scholarly journals Multimodal Optimization with the Local Optimum Ranking 2 Algorithm

2021 ◽  
Author(s):  
Francisco Daniel Filip Duarte
Keyword(s):  
Local Population ◽  
Computation Time ◽  
Efficient Solutions ◽  
Superior Performance ◽  
Local Optimum ◽  
Multimodal Optimization ◽  
Local Optima ◽  
Single Output ◽  
Niching Methods ◽  
Niching Method

Abstract In optimization tasks, it is interesting to achieve a set of efficient solutions instead of one single output, in the case the best solution is not suitable. Many niching methods offer a diversified response, yet some important problems are common: (1) The most interesting solutions of each local optimum are not identified. Thus, the output is the overall population of solutions, which increases the work of the designer in verifying which solution is the most interesting. (2) Existing niching algorithms tend to distribute the solutions on the most promising regions, over-populating some local optima and sub-populating others, what leads to a poor optimization.To solve these challenges, a novel niching method is presented, named local optimum ranking 2. This sorting methodology favors the exploration of a defined number of local optima, and ranks each local population by objective value within each local optimum. Thus, is performed a multi-focus exploration, with an equalized number of solutions on each local optimum, while identifying which solutions are the local apices. Experimental results demonstrate the local optimum ranking 2 provides superior performance than other popular niching methods, for the selected test functions and global optimization algorithms. Also, its versatility is demonstrated in the several ways it can be combined with some of the most well-known methods.In a second experiment, the LOR2 algorithm is applied in the design optimization of a metallic cantilever beam. It is exemplified how the LOR2 algorithm can achieve a set of efficient and diverse design configurations, identifying which are the apices of each local optimum. Thus, the LOR2 facilitates multimodal optimization tasks, while offering both performance and diversity for design challenges.In addition, a third experiment describes how the algorithm can be applied to segment the domain of any function, with any type of input distribution or number of coordinates, into a mesh of similar sized or custom sized elements. Thus, it can segment a response surface named Kriging, significantly simplifying it and reducing computation time.

scholarly journals Multimodal Optimization with the Local Optimum Ranking 2 Algorithm

2021 ◽  
Author(s):  
Francisco Daniel Filip Duarte
Keyword(s):  
Local Population ◽  
Computation Time ◽  
Efficient Solutions ◽  
Superior Performance ◽  
Local Optimum ◽  
Multimodal Optimization ◽  
Local Optima ◽  
Single Output ◽  
Niching Methods ◽  
Niching Method

Abstract In optimization tasks, it is interesting to achieve a set of efficient solutions instead of one single output, in the case the best solution is not suitable. Many niching methods offer a diversified response, yet some important problems are common: (1) The most interesting solutions of each local optimum are not identified. Thus, the output is the overall population of solutions, which increases the work of the designer in verifying which solution is the most interesting. (2) Existing niching algorithms tend to distribute the solutions on the most promising regions, over-populating some local optima and sub-populating others, what leads to a poor optimization.To solve these challenges, a novel niching method is presented, named local optimum ranking 2. This sorting methodology favors the exploration of a defined number of local optima, and ranks each local population by objective value within each local optimum. Thus, is performed a multi-focus exploration, with an equalized number of solutions on each local optimum, while identifying which solutions are the local apices. Experimental results demonstrate the local optimum ranking 2 provides superior performance than other popular niching methods, for the selected test functions and global optimization algorithms. Also, its versatility is demonstrated in the several ways it can be combined with some of the most well-known methods.In a second experiment, the LOR2 algorithm is applied in the design optimization of a metallic cantilever beam. It is exemplified how the LOR2 algorithm can achieve a set of efficient and diverse design configurations, identifying which are the apices of each local optimum. Thus, the LOR2 facilitates multimodal optimization tasks, while offering both performance and diversity for design challenges.In addition, a third experiment describes how the algorithm can be applied to segment the domain of any function, with any type of input distribution or number of coordinates, into a mesh of similar sized or custom sized elements. Thus, it can segment a response surface named Kriging, significantly simplifying it and reducing computation time.

scholarly journals Multimodal Optimization with the Local Optimum Ranking 2 Algorithm

2022 ◽  
Author(s):  
Francisco Daniel Filip Duarte
Keyword(s):  
Structural Design ◽  
Local Population ◽  
Computation Time ◽  
Efficient Solutions ◽  
Local Optimum ◽  
Local Optima ◽  
Single Output ◽  
Niching Methods ◽  
Objective Value ◽  
Niching Method

Abstract In optimization tasks, it is interesting to achieve a set of efficient solutions instead of one single output, in the case the best solution is not suitable. Many niching methods offer a diversified response, yet some important problems are common: (1) The most interesting solutions of each local optimum are not identified. Thus, the output is the overall population of solutions, which increases the work of the designer in verifying which solution is the most interesting. (2) Existing niching algorithms tend to distribute the solutions on the most promising regions, over-populating some local optima and sub-populating others, which leads to poor optimization.To solve these challenges, a novel niching method is presented, named local optimum ranking 2 (LOR2). This sorting methodology favors the exploration of a defined number of local optima and ranks each local population by objective value within each local optimum. Thus, is performed a multi-focus exploration, with an equalized number of solutions on each local optimum, while identifying which solutions are the local apices. To exemplify its application, the LOR2 algorithm is applied in the design optimization of a metallic cantilever beam. It achieves a set of efficient and diverse design configurations, offering both performance and diversity for structural design challenges.In addition, a second experiment describes how the algorithm can be applied to segment the domain of any function, into a mesh of similar sized or custom-sized elements. Thus, it can significantly simplify metamodels and reduce their computation time.

scholarly journals Multimodal Optimization with the Local Optimum Ranking 2 Algorithm

2021 ◽  
Author(s):  
Francisco Daniel Filip Duarte
Keyword(s):  
Structural Design ◽  
Local Population ◽  
Computation Time ◽  
Efficient Solutions ◽  
Local Optimum ◽  
Local Optima ◽  
Single Output ◽  
Niching Methods ◽  
Objective Value ◽  
Niching Method

Abstract In optimization tasks, it is interesting to achieve a set of efficient solutions instead of one single output, in the case the best solution is not suitable. Many niching methods offer a diversified response, yet some important problems are common: (1) The most interesting solutions of each local optimum are not identified. Thus, the output is the overall population of solutions, which increases the work of the designer in verifying which solution is the most interesting. (2) Existing niching algorithms tend to distribute the solutions on the most promising regions, over-populating some local optima and sub-populating others, which leads to poor optimization.To solve these challenges, a novel niching method is presented, named local optimum ranking 2 (LOR2). This sorting methodology favors the exploration of a defined number of local optima and ranks each local population by objective value within each local optimum. Thus, is performed a multi-focus exploration, with an equalized number of solutions on each local optimum, while identifying which solutions are the local apices. To exemplify its application, the LOR2 algorithm is applied in the design optimization of a metallic cantilever beam. It achieves a set of efficient and diverse design configurations, offering both performance and diversity for structural design challenges.In addition, a second experiment describes how the algorithm can be applied to segment the domain of any function, into a mesh of similar sized or custom-sized elements. Thus, it can significantly simplify metamodels and reduce their computation time.

scholarly journals Delayed improvement local search

2021 ◽  
Author(s):  
Heber F. Amaral ◽  
Sebastián Urrutia ◽  
Lars M. Hvattum
Keyword(s):  
Local Search ◽  
Heuristic Algorithms ◽  
Travelling Salesman Problem ◽  
Computation Time ◽  
The Novel ◽  
Local Optima ◽  
New Strategy ◽  
Max Cut Problem ◽  
Novel Method ◽  
Similar Solutions

AbstractLocal search is a fundamental tool in the development of heuristic algorithms. A neighborhood operator takes a current solution and returns a set of similar solutions, denoted as neighbors. In best improvement local search, the best of the neighboring solutions replaces the current solution in each iteration. On the other hand, in first improvement local search, the neighborhood is only explored until any improving solution is found, which then replaces the current solution. In this work we propose a new strategy for local search that attempts to avoid low-quality local optima by selecting in each iteration the improving neighbor that has the fewest possible attributes in common with local optima. To this end, it uses inequalities previously used as optimality cuts in the context of integer linear programming. The novel method, referred to as delayed improvement local search, is implemented and evaluated using the travelling salesman problem with the 2-opt neighborhood and the max-cut problem with the 1-flip neighborhood as test cases. Computational results show that the new strategy, while slower, obtains better local optima compared to the traditional local search strategies. The comparison is favourable to the new strategy in experiments with fixed computation time or with a fixed target.

scholarly journals Lévy-Flight Moth-Flame Algorithm for Function Optimization and Engineering Design Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-22 ◽  
Author(s):  
Zhiming Li ◽  
Yongquan Zhou ◽  
Sen Zhang ◽  
Junmin Song
Keyword(s):  
Engineering Design ◽  
Function Optimization ◽  
Superior Performance ◽  
Local Optimum ◽  
Lévy Flight ◽  
Design Problems ◽  
Levy Flight ◽  
Spiral Path ◽  
Straight Line ◽  
Engineering Design Problems

The moth-flame optimization (MFO) algorithm is a novel nature-inspired heuristic paradigm. The main inspiration of this algorithm is the navigation method of moths in nature called transverse orientation. Moths fly in night by maintaining a fixed angle with respect to the moon, a very effective mechanism for travelling in a straight line for long distances. However, these fancy insects are trapped in a spiral path around artificial lights. Aiming at the phenomenon that MFO algorithm has slow convergence and low precision, an improved version of MFO algorithm based on Lévy-flight strategy, which is named as LMFO, is proposed. Lévy-flight can increase the diversity of the population against premature convergence and make the algorithm jump out of local optimum more effectively. This approach is helpful to obtain a better trade-off between exploration and exploitation ability of MFO, thus, which can make LMFO faster and more robust than MFO. And a comparison with ABC, BA, GGSA, DA, PSOGSA, and MFO on 19 unconstrained benchmark functions and 2 constrained engineering design problems is tested. These results demonstrate the superior performance of LMFO.

scholarly journals Sales Growth Rate Forecasting Using Improved PSO and SVM

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Xibin Wang ◽  
Junhao Wen ◽  
Shafiq Alam ◽  
Xiang Gao ◽  
Zhuo Jiang ◽  
...  
Keyword(s):  
Growth Rate ◽  
Decisive Role ◽  
Convergence Speed ◽  
Classification Model ◽  
Support Vector ◽  
Local Optimum ◽  
Sales Growth ◽  
Local Optima ◽  
Proposed Model ◽  
Forecasting Performance

Accurate forecast of the sales growth rate plays a decisive role in determining the amount of advertising investment. In this study, we present a preclassification and later regression based method optimized by improved particle swarm optimization (IPSO) for sales growth rate forecasting. We use support vector machine (SVM) as a classification model. The nonlinear relationship in sales growth rate forecasting is efficiently represented by SVM, while IPSO is optimizing the training parameters of SVM. IPSO addresses issues of traditional PSO, such as relapsing into local optimum, slow convergence speed, and low convergence precision in the later evolution. We performed two experiments; firstly, three classic benchmark functions are used to verify the validity of the IPSO algorithm against PSO. Having shown IPSO outperform PSO in convergence speed, precision, and escaping local optima, in our second experiment, we apply IPSO to the proposed model. The sales growth rate forecasting cases are used to testify the forecasting performance of proposed model. According to the requirements and industry knowledge, the sample data was first classified to obtain types of the test samples. Next, the values of the test samples were forecast using the SVM regression algorithm. The experimental results demonstrate that the proposed model has good forecasting performance.

scholarly journals Kernel Regression Imputation in Manifolds via Bi-Linear Modeling: The Dynamic-MRI Case

2021 ◽  
Author(s):  
Konstantinos Slavakis ◽  
Gaurav Shetty ◽  
Loris Cannelli ◽  
Gesualdo Scutari ◽  
Ukash Nakarmi ◽  
...  
Keyword(s):  
Reproducing Kernel ◽  
Kernel Regression ◽  
Dynamic Mri ◽  
Efficient Solutions ◽  
Training Data ◽  
Superior Performance ◽  
Linear Modeling ◽  
Modeling Framework ◽  
Geometric Information ◽  
Regression Imputation

This paper introduces a non-parametric kernel-based modeling framework for imputation by regression on data that are assumed to lie close to an unknown-to-the-user smooth manifold in a Euclidean space. The proposed framework, coined kernel regression imputation in manifolds (KRIM), needs no training data to operate. Aiming at computationally efficient solutions, KRIM utilizes a small number of ``landmark'' data-points to extract geometric information from the measured data via parsimonious affine combinations (``linear patches''), which mimic the concept of tangent spaces to smooth manifolds and take place in functional approximation spaces, namely reproducing kernel Hilbert spaces (RKHSs). Multiple complex RKHSs are combined in a data-driven way to surmount the obstacle of pin-pointing the ``optimal'' parameters of a single kernel through cross-validation. The extracted geometric information is incorporated into the design via a novel bi-linear data-approximation model, and the imputation-by-regression task takes the form of an inverse problem which is solved by an iterative algorithm with guaranteed convergence to a stationary point of the non-convex loss function. To showcase the modular character and wide applicability of KRIM, this paper highlights the application of KRIM to dynamic magnetic resonance imaging (dMRI), where reconstruction of high-resolution images from severely under-sampled dMRI data is desired. Extensive numerical tests on synthetic and real dMRI data demonstrate the superior performance of KRIM over state-of-the-art approaches under several metrics and with a small computational footprint.<br>

Local Best Particle Swarm Optimization Using Crown Jewel Defense Strategy

2018 ◽  
pp. 27-52 ◽  
Author(s):  
Jiarui Zhou ◽  
Junshan Yang ◽  
Ling Lin ◽  
Zexuan Zhu ◽  
Zhen Ji
Keyword(s):  
Particle Swarm Optimization ◽  
High Efficiency ◽  
Particle Swarm ◽  
Global Optimum ◽  
Population Diversity ◽  
Local Optimum ◽  
Swarm Optimization ◽  
Local Optima ◽  
Von Neumann ◽  
Swarm Intelligence Algorithm

Particle swarm optimization (PSO) is a swarm intelligence algorithm well known for its simplicity and high efficiency on various problems. Conventional PSO suffers from premature convergence due to the rapid convergence speed and lack of population diversity. It is easy to get trapped in local optima. For this reason, improvements are made to detect stagnation during the optimization and reactivate the swarm to search towards the global optimum. This chapter imposes the reflecting bound-handling scheme and von Neumann topology on PSO to increase the population diversity. A novel crown jewel defense (CJD) strategy is introduced to restart the swarm when it is trapped in a local optimum region. The resultant algorithm named LCJDPSO-rfl is tested on a group of unimodal and multimodal benchmark functions with rotation and shifting. Experimental results suggest that the LCJDPSO-rfl outperforms state-of-the-art PSO variants on most of the functions.

scholarly journals Multi-Searcher Optimization for the Optimal Energy Dispatch of Combined Heat and Power-Thermal-Wind-Photovoltaic Systems

2019 ◽  
Vol 9 (3) ◽  
pp. 537 ◽  
Author(s):  
Jianlin Tang ◽  
Tao Yu ◽  
Xiaoshun Zhang ◽  
Zhuohuan Li ◽  
Junbin Chen
Keyword(s):  
Heuristic Algorithms ◽  
Optimal Solution ◽  
Energy System ◽  
Combined Heat And Power ◽  
Superior Performance ◽  
Local Optimum ◽  
Photovoltaic Systems ◽  
Thermal Wind ◽  
Optimal Energy ◽  
Highly Nonlinear

This paper proposes a novel multi-searcher optimization (MSO) algorithm for the optimal energy dispatch (OED) of combined heat and power-thermal-wind-photovoltaic systems. The available power of wind turbine (WT) units and photovoltaic (PV) units is approximated with the probability density functions of wind speed and solar irradiance, respectively. The chaos theory is used to implement a wide global search, which can effectively avoid a low-quality local optimum for OED. Besides, a double-layer searcher is designed to guarantee fast convergence to a high-quality optimal solution. Finally, three benchmark functions and an energy system with 27 units are used for testing the performance of the MSO compared with nine other frequently used heuristic algorithms. The simulation results demonstrate that the proposed technique not only can solve the highly nonlinear, non-smooth, and non-convex OED problem of an energy system, but can also achieve a superior performance for the convergence speed and the optimum quality.

scholarly journals How to value protection from natural hazards – a step-by-step discrete choice approach

2013 ◽  
Vol 13 (4) ◽  
pp. 913-922 ◽  
Author(s):  
R. Olschewski
Keyword(s):  
Natural Hazards ◽  
Choice Experiment ◽  
Local Population ◽  
Efficient Solutions ◽  
Protection Measures ◽  
Mountainous Regions ◽  
The People ◽  
Technical Measures ◽  
Choice Approach

Abstract. In mountainous regions, forests play a crucial role in protecting the local population from natural hazards. In cases where existing forests are destroyed, e.g. by wind throws or diseases, the protection function has to be restored through technical measures. To determine the willingness to pay (WTP) for protection against avalanches, a choice experiment has been conducted and different experiment specifications have been tested to determine possible impacts on the results. The present study contributes to a comprehensive assessment of protection measures, and helps to identify efficient solutions based on the judgement of the people potentially endangered by natural hazards. The stepwise approach has the advantage to gradually check data fit, thereby didactically showing an operational way of dealing with different model specifications. The detailed case study can serve as a manual for conducting choice experiments with a similar focus and demonstrates the suitability and caveats of this approach to value protection from natural hazards in general.

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