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We propose a parameterized level set method (PLSM) for structural topology optimization based on reaction diffusion equation (RDE) and fuzzy PID control algorithm. By using the proposed method, the structural compliance minimization problem under volume constraints is studied. In this work, the RDE is used as the evolution equation of level set function, and the topological derivative of the material domain is used as the reaction term of the RDE to drive the evolution of level set function, which has little dependence on the initial design domain, and can generate holes in the material domain; the compactly supported radial basis function (CS-RBF) is used to interpolate the level set function and modify the RDE, which can improve the computational efficiency, and keep the boundary smooth in the optimization process. Meanwhile, the fuzzy PID control algorithm is used to deal with the volume constraints, so that the convergence process of the structure volume is relatively stable. Furthermore, the proposed method is applied to 3D structural topology optimization. Several typical numerical examples are provided to demonstrate the feasibility and effectiveness of this method. [ABSTRACT FROM AUTHOR]

This paper proposes a parameter coordination optimization design of a power system stabilizer (PSS) based on an improved quasi-affine transformation evolutionary (QUATRE) algorithm to suppress low-frequency oscillation and improve the dynamic stability of power systems. To begin, the simulated annealing (SA) algorithm randomly updates the globally optimal solution of each QUATRE iteration and matches the inferior solution with a certain probability to escape the local extreme point. This new algorithm is first applied to the power system. Since the damping ratio is one of the criteria with which to measure the dynamic stability of the power system, this paper sets the objective function according to the principle of maximization of the damping coefficient of the electromechanical mode, and uses SA-QUATRE to search a group of global optimal PSS parameter combinations to improve the safety factor of the system as much as possible. Finally, the method's rationality and validity were validated by applying it to the simulation examples of the IEEE 4-machine 2-area system with different operation states. The comparison with the traditional optimization algorithm shows that the proposed method has more advantages for multi-machine PSS parameter coordination optimization, can restrain the low-frequency oscillation of the power system more effectively and can enhance the system's stability. [ABSTRACT FROM AUTHOR]

The most important and demanding part of the artificial neural network is the training process which involves finding the most suitable values for the weights in the network architecture, a challenging optimization problem. Gradient approaches and the meta-heuristic approaches are two methods extensively used to optimize the weights in the network. Gradient approaches have serious disadvantages including getting stuck in local optima, inadequate exploration, etc. To overcome these disadvantages, meta-heuristic approaches are preferred in training the artificial neural network instead of gradient methods. Therefore, in this study, an improved animal migration optimization algorithm with the Lévy flight feature was proposed to train the multilayer perceptron. The proposed hybrid algorithm is named IAMO-MLP. The main contributions of this article are that the IAMO algorithm was developed, the IAMO-MLP algorithm can successfully escape from local optima, and the initial positions did not affect the performance of the IAMO-MLP algorithm. The enhanced algorithm was tested and validated against a wider set of benchmark functions and indicated that it substantially outperformed the original implementation. Afterward, the IAMO-MLP was compared with ten algorithms on five classification problems (xor, balloon, iris, breast cancer, and heart) and one real-world problem in terms of mean squared error, classification accuracy, and nonparametric statistical Friedman test. According to the results, the IAMO was successful in training the multilayer perceptron. [ABSTRACT FROM AUTHOR]

In order to overcome the drawbacks of Archimedes optimization algorithm( AOA), such as weak global search ability, easily trapping into local optimum and prematurely converge, this paper put forward Archimedes optimization algorithm improved by multi-strategy collaborative( MAOA ) . Initially, it used the random Gaussian mutation strategy to increase the diversity of the population in the iterative process and strengthen the global search ability. Then, based on the randomness, ergodicity and diversity of multiple chaotic models, it introduced the local chaotic search strategy to expand the scope range of the chaotic space and enhance the local development capabilities of the algorithm. At the same time, it proposed a nonlinear dynamic density decreasing factor to coordinate the global exploration ability and local development ability of the algorithm. Finally, for the sake of increasing the diversity of the population during the iteration process, this paper adopted the golden sine strategy of the Levy flight guidance mechanism to perturb the population position and improve the ability of the algorithm to jump out of the local optimum. Through simulation experiments on 12 benchmark functions and part of the CEC2014 function set, the results show that the proposed algorithm can overcome the shortcomings of AOA' s weak global exploration ability and easy to fall into local optimality, and improve the accuracy and stability of AOA . In addition, the introduction of mechanical optimization design cases for testing and analysis will further verify the feasibility and applicability of MAOA on practical issues. [ABSTRACT FROM AUTHOR]

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The flower pollination algorithm (FPA) is a highly efficient metaheuristic optimization algorithm that is inspired by the pollination process of flowering species. FPA is characterised by simplicity in its formulation and high computational performance. Previous studies on FPA assume fixed parameter values based on empirical observations or experimental comparisons of limited scale and scope. In this study, a comprehensive effort is made to identify appropriate values of the FPA parameters that maximize its computational performance. To serve this goal, a simple non-iterative, single-stage sampling tuning method is employed, oriented towards practical applications of FPA. The tuning method is applied to the set of 28 functions specified in IEEE-CEC'13 for real-parameter single-objective optimization problems. It is found that the optimal FPA parameters depend significantly on the objective functions, the problem dimensions and affordable computational cost. Furthermore, it is found that the FPA parameters that minimize mean prediction errors do not always offer the most robust predictions. At the end of this study, recommendations are made for setting the optimal FPA parameters as a function of problem dimensions and affordable computational cost. [ABSTRACT FROM AUTHOR]

Past present future (PPF) is a new stochastic optimization algorithm inspired by the phenomena of the way an individual learns from a successful person in society. PPF is based on the concept of "future improvement of a person's life depending on his/her past experience and present work." The influence of successful persons also affects the improvement of the future life of an individual. This work develops a mathematical model for PPF following the above facts. In this new algorithm, the population is divided into subpopulations and a switching mechanism is followed among the subpopulations to track the change in optimal positions of an individual thereby accelerating the convergence rate. In addition, this switching mechanism also prevents pre-mature convergence. PPF was found to possess low computational complexity with fast convergence characteristics. The proposed PPF is compared with 41 up-to-date meta-heuristic algorithms taking an extensive set of benchmark functions to verify the efficiency. In addition, five classical engineering design problems are simulated to estimate the efficacy of the PPF algorithm in optimizing engineering problems. The results confirm the superior performance of the proposed algorithm to get the optimal solution with less iteration and have shown the best competitive performance compared to all other algorithms. [ABSTRACT FROM AUTHOR]

Computational efficiency in simulation-based optimization algorithms is essential when the system objective functions are expensive to evaluate and computational resources are limited. This article proposes a hybrid Bayesian BFGS algorithm (HB2O) to address this efficiency problem. An adaptive expected improvement (AEI) acquisition function is developed to realize a self-adaptive sampling strategy by dynamically balancing the design space exploration and exploitation. A series of computational experiments is conducted on a diverse set of test functions to benchmark the optimization performance of the HB2O against six commonly used alternative optimizers, and to validate the effectiveness of AEI against four alternative acquisition functions. The computational results show that the proposed HB2O can robustly converge on the functions' optima with limited simulation samples, and it significantly outperforms other optimizers for various test functions. This article provides a sample-efficient solution to complex optimization problems where taking a large number of system simulations is computationally prohibitive. [ABSTRACT FROM AUTHOR]

This paper proposes a new dynamic multi-objective optimization algorithm by integrating a new fitting-based prediction (FBP) mechanism with regularity model-based multi-objective estimation of distribution algorithm (RM-MEDA) for multi-objective optimization in changing environments. The prediction-based reaction mechanism aims to generate high-quality population when changes occur, which includes three subpopulations for tracking the moving Pareto-optimal set effectively. The first subpopulation is created by a simple linear prediction model with two different stepsizes. The second subpopulation consists of some new sampling individuals generated by the fitting-based prediction strategy. The third subpopulation is created by employing a recent sampling strategy, generating some effective search individuals for improving population convergence and diversity. Experimental results on a set of benchmark functions with a variety of different dynamic characteristics and difficulties illustrate that the proposed algorithm has competitive effectiveness compared with some state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Given the outstanding effectiveness and efficiency performance in different fields such as image processing and energy dispatching, the virus optimization algorithm (VOA), a newly developed metaheuristic for general optimization purposes, has been further improved. Similar to other metaheuristic methods, VOA performance to some degree relies on proper parameter settings, which may require large numbers of experiments to determine. Therefore, this study proposes a self-adaptive version of VOA (SaVOA) to decrease the number of controllable parameters in the algorithm and thus reduce the time needed to determine proper parameter values by any sort of experimental design process. Having an SaVOA ensures the ease access of the algorithm for different types of continuous domain problems, whereas previous different optimization problems may have needed different parameter settings. To perform the comparison, SaVOA is tested by optimizing the same set of benchmark functions used when proposing the original VOA. Computational results indicate some major advances were achieved by the SaVOA in addition to competitive results obtained. Most importantly, SaVOA proved its superiority on functions where the original VOA was not powerful enough to perform well, such as Rosenbrock, Schwefel, Drop Wave, Levy, and Easom's functions. In terms of implementation, the number of controllable parameters in SaVOA was greatly reduced to only one—the stopping criterion. This promises a significant improvement in the utility of SaVOA for any type of continuous domain optimization problem. [ABSTRACT FROM AUTHOR]

We present a near-optimal reduction from approximately counting the cardinality of a discrete set to approximately sampling elements of the set. An important application of our work is to approximating the partition function Z of a discrete system, such as the Ising model, matchings or colorings of a graph. The typical approach to estimating the partition function Z(β*) at some desired inverse temperature β* is to define a sequence, which we call a cooling schedule, β0 = 0 < β1 < ߪ < βl = β* where Z(0) is trivial to compute and the ratios Z(βi+1)/Z(βi) are easy to estimate by sampling from the distribution corresponding to Z(βi). Previous approaches required a cooling schedule of length O*(In A) where A = Z(0), thereby ensuring that each ratio Z(βi+1)/Z(βi) is bounded. We present a cooling schedule of length l = O*(√In A). For well-studied problems such as estimating the partition function of the Ising model, or approximating the number of colorings or matchings of a graph, our cooling schedule is of length O*(√n), which implies an overall savings of O*(n) in the running time of the approximate counting algorithm (since roughly l samples are needed to estimate each ratio). A similar improvement in the length of the cooling schedule was recently obtained by Lovász and Vempala in the context of estimating the volume of convex bodies. While our reduction is inspired by theirs, the discrete analogue of their result turns out to be significantly more difficult. Whereas a fixed schedule suffices in their setting, we prove that in the discrete setting we need an adaptive schedule, that is, the schedule depends on Z. More precisely, we prove any nonadaptive cooling schedule has length at least O*(In A), and we present an algorithm to find an adaptive schedule of length O*(√In A). [ABSTRACT FROM AUTHOR]

Biogeography-Based Optimization (BBO), a good meta-heuristic optimization algorithm, has drawn much attention and been applied widely to many areas. However, BBO can not do well in solving some complex and diversified optimization problems. In order to obtain an algorithm with better optimization performance, this paper presents a hybrid BBO with Shuffled Frog Leaping Algorithm (SFLA), named HBBOS. Firstly, we improve BBO. BBO's mutation operator is got rid of and its migration operator is improved. Two novel updating mechanisms, i.e. a hybrid cross mechanism and a hybrid disturbance mechanism, are introduced instead of the original migration mechanism to update the immigration habitats' Suitability Index Variables (SIVs) and non-immigration habitats' SIVs, respectively. A differential mechanism is also introduced to prevent the algorithm from falling into local optima to some degree. These improvements can enhance exploration and exploitation and balance them. Secondly, we merge the improved migration operator into SFLA's group structure framework. This can balance exploration and exploitation further. So HBBOS is obtained. HBBOS can effectively maximize the two algorithms' advantages and minimize the defects so that it can obtain better optimization performance. A large number of experiments are made on benchmark functions with various types and complexities, such as a set of classic functions and CEC2014 test set. HBBOS is also applied to minimum spanning tree problems. The experimental results show that HBBOS outperforms quite a few state-of-the-art algorithms. • A hybrid BBO with SFLA, named HBBOS, is proposed to maximize the two algorithms' advantages and minimize their defects. • Hybrid cross and hybrid disturbance mechanisms are introduced into BBO's migration operator to enhance the performance. • A differential mechanism is introduced to prevent the algorithm from falling into local optima to some degree. • The improved migration operator is merged into SFLA's group structure framework to balance exploration and exploitation. • HBBOS can obtain superior performance on benchmark functions and solve the minimum spanning tree problems better. [ABSTRACT FROM AUTHOR]

This paper presents an accurate implicit re-initialization approach in the framework of a level set method. The improved method includes two schemes for keeping the zero level set unperturbed. The first scheme is to derive and use a new formula for the smoothing parameter in the conventional re-initialization equation based on the principle of the interface not moving. The second scheme is to reduce the local time step to avoid the interface moving across grid points when the sign of the level set function near the interface is changed. The example presented suggests that the new algorithm has a better approximation to the signed distance function and obtains a more accurate interface than the algorithm presented by Sussman et al. (1994). For shape and topology optimization of fluid, the effectiveness of the developed method in this paper was demonstrated by the internal and external flow examples. [ABSTRACT FROM AUTHOR]

• A novel index is proposed to evaluate the signal complexity. • The envelope signal is Fourier transformed twice in the objective function. • A novel adaptive VMD method based on the AOA is proposed. Variational mode decomposition (VMD) is widely used in rotating machinery fault diagnosis. However, the choice of its main parameters is often based on experience, affecting the decomposition results. Aiming to mitigate this drawback, an adaptive VMD method using the Archimedes optimization algorithm (AOA) is presented. Firstly, the computational domain of the objective function is set to the amplitude spectrum of the signal envelope spectrum. Secondly, a correlation waveform index (Cwi) is proposed to evaluate the complexity of the signal. The minimum average value of the Cwi of all intrinsic modal functions (IMFs) is taken as the objective function. Finally, the AOA is used to search for the optimal mode number and penalty factor to find IMFs which are sensitive to fault features. Compared to the other improved VMD methods, the proposed method has a better performance in extracting the fault characteristics from the simulated and actual cases. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a new topology optimization method, which can adjust the geometrical complexity of optimal configurations, using the level set method and incorporating a fictitious interface energy derived from the phase field method. First, a topology optimization problem is formulated based on the level set method, and the method of regularizing the optimization problem by introducing fictitious interface energy is explained. Next, the reaction–diffusion equation that updates the level set function is derived and an optimization algorithm is then constructed, which uses the finite element method to solve the equilibrium equations and the reaction–diffusion equation when updating the level set function. Finally, several optimum design examples are shown to confirm the validity and utility of the proposed topology optimization method. [ABSTRACT FROM AUTHOR]

Recently, many dynamic optimization algorithms based on metaheuristic methods have been proposed. Although these schemes are highly efficient in determining a single global optimum, they fail in locating multiple optimal solutions. The central goal of dynamic multimodal optimization is to detect multiple optimal solutions for an optimization problem where its objective function is modified over time. Locating many optimal solutions (global and local) in a dynamic multimodal optimization problem is particularly crucial for several applications since the best solution could not always be the best implementable alternative due to various practical limitations. In spite of its importance, the problem of dynamic multimodal optimization through evolutionary principles has been scarcely considered in the literature. On the other hand, mean shift is a non-parametric and iterative process for detecting local maxima in a density function represented by a set of samples. Mean shift maintains interesting adaptive characteristics that allow it to find local maxima under dynamic environments. In this paper, the mean shift scheme is proposed to detect global and local optima in dynamic optimization problems. In the proposed method, the search strategy of the mean shift is modified to consider not only the density but also the fitness value of the candidate solutions. A competitive memory, along with a dynamic strategy, has also been added to accelerate the convergence process by using important information from previous environments. As a result, the proposed approach can effectively identify most of the global and local optima in dynamic environments. To demonstrate the performance of the proposed algorithm, a set of comparisons with other well-known dynamic optimization methods has been conducted. The study considers the benchmark generator of the CEC competition for dynamic optimization. The experimental results suggest a very competitive performance of the proposed scheme in terms of accuracy and robustness. • Mean shift scheme is proposed to detect global and local optima in dynamic problems. • The original mean shift is modified to consider the fitness value. • A competitive memory, along with a dynamic strategy, has also been added. • The proposed approach can effectively identify most of the global and local optima. [ABSTRACT FROM AUTHOR]

Numerous optimization problems have been defined in different disciplines of science that must be optimized using effective techniques. Optimization algorithms are an effective and widely used method of solving optimization problems that are able to provide suitable solutions for optimization problems. In this paper, a new nature-based optimization algorithm called Snow Leopard Optimization Algorithm (SLOA) is designed that mimics the natural behaviors of snow leopards. SLOA is simulated in four phases including travel routes, hunting, reproduction, and mortality. The different phases of the proposed algorithm are described and then the mathematical modeling of the SLOA is presented in order to implement it on different optimization problems. A standard set of objective functions, including twenty-three functions, is used to evaluate the ability of the proposed algorithm to optimize and provide appropriate solutions for optimization problems. Also, the optimization results obtained from the proposed SLOA are compared with eight other well-known optimization algorithms. The optimization results show that the proposed SLOA has a high ability to solve various optimization problems. Also, the analysis and comparison of the optimization results obtained from the SLOA with the other eight algorithms shows that the SLOA is able to provide more appropriate quasi-optimal solutions and closer to the global optimal, and with better performance, it is much more competitive than similar algorithms. [ABSTRACT FROM AUTHOR]

We consider a production/distribution system represented by a general directed acyclic network. Each node is associated with a specific "product" at a given location and/or production stage. An arc (i, j) indicates that item i is used to "produce" item j. External demands may occur at any of the network's nodes. These demands occur continuously at item-specific constant rates. Components may be assembled in any given proportions. The cost structure consists of inventory carrying, variable, and fixed production/distribution costs. The latter depend, at any given replenishment epoch, on the specific set of items being replenished, according to an arbitrary set function merely assumed to be monotone and submodular. It has been shown that a simply structured, so-called power-of-two policy is guaranteed to come within 2% of a lower bound for the minimum cost. In this paper, we derive efficient algorithms for the computation of an optimal power-of-two policy, possibly in combination with this lower bound. These consist of a limited number of polymatroidal maximum flow calculations in networks closely associated with the original production/distribution network. [ABSTRACT FROM AUTHOR]

Consider a set function v(·) defined on all subsets of a finite set N. This paper presents a class of set function maximization problems of the form Max(v(S)|S ⊆ N) that are solved optimally by the greedy algorithm. In particular, it is shown that there exists a nested sequence of subsets S[sup *, sub l] ... S[sup *, sub m] that increase to the optimal policy and S[sup *, sub k] maximizes v(S) over all subsets of cardinality k. The class is characterized by conditions on the set function v(·) and related to the notion of submodularity. These results are then applied to two order-preserving machine scheduling problems. The greedy algorithm is shown to be optimal for these problems thereby providing a new algorithm different from previous approaches based on dynamic programming. [ABSTRACT FROM AUTHOR]

The optimum Steiner Tree problem in a (nondirected) graph is known to belong to the class of NP-hard problems. However large scale instances (typically hundreds or thousands of nodes) arise in such important applications as optimal communication network design, or VLSI routing. There is therefore a strong need for efficient heuristics. We discuss in this paper efficient implementations of greedy-type procedures for approximate solution of symmetric Steiner Tree problems with arbitrary nonnegative lengths on the edges. A special subclass of problems (meeting the so-called "nonadjacency condition") is also introduced and studied. Various ways of improving the computational efficiency of the basic greedy algorithm are examined, among which the use of reoptimization procedures and proper exploitation of a supermodularity property of an associated set function; thanks to the latter the total number of minimum spanning tree computations can be significantly reduced according to the "accelerated greedy algorithm" principle (Minoux 1977), and lower bounds can be derived (thus providing estimates of the quality of the approximate solutions obtained). [ABSTRACT FROM AUTHOR]