the specific analytic solution and can obtain global optimal solution.

AO-BBO: A Novel Optimization Algorithm and Its Application in Plant Drug Extraction

2019 ◽  
Vol 19 (2) ◽  
pp. 139-145 ◽  
Author(s):  
Bote Lv ◽  
Juan Chen ◽  
Boyan Liu ◽  
Cuiying Dong
Keyword(s):  
Optimization Algorithm ◽  
Learning Strategy ◽  
Optimal Solution ◽  
Population Diversity ◽  
Global Optimal Solution ◽  
Plant Medicine ◽  
Suitability Index ◽  
Sensing Model ◽  
Local Optimal Solution ◽  
Global Optimal

<P>Introduction: It is well-known that the biogeography-based optimization (BBO) algorithm lacks searching power in some circumstances. </P><P> Material & Methods: In order to address this issue, an adaptive opposition-based biogeography-based optimization algorithm (AO-BBO) is proposed. Based on the BBO algorithm and opposite learning strategy, this algorithm chooses different opposite learning probabilities for each individual according to the habitat suitability index (HSI), so as to avoid elite individuals from returning to local optimal solution. Meanwhile, the proposed method is tested in 9 benchmark functions respectively. </P><P> Result: The results show that the improved AO-BBO algorithm can improve the population diversity better and enhance the search ability of the global optimal solution. The global exploration capability, convergence rate and convergence accuracy have been significantly improved. Eventually, the algorithm is applied to the parameter optimization of soft-sensing model in plant medicine extraction rate. Conclusion: The simulation results show that the model obtained by this method has higher prediction accuracy and generalization ability.</P>

scholarly journals Best Proximity Point Results in Complex Valued Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Binayak S. Choudhury ◽  
Nikhilesh Metiya ◽  
Pranati Maity
Keyword(s):  
Minimum Distance ◽  
Metric Spaces ◽  
Optimal Solution ◽  
Global Optimal Solution ◽  
Complex Valued Metric Space ◽  
Fixed Point Equation ◽  
Point Equation ◽  
Global Optimal ◽  
Metric Function ◽  
Complex Valued

We introduce the concept of proximity points for nonself-mappings between two subsets of a complex valued metric space which is a recently introduced extension of metric spaces obtained by allowing the metric function to assume values from the field of complex numbers. We apply this concept to obtain the minimum distance between two subsets of the complex valued metric spaces. We treat the problem as that of finding the global optimal solution of a fixed point equation although the exact solution does not in general exist. We also define and use the concept of P-property in such spaces. Our results are illustrated with examples.

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