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The meta-heuristic algorithms have aroused great attention for controller optimization. However, most of them are inseparable from the explicit system models when addressing a constrained optimization problem (COP). In this paper, we propose a data-driven constrained bat algorithm via a gradient-based depth-first search (GDFS) strategy. In the proposed scheme, the GDFS strategy can predetermine a search space that satisfies some strict constraints (e.g., stability requirements) of the optimized system. Meanwhile, an improved boundary constraint handling method is proposed to limit the exploration process to the predetermined space. In this way, the proposed algorithm can solve the COP by utilizing experimental data from real scenes, thereby relieving the dependence on precisely modeling the complex system. Together with an ɛ -constraint-handling method, the bat algorithm is employed to seek the global optimum of the COP. The search performance is enhanced by the designed linear-varying elite layer-based local search and a social learning-based walk mechanism to dynamically balance exploration and exploitation. The convergence is ensured based on the criteria of the stochastic optimization algorithm. Experimental results on a servo drive system and benchmark test functions verify the effectiveness of the proposed algorithm. • Design a data-driven optimization method for the constrained controller tuning. • Design a gradient-based depth-first search strategy for strict constraints. • BA integrates a novel search mechanism to prevent premature convergence. • An improved boundary constraint handling scheme is proposed. [ABSTRACT FROM AUTHOR]

• This paper proposes an enhanced SCA algorithm variant, called ARSCA. • ARSCA improves the convergence accuracy and avoids premature convergence. • This paper compares ARSCA with classical algorithms, variations of other algorithms. • ARSCA is applied to six engineering design problems and its results are satisfactory. The sine cosine algorithm (SCA) is a well-known meta-heuristic optimization algorithm. SCA has received much attention in various optimization fields due to its simple structure and excellent optimization capabilities. However, the dimension of objective function also increases with the increasing complexity of optimization tasks. This makes the original SCA appear to have insufficient optimization capability and likely to fall into premature convergence. A multi-mechanism acting variant of SCA, called ARSCA, is proposed to address the above deficiencies. ARSCA is an enhanced SCA algorithm based on the adaptive quadratic interpolation mechanism (AQIM) and Rounding mechanism (RM). RM enables a more balanced state between exploration and exploitation of the ARSCA. AQIM enhances local exploitation capabilities. To verify the performance of ARSCA, we compared ARSCA with some advanced traditional optimization algorithms and variants of algorithms for 30 consecutive benchmark functions of IEEE CEC2014. In addition, ARSCA was applied to 6 constrained engineering optimization problems. These six algorithms include the tension–compression spring design problem, the welded beam design problem, the pressure vessel design problem, the I-beam design problem, the speed reducer design problem, and the three-bar design problem. Experimental results show that ARSCA outperforms its competitors in both the solution quality and the ability to jump out of the local optimum. The relevant codes for the paper are publicly available at https://github.com/YangXiao9799/paper_ARSCA. [ABSTRACT FROM AUTHOR]

This paper presents a deterministic optimization strategy to solve the economic-environmental power dispatch (EEPD) problem of an electrical power system, using a Broyden Fletcher Goldfarb Shanno based on the augmented Lagrangian (BFGS-AL) algorithm. This problem is a nonlinear constrained multi-objective optimization. The objectives of this optimization are minimized the total fuel cost and emission amount for thermal generators while satisfying electric power systems equality and inequality constraints. The proposed approach is applied on the standard IEEE 30 bus test system, where the power transmission losses are taken into account. Simulation results proved that the proposed approach gives better-quality solution in terms of accuracy and convergence to the best compromise solution compared to other deterministic and meta-heuristic optimization techniques. [ABSTRACT FROM AUTHOR]

With continuous scale expansion and higher safety requirements in modern aluminum electrolysis, it is more and more necessary to realize an intelligent decision-making for shutting-down and running of aluminum reduction cells (SRARC). However, this realization needs to solve a special single-objective constrained integer optimization problem (SCIOP), where the key challenge is a high requirement for the constraint-handling ability. In this paper, based on a high-scalability intelligent optimization algorithm called discrete state transition algorithm (DSTA), a population-based DSTA with decomposition and knowledge guidance (PDSTA/D-S) is proposed. This PDSTA/D-S improves the constraint-handling ability of DSTA from three aspects. Firstly, a hybrid framework combining DSTA with genetic algorithm is proposed. Secondly, a decomposition-based multi-objective optimization for constrained problems with uniformly-angled weighted sum vector is proposed. Thirdly, the manual decision-making is transferred to a knowledge-based transformation operator of DSTA. Therefore, a high-level performance of decision-making for SRARC can be obtained. The related experiments on a SRARC which is built from the practical production have demonstrated that the proposed PDSTA/D-S not only makes an effective improvement of DSTA from three aspects, but also has a more advanced performance compared with other existing high-performance intelligent optimization algorithms. • A large-scale and multi-constrained integer optimization problem is established for shutting-down and running of aluminum reduction cells. • A hybrid framework combining discrete state transition with genetic algorithm is proposed. • A decomposition-based multi-objective optimization for constrained problems with uniformly-angled weighted sum vector is proposed. • The manual decision-making is transferred to a knowledge-based transformation operator of discrete state transition algorithm. • The experiments on a practical production show the proposed framework can easily find a higher-quality feasible solution. [ABSTRACT FROM AUTHOR]

This study considers a constrained huge-scale optimization problem over networks where the objective is to minimize the sum of nonsmooth local loss functions. To solve this problem, many optimization algorithms have been proposed by employing (sub)gradient descent methods to handle high-dimensional data, but the computation of the entire sub(gradient) becomes a computational bottleneck. To reduce the computational burden of each agent and preserve privacy of data in time-varying networks, we propose a privacy-preserving decentralized randomized block-coordinate subgradient projection algorithm over time-varying networks, in which the coordinates of the subgradient vector is randomly chosen to update the optimized parameter and the partially homomorphic cryptography is used to protect the privacy of data. Further, we prove that our algorithm is convergent asymptotically. Moreover, the rates of convergence are also established by choosing appropriate step sizes, i.e., O (log K / K) under local strong convexity and O (log K / K) under local convexity, in which K represents the number of iterations. Meanwhile, we show that the privacy of data can be protected by the proposed algorithm. The results of experiments demonstrate the computational benefit of our algorithm on two real-world datasets. The theoretical results are also verified by different experiments. • This paper proposes a privacy-preserving decentralized randomized block-coordinate subgradient projection algorithm. • It proves that the proposed algorithm is asymptotically convergent. • It proves that the proposed algorithm can protect the privacy of data. • It proves that the rate of convergence is achieved, i.e., O (log K / K) and O (log K / K). [ABSTRACT FROM AUTHOR]

• Optimal foraging algorithm with direction prediction & Gaussian oscillation is built. • New algorithm includes two update methods: prediction model and random model. • Prediction model mends exploitation ability by predicting the evolutionary direction. • Random model mends exploration by exploring the space with Gaussian distribution. • The superiority of algorithm is verified on benchmark set and engineering problems. Optimal foraging algorithm (OFA) is a newly stochastic optimization technique and is famous for its computational accuracy. However, the high computational accuracy leads to slow convergence speed. Experimental results demonstrate that OFA is good at unimodal functions but poor at multimodal functions. To improve these drawbacks, in this paper a novel modified OFA with direction prediction and Gaussian oscillation, named OFA/P&G is introduced. In OFA/P&G, a transition matrix is constructed when a new global optimum is found to generate the candidate individuals. If the current global optimum does not change, the Gaussian oscillation is employed in a low probability and OFA update method is used in a high probability to generate the candidate individuals. The superior performance of OFA/P&G is verified on the 12 CEC2017 benchmark functions, 13 constrained benchmark functions and 5 engineering problems. Experimental results demonstrate that OFA/P&G outperforms other comparative algorithms. Finally, a real-world problem, drilling path optimization, is solved by OFA/P&G. [ABSTRACT FROM AUTHOR]

Energy systems optimization problems are complex due to strongly non-linear system behavior and multiple competing objectives, e.g. economic gain vs. environmental impact. Moreover, a large number of input variables and different variable types, e.g. continuous and categorical, are challenges commonly present in real-world applications. In some cases, proposed optimal solutions need to obey explicit input constraints related to physical properties or safety-critical operating conditions. This paper proposes a novel data-driven strategy using tree ensembles for constrained multi-objective optimization of black-box problems with heterogeneous variable spaces for which underlying system dynamics are either too complex to model or unknown. In an extensive case study comprised of synthetic benchmarks and relevant energy applications we demonstrate the competitive performance and sampling efficiency of the proposed algorithm compared to other state-of-the-art tools, making it a useful all-in-one solution for real-world applications with limited evaluation budgets. • We develop a new data-driven optimization strategy using tree ensembles. • Our approach enables constrained multi-objective optimization of black-box problems. • We consider heterogeneous variable spaces with unknown underlying system dynamics. • ENTMOOT outperforms state-of-the-art tools on synthetic benchmarks and relevant energy applications. [ABSTRACT FROM AUTHOR]

• Proposing an improved group teaching optimization algorithm for UAV route planning. • A mathematical model of UAV route planning with various obstacles is established. • Introducing a segment-based fitness strategy to deal with the constraints. • Performance of the method is assessed on 3 different UAV flight environment models. • The proposed algorithm is very competitive and superior to the compared algorithms. The complexity and diversity of the flight environment pose great challenges to unmanned aerial vehicle route planning, which demands feasible flight strategies and efficient route planning algorithms. To address the issue, this paper constructs a 3-D flight environment model with multiple obstacles, and designs a novel diversified group teaching optimization algorithm for the generation of flight routes of unmanned aerial vehicles. In the environment model, a variety of obstacles are taken into consideration to make the flying scenarios more realistic, including mountain, cuboid, cylinder and triangular prism, and corresponding strategies are presented for unmanned aerial vehicles to safely avoid these obstacles. In the proposed algorithm, three novel teaching methods are introduced to balance the exploitation and exploration phases. Besides, a novel constrained optimization strategy is adopted, in which constraints are incrementally added to the fitness function to avoid the premature phenomenon in the initial iteration stage of algorithm. The experimental results show that compared with several state-of-the-art optimization algorithms, the proposed algorithm is significantly superior and can always generate the optimal flight route in complicated environments. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the application of imperialist competitive algorithm (ICA) for optimization of a cross-flow plate fin heat exchanger. Minimization of total weight and total annual cost are considered as objectives. Seven design parameters, namely, heat exchanger length at hot and cold sides, fin height, fin frequency, fin thickness, fin-strip length and number of hot side layers are selected as optimization variables. A case study from literature is presented to show the effectiveness of the proposed algorithm. The numerical results reveal that ICA can find optimum configuration with higher accuracy in less computational time when compared to conventional genetic algorithm (GA). [Copyright &y& Elsevier]

Abstract: A directed searching optimization algorithm (DSO) is proposed to solve constrained optimization problems in this paper. The proposed algorithm includes two important operations — position updating and genetic mutation. Position updating enables the non-best solution vectors to mimic the best one, which is beneficial to the convergence of the DSO; genetic mutation can increase the diversity of individuals, which is beneficial to preventing the premature convergence of the DSO. In addition, we adopt the penalty function method to balance objective and constraint violations. We can obtain satisfactory solutions for constrained optimization problems by combining the DSO and the penalty function method. Experimental results indicate that the proposed algorithm can be an efficient alternative on solving constrained optimization problems. [Copyright &y& Elsevier]

Abstract: This paper presents an augmented Lagrangian methodology with a stochastic population based algorithm for solving nonlinear constrained global optimization problems. The method approximately solves a sequence of simple bound global optimization subproblems using a fish swarm intelligent algorithm. A stochastic convergence analysis of the fish swarm iterative process is included. Numerical results with a benchmark set of problems are shown, including a comparison with other stochastic-type algorithms. [Copyright &y& Elsevier]

Abstract: The paper introduces a smoothing technique for a lower order penalty function for constrained optimization problems (COP). It is proved that the optimal solution to the smoothed penalty optimization problem is a -approximate optimal solution to the original optimization problem under some mild assumptions. Based on the smoothed penalty function, an algorithm for solving COP is proposed and some numerical examples are given. [Copyright &y& Elsevier]

Abstract: A novel modified differential evolution algorithm (NMDE) is proposed to solve constrained optimization problems in this paper. The NMDE algorithm modifies scale factor and crossover rate using an adaptive strategy. For any solution, if it is at a standstill, its own scale factor and crossover rate will be adjusted in terms of the information of all successful solutions. We can obtain satisfactory feasible solutions for constrained optimization problems by combining the NMDE algorithm and a common penalty function method. Experimental results show that the proposed algorithm can yield better solutions than those reported in the literature for most problems, and it can be an efficient alternative to solving constrained optimization problems. [Copyright &y& Elsevier]

Abstract: This paper presents two hybrid differential evolution algorithms for optimizing engineering design problems. One hybrid algorithm enhances a basic differential evolution algorithm with a local search operator, i.e., random walk with direction exploitation, to strengthen the exploitation ability, while the other adding a second metaheuristic, i.e., harmony search, to cooperate with the differential evolution algorithm so as to produce the desirable synergetic effect. For comparison, the differential evolution algorithm that the two hybrids are based on is also implemented. All algorithms incorporate a generalized method to handle discrete variables and Deb''s parameterless penalty method for handling constraints. Fourteen engineering design problems selected from different engineering fields are used for testing. The test results show that: (i) both hybrid algorithms overall outperform the differential evolution algorithms; (ii) among the two hybrid algorithms, the cooperative hybrid overall outperforms the other hybrid with local search; and (iii) the performance of proposed hybrid algorithms can be further improved with some effort of tuning the relevant parameters. [Copyright &y& Elsevier]

Abstract: This paper is concerned with a kind of QP-free feasible algorithm which solves an inequality constrained nonlinear optimization problem. Under some weaker conditions than those in [H. Qi, L. Qi, A New QP-free, globally convergent, locally superlinear convergent algorithm for inequality constrained optimization, SIAM J. Optim. 11 (2000) 113–132], we prove that the algorithm is implementable and globally convergent. Moreover, some numerical test results are given to indicate that the algorithm is quite promising. [Copyright &y& Elsevier]

Tree-Seed Algorithm (TSA) is a meta-heuristic optimization algorithm with good performance in solving continuous optimization problems. However, there is an imbalance between its exploration and exploitation when solving complex problems, mainly lack exploration. To overcome this problem, this paper proposes two tree migration mechanisms: triple-learning-based migration mechanism and sine-random-distribution migration mechanism. The target tree position is migrated by learning from the first three trees in the current iteration. The sine function is added to the tree migration formula to enhance the randomness of tree distribution. In order to verify these migration mechanisms, Triple Tree-Seed Algorithm (TriTSA) has been proposed and compared with TSA on 30 well-known test functions from IEEE CEC 2014. In addition, STSA, SCA, PSO, ABC, Jaya, and TLBO are adopted in some comparative experiments on different dimensions. The experiments show that the tree migration mechanism can improve the optimization capability of the original algorithm effectively. On all 30 benchmark test functions, TriTSA outperforms TSA on 10, 30, 50, and 100 dimensions by 70%, 90%, 90%, and 97% respectively. Finally, the proposed TriTSA is compared with TSA, ABC, PSO, and SCA on solving two classical engineering design problems. It is proved that the proposed algorithm is more applicable in solving practical problems. [ABSTRACT FROM AUTHOR]

In this paper a method is presented to fair the limit surface of a subdivision algorithm locally around an extraordinary point. The dominant six eigenvalues of the subdivision matrix have to satisfy linear and quadratic equality- and inequality-constraints in order to guarantee normal-continuity and bounded curvature at the extraordinary point. All other eigenvalues can be chosen arbitrarily within certain intervals and therefore can be used to optimize the shape of the subdivision surface by minimizing quadratic energy functionals. Additionally, if the sub- and subsub-dominant eigenvalues vary within predefined intervals, -regularity of the surface and locality of the stencils can be guaranteed, although eigenvectors are changed. [Copyright &y& Elsevier]

Abstract: In this paper, a kind of nonlinear optimization problems with nonlinear inequality constraints are discussed, and a new SQP feasible descent algorithm for solving the problems is presented. At each iteration of the new algorithm, a convex quadratic program (QP) which always has feasible solution is solved and a master direction is obtained, then, an improved (feasible descent) direction is yielded by updating the master direction with an explicit formula, and in order to avoid the Maratos effect, a height-order correction direction is computed by another explicit formula of the master direction and the improved direction. The new algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Furthermore, the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted. Finally, some numerical tests are reported. [Copyright &y& Elsevier]

In this paper, we present a nonmonotone trust-region algorithm with nonmonotone penalty parameters for the solution of optimization problems, with nonlinear equality constraints and bound constraints. The proposed algorithm combines an SQP approach with a trust-region strategy to globalize the process. Each step is obtained through the computation of a normal step (to reduce infeasibility) and a tangential step (to decrease some merit function). The algorithm makes use of an augmented Lagrangian function as merit function, and allows the value of this merit function and the penalty parameter involved in it to decrease nonmonotonically. The global convergence theory for the proposed algorithm is developed without regularity assumption, and shows that any limit point of the sequence generated by the algorithm is a ϕ-stationary point, while at least one limit point, under the suitable assumptions, is a substationary point (and a stationary point if it is feasible). Some preliminary numerical experiments are also reported. [Copyright &y& Elsevier]

This paper introduces a bio-inspired metaheuristic optimization algorithm named Tunicate Swarm Algorithm (TSA). The proposed algorithm imitates jet propulsion and swarm behaviors of tunicates during the navigation and foraging process. The performance of TSA is evaluated on seventy-four benchmark test problems employing sensitivity, convergence and scalability analysis along with ANOVA test. The efficacy of this algorithm is further compared with several well-regarded metaheuristic approaches based on the generated optimal solutions. In addition, we also executed the proposed algorithm on six constrained and one unconstrained engineering design problems to further verify its robustness. The simulation results demonstrate that TSA generates better optimal solutions in comparison to other competitive algorithms and is capable of solving real case studies having unknown search spaces. Note that the source codes of the proposed TSA algorithm are available at [ABSTRACT FROM AUTHOR]

The design optimization of mechanical system components, like bearings, pulleys, springs, etc. is an essential issue due to the current competitive market. The performance of any mechanical system depends on the design of their mechanical components. The design optimization of these mechanical components is a difficult task due to the intricate design constraints and mixed type design variables (i.e., continuous, discrete, and integer). This paper explores the performance of Rao algorithms on the design optimization of selected mechanical system components. The designs obtained using Rao algorithms are compared with the designs obtained using other optimization algorithms in previous studies. The comparison of results shows the ability and the efficiency of Rao algorithms for solving complex design optimization problems of mechanical components. • Three metaphor-less, simple and algorithm-specific parameter-less Rao algorithms are presented. • Performance of Rao algorithms is explored over ten complex design optimization problems of mechanical system components. • The computational results reveal that the Rao algorithms are superior to or competitive with other algorithms. • Rao algorithms are found computationally inexpensive because of less time taken by the algorithms to execute. [ABSTRACT FROM AUTHOR]

Abstract: Optimization of directional over-current relay (DOCR) settings is an important problem in electrical engineering. The optimization model of the problem turns out to be non-linear and highly constrained in which two settings namely time dial setting (TDS) and plug setting (PS) of each relay are considered as decision variables; the sum of the operating times of all the primary relays, which are expected to operate in order to clear the faults of their corresponding zones, is considered as an objective function. In the present study, three models are considered namely IEEE 3-bus model, IEEE 4-bus model and IEEE 6-bus model. To solve the problem, we have applied five newly developed versions of differential evolution (DE) called modified DE versions (MDE1, MDE2, MDE3, MDE4, and MDE5). The results are compared with the classical DE algorithm and with five more algorithms available in the literature; the numerical results show that the modified DE algorithms outperforms or perform at par with the other algorithms. [Copyright &y& Elsevier]