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 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 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 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.

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 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.

Development of a Common Platform for Testing Metamodel Based Design Optimization Methods

2013 ◽  
Author(s):  
Adel A. Younis ◽  
George H. Cheng ◽  
G. Gary Wang ◽  
Zuomin Dong
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Computation Time ◽  
Optimization Methods ◽  
Global Optimum ◽  
Test Problems ◽  
Test Bed ◽  
Test Procedures ◽  
Local Optima

Metamodel based design optimization (MBDO) algorithms have attracted considerable interests in recent years due to their special capability in dealing with complex optimization problems with computationally expensive objective and constraint functions and local optima. Conventional unimodal-based optimization algorithms and stochastic global optimization algorithms either miss the global optimum frequently or require unacceptable computation time. In this work, a generic testbed/platform for evaluating various MBDO algorithms has been introduced. The purpose of the platform is to facilitate quantitative comparison of different MBDO algorithms using standard test problems, test procedures, and test outputs, as well as to improve the efficiency of new algorithm testing and improvement. The platform consists of a comprehensive test function database that contains about 100 benchmark functions and engineering problems. The testbed accepts any optimization algorithm to be tested, and only requires minor modifications to meet the test-bed requirements. The testbed is useful in comparing the performance of competing algorithms through execution of same problems. It allows researchers and practitioners to test and choose the most suitable optimization tool for their specific needs. It also helps to increase confidence and reliability of the newly developed MBDO tools. Many new MBDO algorithms, including Mode Pursuing Sampling (MPS), Pareto Set Pursuing (PSP), and Space Exploration and Unimodal Region Elimination (SEUMRE), were tested in this work to demonstrate its functionality and benefits.

scholarly journals A Biological Immune Mechanism-Based Quantum PSO Algorithm and Its Application in Back Analysis for Seepage Parameters

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jiacheng Tan ◽  
Liqun Xu ◽  
Kailai Zhang ◽  
Chao Yang
Keyword(s):  
Back Analysis ◽  
Computation Time ◽  
Vaccination Strategy ◽  
Pso Algorithm ◽  
Population Diversity ◽  
Local Optimum ◽  
Immune Mechanism ◽  
Convergence Performance ◽  
Poor Convergence ◽  
Quantum Pso

Back analysis for seepage parameters is a classic issue in hydraulic engineering seepage calculations. Considering the characteristics of inversion problems, including high dimensionality, numerous local optimal values, poor convergence performance, and excessive calculation time, a biological immune mechanism-based quantum particle swarm optimization (IQPSO) algorithm was proposed to solve the inversion problem. By introducing a concentration regulation strategy to improve the population diversity and a vaccination strategy to accelerate the convergence rate, the modified algorithm overcame the shortcomings of traditional PSO which can easily fall into a local optimum. Furthermore, a simple multicore parallel computation strategy was applied to reduce computation time. The effectiveness and practicability of IQPSO were evaluated by numerical experiments. In this paper, taking one concrete face rock-fill dam (CFRD) as a case, a back analysis for seepage parameters was accomplished by utilizing the proposed optimization algorithm and the steady seepage field of the dam was analysed by the finite element method (FEM). Compared with immune PSO and quantum PSO, the proposed algorithm had better global search ability, convergence performance, and calculation rate. The optimized back analysis could obtain the permeability coefficient of CFRD with high accuracy.

Effective Algorithms for Scheduling Workflow Tasks on Mobile Clouds

2020 ◽  
Vol 29 (16) ◽  
pp. 2050255
Author(s):  
Heng Li ◽  
Yaoqin Zhu ◽  
Meng Zhou ◽  
Yun Dong
Keyword(s):  
Mobile Devices ◽  
Solution Space ◽  
Iterated Local Search ◽  
Mobile Cloud ◽  
Local Optimum ◽  
Perturbation Operator ◽  
Evolutionary Mechanisms ◽  
Local Optima ◽  
Np Hard Problem ◽  
Workflow Tasks

In mobile cloud computing, the computing resources of mobile devices can be integrated to execute complicated applications, in order to tackle the problem of insufficient resources of mobile devices. Such applications are, in general, characterized as workflows. Scheduling workflow tasks on a mobile cloud system consisting of heterogeneous mobile devices is a NP-hard problem. In this paper, intelligent algorithms, e.g., particle swarm optimization (PSO) and simulated annealing (SA), are widely used to solve this problem. However, both PSO and SA suffer from the limitation of easily being trapped into local optima. Since these methods rely on their evolutionary mechanisms to explore new solutions in solution space, the search procedure converges once getting stuck in local optima. To address this limitation, in this paper, we propose two effective metaheuristic algorithms that incorporate the iterated local search (ILS) strategy into PSO and SA algorithms, respectively. In case that the intelligent algorithm converges to a local optimum, the proposed algorithms use a perturbation operator to explore new solutions and use the newly explored solutions to start a new round of evolution in the solution space. This procedure is iterated until no better solutions can be explored. Experimental results show that by incorporating the ILS strategy, our proposed algorithms outperform PSO and SA in reducing workflow makespans. In addition, the perturbation operator is beneficial for improving the effectiveness of scheduling algorithms in exploring high-quality scheduling solutions.

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