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Reducing the number of lower-level function evaluations (LFEs) is crucial to designing a bilevel evolutionary algorithm (BLEA) for bilevel optimization. Direct neighbor solution transfer (DST) is regularly used in BLEA because it can improve the lower-level search efficiency and reduce the number of LFEs. But this method still faces the challenge of misleading searches to make the algorithm converge to the wrong optimum. This paper proposes a bilevel improved multi-operator differential evolution algorithm (BL-IMODE) for bilevel optimization, which uses the knowledge transfer and adaptive coordinate systems approach. Specifically, this paper proposes a lower-level search knowledge transfer (LLS-KT) and a lower-level (LL) optimal solution distribution information transfer (LLO-DIT) mechanism to implement knowledge transfer. In LLS-KT, transferring LL solutions to the LL optimizer is similar to DST, but the LLS-KT transfers multiple solutions and thus has less possibility of misleading searches than DST. Moreover, the LLO-DIT transfers the LL optimal solution distribution information to the LL optimizer for generating promising offspring solutions. Since this method does not directly transfer LL solutions, it avoids misleading searches. Additionally, the adaptive coordinate systems (ACS) approach is used in two-level optimizers to suit different fitness landscapes and further reduce the number of LFEs. In ACS, three differential evolution mutation operators are produced in two coordinate systems. An adaptive strategy is used to select the suitable differential evolution mutation operator to generate promising offspring solutions in the Eigen coordinate or original coordinate system. Experimental studies on three test suites benchmark problems for comparison with seven state-of-the-art algorithms are conducted. The results show BL-IMODE has a significant advantage over the comparative algorithms. Finally, BL-IMODE is applied to tackle the inverse optimal control problem. • We propose a bilevel improved multi-operator differential evolution algorithm. • We propose a knowledge transfer approach to avoid misleading search. • We propose an adaptive coordinate systems approach to improve search efficiency. • We outperform all existing approaches in most test instances. [ABSTRACT FROM AUTHOR]

In this study, an energy efficiency study has been carried out through the moment values of a quadrotor applied in the position control with the differential evolution algorithm (DE), which is under the evolutionary algorithms among meta-heuristic algorithms particle swarm optimization (PSO) which is among swarm-based algorithms and gravity search algorithm (GSA) among physics-based algorithms and charged system search (CSS) algorithm, which are all well-known in the literature. The efficient use of energy in electrically powered flying mechanisms is important in terms of completing its task. The aim of this study is to obtain proportional–integral–derivative (PID) coefficients that minimize the energy consumption caused by quadrotor moments. First of all, 12 PID coefficients calculated with traditional Ziegler Nicholes, and trying-error methods for the control of the quadrotor have been trained with DE, PSO, GSA and CSS algorithms and their cost values have been found for this problem. In the study, optimum PID coefficients have been found separately with each algorithm and torque data giving energy efficiency have been obtained by applying them to the state equations. Although the cost minimization convergence value obtained from DE does not look good compared to other algorithms, it has been observed that the moment values of the obtained PID coefficients in the control program are lower. In the study, it has been shown that the PID coefficients obtained from DE reach the target with approximately less energy than the maximum-moment value of the PSO, which provides the closest moment value. It can be thought that this value contributes to energy consumption in each orbital movement of the quadrotor. The simulation results show that the coefficients obtained from DE provide better energy efficiency and are superior to other algorithms compared in terms of energy efficiency. • PID coefficients for quadrotor control are optimized with DE,PSO,CSS,GSA algorithms • The torque values to be applied to each motor were adjusted with these coefficients • The total force applied with DEPID in the z direction is smaller than others • DEPID consumes less energy than the other algorithms in the paper [ABSTRACT FROM AUTHOR]

In this study, an energy efficiency study has been carried out through the moment values of a quadrotor applied in the position control with the differential evolution algorithm (DE), which is under the evolutionary algorithms among meta-heuristic algorithms particle swarm optimization (PSO) which is among swarm-based algorithms and gravity search algorithm (GSA) among physics-based algorithms and charged system search (CSS) algorithm, which are all well-known in the literature. The efficient use of energy in electrically powered flying mechanisms is important in terms of completing its task. The aim of this study is to obtain proportional–integral–derivative (PID) coefficients that minimize the energy consumption caused by quadrotor moments. First of all, 12 PID coefficients calculated with traditional Ziegler Nicholes, and trying-error methods for the control of the quadrotor have been trained with DE, PSO, GSA and CSS algorithms and their cost values have been found for this problem. In the study, optimum PID coefficients have been found separately with each algorithm and torque data giving energy efficiency have been obtained by applying them to the state equations. Although the cost minimization convergence value obtained from DE does not look good compared to other algorithms, it has been observed that the moment values of the obtained PID coefficients in the control program are lower. In the study, it has been shown that the PID coefficients obtained from DE reach the target with approximately less energy than the maximum-moment value of the PSO, which provides the closest moment value. It can be thought that this value contributes to energy consumption in each orbital movement of the quadrotor. The simulation results show that the coefficients obtained from DE provide better energy efficiency and are superior to other algorithms compared in terms of energy efficiency. • PID coefficients for quadrotor control are optimized with DE,PSO,CSS,GSA algorithms • The torque values to be applied to each motor were adjusted with these coefficients • The total force applied with DEPID in the z direction is smaller than others • DEPID consumes less energy than the other algorithms in the paper [ABSTRACT FROM AUTHOR]

A Meta-evolutionary Selection of Constituents in Ensemble DE (MeSCEDE) framework is proposed in this paper to automate the design of high-level multi-population ensemble Differential Evolution (DE) algorithms. The automated design of high-level multi-population ensemble DE algorithms involves both automated selection of constituent DE algorithms for the ensemble and automated configuration of ensemble related parameters. Grammatical Evolution has been used as the meta-evolutionary algorithm in MeSCEDE to search the space of design choices so as to evolve effective ensemble design(s) for given problem(s). The simulation experiments carried out in this paper involve applying MeSCEDE to evolve ensemble DE designs for solving 30-dimensional CEC'17 benchmark functions. The effectiveness of the evolved designs are validated on 30 and 50-dimensional CEC'14 functions as well as on 22 real-world problem instances from CEC'11 benchmark suite. The MeSCEDE evolved designs have exhibited a competitive performance against state-of-the-art ensemble DE algorithms. In addition, the potential of MeSCEDE has been demonstrated against irace , a state-of-the-art algorithm configurator. All simulation experiments reiterate the potential of MeSCEDE towards evolving effective and robust ensemble DE designs. • Automated design of ensemble differential evolution (DE) algorithm is presented. • The proposed approach is Meta-evolutionary Selection of Constituents in Ensemble DE. • The approach uses grammatical evolution as the meta evolutionary algorithm. • The approach is demonstrated on CEC'17, CEC'14 and CEC'11 benchmark suites. • Relieves the practitioners from the difficult task of algorithm configuration. [ABSTRACT FROM AUTHOR]

• A generalized decoupling metaheuristic RBDO framework is proposed. • A particle's memory saving strategy is developed to provide effective guidance. • A new adaptive fractional-order equilibrium optimizer algorithm is developed. • Numerical and engineering examples illustrate the superiority of the proposed algorithm. Reliability-based design optimization (RBDO) algorithm is to minimize the objective under the probabilistic factors. While gradient-based and classical evolutionary RBDO algorithms provide promising performance on simple optimization problems, they are likely to perform poorly on challenging problems, including the multimodal functions, discrete design spaces, non-differential problems, etc. This paper proposes a unified framework to improve the performance of existing RBDO algorithms for complex RBDO problems. Our framework is based on three new strategies: generalized decoupling evolutionary and metaheuristic RBDO framework, particle's memory saving strategy, and adaptive fractional-order equilibrium optimizer algorithm. The proposed algorithm is characterized by a decoupling strategy to enable the parallel operation of the inner reliability computation and outer deterministic optimization, a particle's memory saving strategy to provide effective guidance from the previous iteration, and the adaptive fractional-order equilibrium optimizer algorithm to enhance the search efficiency and global convergence capacity. To evaluate the performance of the proposed algorithm, a wide range of experiments are conducted on different types of use cases. The experimental results demonstrate that our algorithm provides superior performance over other comparative algorithms. [ABSTRACT FROM AUTHOR]