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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]

• Stego distribution optimization achieves efficient adversarial steganography. • Optimizing embedding modification probabilities enables end-to-end gradient descent. • Cover enhancement and distortion optimization can be collaborated. • Pairing cover-stego in loss removes mode collapses in steganographic min-max games. Adversarial steganography aims to fool steganalysis models and enhance embedding security. Its application in the sequential min-max steganographic game has recently shown state-of-the-art embedding security. However, current methods suffer from high computational costs and inferior convergence. These issues could be caused by unnecessary optimization on distortions and the monotonous criterion for adversaries. This paper introduces a novel and concise scheme for conducting adversarial steganography and refines the criterion for adversaries. The suggested adversarial optimizations leave out distortions and focus on optimizing the stego distribution, whose difference with the intrinsic cover distribution is the primary factor affecting embedding security. These optimization techniques are accomplished by utilizing gradient descent on embedding modification probabilities and introducing a novel protocol for cover enhancement. Moreover, the proposed criteria for adversaries prioritize enhancing the similarity between each cover-stego pair, rather than evading steganalysis models, to break monotony and enhance convergence. The discussion and refinement of the loss function and termination setting of the optimization process are also provided. The proposed method demonstrates its benefits in increased security and computation efficiency in experiments. After collaborating with the steganographic min-max game, the state-of-the-art embedding security and stronger resistance to various and unexpected steganalysis models are seen. [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]

Illusory contour reconstruction can be modeled as a minimization problem with a tractable variational level set formulation, utilizing Euler's elastica to reconstruct the illusory boundaries. However, this kind of formulation is very difficult to solve numerically as it is hard to implement such optimization algorithms efficiently in practice. In this paper, we propose an equivalently reduced variational level set formulation by taking the level set functions as signed distance functions. Technically, an alternating direction method of multipliers (ADMM) is developed by introducing some auxiliary variables, Lagrange multipliers and applying an alternating optimization strategy. With the proposed ADMM method, the minimization problem can be transformed into a series of sub-problems, which can be solved easily via using the Gauss-Seidel iterations and Fast Fourier Transform (FFT). The corresponding level set functions are regarded as signed distance functions during computation process using a simple algebraic projection method, which avoids the traditional re-initialization process for conventional level set functions. Extensive experiments have been conducted on both synthetic and real images, which validated the proposed approach, and demonstrated the advantages of the proposed ADMM-Projection (ADMM-P) method over the existing algorithms based on traditional gradient descent method (GDM) in terms of computational efficiency. [ABSTRACT FROM AUTHOR]

This study constructs a reinforcement learning-based hybrid algorithm for Aquila Optimizer (AO) and improved Arithmetic Optimization Algorithm (IAOA). The point of the hybrid algorithm is that Q-learning can dynamically select the AO and the IAOA at different stages for different problems. In Arithmetic Optimization Algorithm (AOA), the mathematical optimization acceleration (MOA) function is restructured to balance global search and local exploitation, which can effectively stay away from the local optimum. Moreover, an improved reward function is modeled for Q-learning, which makes our hybrid algorithm more efficient and accurate. A set of benchmark functions and two engineering optimization problems are employed to test the performance of the proposed hybrid algorithm in this paper. Compared with other algorithms, the results show that the proposed hybrid algorithm has higher convergence speed and accuracy. [ABSTRACT FROM AUTHOR]

By generalizing a recent result of Hong, Liu and Lai on characterizing the degree-sequences of simple strongly connected directed graphs, a characterization is provided for degree-sequences of simple k-node-connected digraphs. More generally, we solve the directed node-connectivity augmentation problem when the augmented digraph is degree-specified and simple. As for edge-connectivity augmentation, we solve the special case when the edge-connectivity is to be increased by one and the augmenting digraph must be simple. [ABSTRACT FROM AUTHOR]

This paper develops an extended bi-directional evolutionary structural optimization (BESO) method for topology optimization of continuum structures with smoothed boundary representation. In contrast to conventional zigzag BESO designs and removal/addition of elements, the newly proposed evolutionary topology optimization (ETO) method, determines implicitly the smooth structural topology by a level-set function (LSF) constructed by nodal sensitivity numbers. The projection relationship between the design model and the finite element analysis (FEA) model is established. The analysis of the design model is replaced by the FEA model with various elemental volume fractions, which are determined by the auxiliary LSF. The introduction of sensitivity LSF results in intermediate volume elements along the solid-void interface of the FEA model, thus contributing to the better convergence of the optimized topology for the design model. The effectiveness and robustness of the proposed method are verified by a series of 2D and 3D topology optimization design problems including compliance minimization and natural frequency maximization. It has been shown that the developed ETO method is capable of generating a clear and smooth boundary representation; meanwhile the resultant designs are less dependent on the initial guess design and the finite element mesh resolution. [ABSTRACT FROM AUTHOR]

Consider the problem of selecting k items that maximize the value of a monotone submodular set function f, where f can be accessed using value queries. It is well known that polynomially many queries suffice in order to obtain an approximation ratio of $$1 - \frac{1}{e}$$ . We consider a variation on this problem in which the value queries are required to be of uniform size: each queried set, like the desired solution itself, must contain k items. We show that polynomially many uniform size queries suffice in order to obtain an approximation ratio of $$\frac{1}{2}$$ , and that an approximation ratio of $$\frac{1 + \epsilon }{2}$$ requires a number of queries that is exponential in $$\epsilon k$$ . For the interesting special case of coverage functions, we show that an approximation ratio strictly better than $$\frac{1}{2}$$ is attainable with polynomially many uniform size queries. The 'uniform size' requirement is motivated by situations in which a firm may offer a menu of exactly k items to its clients, where k is a parameter determined by external considerations. Performing a query corresponds to physically changing the identities of the items offered, and the reply to the query is deduced by observing the behavior of clients in response to the change. Queries that involve a number of items that differs from k may not be desirable due to these external considerations. In such situations it is natural to ask whether the same approximation ratios that can be guaranteed by general value queries can also be obtained by uniform size queries. [ABSTRACT FROM AUTHOR]

Finite element (FE) model of updating is the process of calibrating model parameters to improve the accuracy of numerical prediction. This goal is usually achieved by solving an optimization problem with the objective function measuring the misfit between simulated responses and experimental data. The sensitivity method is the predominate class of algorithms to FE model updating problems, and has opened a wide range of applications. However, this method often suffers from large errors due to linearization. To address this challenge, this paper proposes to utilize the unscented Kalman inversion (UKI) method to solve the FE model updating problems in a derivative-free manner. As an iterative optimization method, the UKI determines the new iterate using function values at a set of sample points rather than the derivative information. Implementation details, such as handling constraints during the optimization process, are presented in the paper. To validate the proposed UKI, model updating of a pedestrian bridge is conducted using the simulated and experimental data. Both validation examples show that the UKI is a competitive method for solving FE model updating problems. • The UKI method solves FE model updating problems in a derivative-free manner. • The UKI takes the effect of noises into account in a natural way. • Method is proposed to incorporate constraints during iterative process of the UKI. • The UKI is compared with the Levenberg–Marquardt algorithm. • The UKI is applied to updating a pedestrian bridge model using field test data. [ABSTRACT FROM AUTHOR]

This paper introduces a new version of a hyper-heuristic framework: Generalized Self-Adapting Particle Swarm Optimization with samples archive (M-GAPSO). This framework is based on the authors previous works on hybridization of optimization algorithms and enhancing population based optimization with model based optimization. The paper presents the structure of the proposed framework and analyzes the impact of its modules on the final system performance. M-GAPSO hybridizes Particle Swarm Optimization, Differential Evolution and model based optimizers. A ratio of particular algorithms within a population is regulated by an adaptation scheme. The applicability of the proposed hybrid method to black-box optimization is verified on 24 continuous benchmark functions from the COCO test set and 29 functions from the CEC-2017 test set. On the BBOB test set a hybrid of PSO and DE with adaptation obtained 11 significantly better and 2 significantly worse results on 5 and 20 dimensional functions than the basic DE. Further inclusion of the model based optimizers led to 15 significantly better and 2 significantly worse results compared to the PSO-DE hybrid. On the CEC-2017 test set, M-GAPSO was significantly better than both Red Fox Optimization and Dual Opposition-Based Learning for Differential Evolution (DOBL) on 7 functions in 30 dimensions and 12 functions in 50 dimensions. • A hyper-heuristic approach to continuous global optimization problems. • An archive of function samples stored in an R-Tree based indexed. • Seamless hybridization of population-based and model-based optimizers. • A roulette-based algorithm selector. • Restart methods considering locations of discovered optima. [ABSTRACT FROM AUTHOR]

PM 2.5 forecasting has always been difficult. Neural networks are widely used in the forecasting of PM 2.5 , however, the accuracy is not satisfactory due to uncertainty. In order to solve this problem, a new PM 2.5 forecasting system based on data preprocessing, combined neural network, and the unconstrained weighting method based on an improved multi-objective optimization algorithm is proposed. A new chaotic map is introduced to our model to improve the traditional population initialization. In addition, a new unconstrained weighting method was proposed, and a combination of MAPE value (prediction accuracy) and STD value (prediction stability) were set as the objective functions. The predicted results of each neural network were judged by statistical index and a dynamic weight was given to different neural networks to achieve the optimal prediction result. We demonstrated the superiority, accuracy and generalization ability of our proposed model through experiments on the PM 2.5 data of four cities around the Bohai Economic Belt in China: Beijing, Tianjin, Dalian, and Yantai. • VMD method is robust to the sampling and noise which can effectively avoid the mode aliasing. • The combination of ANN, RNN, CNN is adopted, which greatly improves the prediction ability of the model. • The unconstrained weighting algorithm is used to obtain the optimal weight of different neural networks. • A new chaotic mapping is proposed, which can effectively improve the global search ability. • The combination of point prediction and interval prediction can provide more effective information. [ABSTRACT FROM AUTHOR]

In the present paper, the task of designing a compliant mechanism is accomplished by solving a multi-objective topology optimization problem. The objective function includes a target displacement at the output port and compliances of two load cases. The design variables include two types of boundaries, i.e., the traction free boundary and the Dirichlet boundary. The topology optimization of compliant mechanism and its support is solved by using a level set method. Two level set functions are used to represent a compliant mechanism and the two types of boundaries. Each of the two boundaries is represented by a part of the zero level set of one level set function. Evolution of the two boundaries is modeled by two independent Hamilton–Jacobi equations, thus the shape and topology of the two boundaries change independently. The shape derivatives are derived by using a Lagrangian function and the adjoint method. The finite element analysis is done by modifying a fixed background mesh, and the artificial weak material is not used. Numerical examples in two dimensions are investigated. [ABSTRACT FROM AUTHOR]

A level-set based multi-material topology optimization method using a reaction diffusion equation is proposed in this paper. Each phase is represented by a combined formulation of different level set functions. This description model is modified from Multi-Material Level Set (MM-LS) topology description model. With a total number of M level set functions, this approach provides a representation of M materials and one void phase (totally M + 1 phases). By this approach, the mathematic model of the multi-material topology optimization problem using a reaction diffusion equation is established. With this model, the geometrical complexity of optimal solutions can be easily controlled by appropriately setting a regularization parameter. Some implementation details for solving this model are also presented in this paper. Finally, several typical numerical examples are shown to confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we study sub-topical functions in the framework of abstract convexity and examine the relevant properties such as support sets, polar sets and sub-differentials for these functions. Plus-radiant and plus-co-radiant sets, and their relations with sub-topical functions are studied. Applying sub-topical functions, we present some separation theorems for both plus-radiant and plus-co-radiant sets. [ABSTRACT FROM AUTHOR]

Decision support systems focus on their interpretability with a different caution. The majority of approaches utilize reliable optimization techniques to achieve high recognition accuracy. However, accuracy improvement is done at the cost of the readability of the decision support system. This paper proposes a novel technique of linguistic rule extraction focused on: explainability, interpretability, and reliability, called EasIeR. Proposed solution performs a direct analysis of the learning set without omitting real data imperfections. The proposed algorithm processes the imprecision of data with linguistic values described by fuzzy membership functions and the uncertainty of knowledge employing a fuzzy belief function. It describes the learning set with the most appropriate fuzzy if-then rules. For this purpose, a new method of evaluation of membership functions in a set of rules and their iterative refinement is proposed. EasIeR achieves the best results of trade-off criteria between the generalization quality and the interpretability of the knowledge base when compared with state-of-art fuzzy rule-based classification approaches. Achieving the simplest rule base and competitive generalization quality is verified by cross-validation experiments with benchmark data sets. The new method of rule evaluation allows for better determination of their quality in decision support, and the selection algorithm quickly provides a clear and easy to interpret knowledge base. This rule evaluation technique will be proficient for all fuzzy rule-based classification systems. • Efficient algorithm of rule extraction provides interpretable data-driven knowledge. • Fuzzy rules and belief measure ensure classification reliability and explainability. • New rule evaluation method allows extracting effective rule-based knowledge. • Approach achieves competitive generalization quality with the simplest knowledge base. [ABSTRACT FROM AUTHOR]

With the correction of the level set function by the use of Lagrangian maker particles, the particle level method has been proven to be an accurate and robust scheme to capture the evolution of moving interface [1] . In this work, together with the later improved version [2] , the drawbacks of the particle correction procedure in the original particle level set method were investigated in detail and an optimized particle correction procedure was developed to improve the accuracy and robustness of the implicitly represented moving interface. A refined grid point level set value selection process has been proposed and shown to effectively improve the interface location accuracy through a set of standard advection test cases when using a fast first order accurate semi-Lagrangian solver firstly proposed in [3] . With the implementation of our enhanced level set value selection procedure during the particle correction stage, it was observed that the particle reseeding was not required, which allowed for faster runtime performance of the fast particle level set method without compromising interface position accuracy. [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]

Biogeography-based optimization (BBO) is a swarm intelligence optimization algorithm based on migration and mutation operations, which is usually used to solve the complex optimization problems. However, it is also a challenging task for conventional BBO to solve some complex and diversified optimization problems with a perfect balance between the performance of exploration and exploitation. In this paper, we propose a variant of BBO approach called BBO with improved migration and adaptive mutation (BBOIMAM) to improve the performance of conventional BBO for dealing with different optimization problems. First, BBOIMAM introduces an improved migration strategy which includes the generalized sinusoidal migration model and immigration strategy based on elite-learning mechanism for the improvement of the local search ability. Second, we propose an adaptive mutation strategy based on the spring vibration to further enhance the population diversity, so that improving the global search ability of the algorithm. By the combination of the proposed improved migration and adaptive mutation strategies, the exploration and exploitation performance of the algorithm can be balanced. We make a large number of experiments on a set of various kinds of benchmark functions, and the experimental results demonstrate that the proposed BBOIMAM approach achieves better performance than several state-of-the-art peer algorithms on CEC 2017 and CEC 2020 test function sets and three cases of the antenna array beam pattern optimization problems. • A BBO with improved migration and adaptive mutation (BBOIMAM) is proposed. • An improved migration strategy based on the sinusoidal and elite-learning is proposed. • An adaptive mutation strategy based on spring vibration is proposed. • BBOIMAM has the overall best performance on test functions and real applications. [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]

Particle swarm optimization (PSO) is a popular method widely used in solving different optimization problems. Unfortunately, in the case of complex multidimensional problems, PSO encounters some troubles associated with the excessive loss of population diversity and exploration ability. This leads to a deterioration in the effectiveness of the method and premature convergence. In order to prevent these inconveniences, in this paper, a learning competitive swarm optimization algorithm (LCSO) based on the particle swarm optimization method and the competition mechanism is proposed. In the first phase of LCSO, the swarm is divided into sub-swarms, each of which can work in parallel. In each sub-swarm, particles participate in the tournament. The participants of the tournament update their knowledge by learning from their competitors. In the second phase, information is exchanged between sub-swarms. The new algorithm was examined on a set of test functions. To evaluate the effectiveness of the proposed LCSO, the test results were compared with those achieved through the competitive swarm optimizer (CSO), comprehensive particle swarm optimizer (CLPSO), PSO, fully informed particle swarm (FIPS), covariance matrix adaptation evolution strategy (CMA-ES) and heterogeneous comprehensive learning particle swarm optimization (HCLPSO). The experimental results indicate that the proposed approach enhances the entropy of the particle swarm and improves the search process. Moreover, the LCSO algorithm is statistically and significantly more efficient than the other tested methods. [ABSTRACT FROM AUTHOR]

The article offers information on the scientific contributions of András Prékopa in various areas of mathematics. It states that in the area of stochastic set functions, he was able to proved the Radon-Nikodym theorems, Poisson type, and complete an additive random set of function. It says that in area of logconcavity, he was able to proved that probability distribution in optimum value is normal.

In this paper, we consider Levitin-Polyak well-posedness of parametric generalized equilibrium problems and optimization problems with generalized equilibrium constraints. Some criteria for these types of well-posedness are derived. In particular, under certain conditions, we show that generalized Levitin-Polyak well-posedness of a parametric generalized equilibrium problem is equivalent to the nonemptiness and compactness of its solution set. Finally, for an optimization problem with generalized equilibrium constraints, we also obtain that, under certain conditions, Levitin-Polyak well-posedness in the generalized sense is equivalent to the nonemptiness and compactness of its solution set. [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]

A level set-based topological shape optimization method considering design-dependent convection boundaries is developed for steady-state heat conduction problems. We embed the level set function obtained from a Hamilton-Jacobi type of equation into a fixed initial domain to implicitly represent thermal boundaries. The effects of the implicit convection boundary obtained from topological shape variations are represented by numerical Dirac delta and Heaviside functions. The method minimizes the thermal compliance of systems by varying the implicit boundary, satisfying the constraint of allowable material volume. During design optimization, the boundary velocity to integrate the Hamilton-Jacobi equation is derived from an optimality condition. [ABSTRACT FROM AUTHOR]

The probability of the basic HHO algorithm in choosing different search methods is symmetric: about 0.5 in the interval from 0 to 1. The optimal solution from the previous iteration of the algorithm affects the current solution, the search for prey in a linear way led to a single search result, and the overall number of updates of the optimal position was low. These factors limit Harris Hawks optimization algorithm. For example, an ease of falling into a local optimum and the efficiency of convergence is low. Inspired by the prey hunting behavior of Harris's hawk, a multi-strategy search Harris Hawks optimization algorithm is proposed, and the least squares support vector machine (LSSVM) optimized by the proposed algorithm was used to model the reactive power output of the synchronous condenser. Firstly, we select the best Gauss chaotic mapping method from seven commonly used chaotic mapping population initialization methods to improve the accuracy. Secondly, the optimal neighborhood perturbation mechanism is introduced to avoid premature maturity of the algorithm. Simultaneously, the adaptive weight and variable spiral search strategy are designed to simulate the prey hunting behavior of Harris hawk to improve the convergence speed of the improved algorithm and enhance the global search ability of the improved algorithm. A numerical experiment is tested with the classical 23 test functions and the CEC2017 test function set. The results show that the proposed algorithm outperforms the Harris Hawks optimization algorithm and other intelligent optimization algorithms in terms of convergence speed, solution accuracy and robustness, and the model of synchronous condenser reactive power output established by the improved algorithm optimized LSSVM has good accuracy and generalization ability. [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]

In this paper, we obtained results on the properties of Lipschitz, upper and lower semicontinuities of optimal multifunctions and optimal solution-set functions in parametric programming, where the objective and constrain functions are set-valued. [ABSTRACT FROM AUTHOR]

In this paper, we deal with single facility location problems in a general normed space in which the existing facilities are represented by convex sets of points. The criterion to be satisfied by the service facility is the minimization of an increasing, convex function of the distances from the service facility to the closest point of each demand set. We obtain a geometrical characterization of the set of optimal solutions for this problem. Two remarkable cases--the classical Weber problem and the minimax problem with demand sets--are studied as particular instances of our problem. Finally, for the planar polyhedral case, we give an algorithm to find the solution set of the considered problems. [ABSTRACT FROM AUTHOR]

The concept of M-convex functions plays a central role in “discrete convex analysis”, a unified framework of discrete optimization recently developed by Murota and others. This paper gives two new characterizations of M- and M♮-convex functions generalizing Gul and Stacchetti''s results on the equivalence among the single improvement condition, the gross substitutes condition and the no complementarities condition for set functions (utility functions on {0,1} vectors) as well as Fujishige and Yang''s observation on the connection to M-convexity. We also discuss implications of our results in an exchange economy with indivisible goods. [Copyright &y& Elsevier]

In this paper we examine a number of different definitions of strategic stability and the relations among them. In particular, we show that the stability requirement given by Hillas (1990) is weaker than the requirements involved in the various definitions of stability in Mertens' reformulation of stability (Mertens 1989,1991). To this end, we introduce a new definition of stability and show that it is equivalent to (a variant of ) the definition given by Hillas (1990). We also use the equivalence of our new definition with the definition of Hillas to provide correct proofs of some of the results that were originally claimed (and incorrectly 'proved') in Hillas (1990). [ABSTRACT FROM AUTHOR]

In many practical problems, we must optimize a set function, i.e., find a set A for which f(A)→max, where f is a function defined on the class of sets. Such problems appear in design, in image processing, in game theory, etc. Most optimization problems can be solved (or at least simplified) by using the fact that small deviations from an optimal solution can only decrease the value of the objective function; as a result, some derivative must be equal to 0. This approach has been successfully used, e.g., for set functions in which the desired set A is a shape, i.e., a smooth (or piece-wise smooth) surface. In some real-life problems, in particular, in the territorial division problem, the existing methods are not directly applicable. For such problems, we design a new simple differential formalism for optimizing set functions. ©1999 John Wiley & Sons, Inc. [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 multi-commodity minimum disconnecting set in a given network is of considerable interest in military operations. The present known methods of finding the multi-commodity minimum disconnecting set consist of implicit enumeration techniques or techniques which involve the solution of several specially structured linear integer programs known as set-covering problems. In this paper we present an efficient method of finding the multi-commodity minimum disconnecting set by solving a single set-covering problem. Extensions and computational experience are also discussed. [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]

We present a level-set based topology optimization algorithm for design optimization problems involving an arbitrary number of different materials, where the evolution of a design is solely guided by topological derivatives. Our method can be seen as an extension of the algorithm that was introduced in Amstutz and Andrä (2006) for two materials to the case of an arbitrary number M of materials. We represent a design that consists of multiple materials by means of a vector-valued level set function which maps into R M − 1. We divide the space R M − 1 into M sectors, each corresponding to one material, and establish conditions for local optimality of a design based on certain generalized topological derivatives. The optimization algorithm consists in a fixed point iteration striving to reach this optimality condition. Like the two-material version of the algorithm, also our method possesses a nucleation mechanism such that it is not necessary to start with a perforated initial design. We show numerical results obtained by applying the algorithm to an academic example as well as to the compliance minimization in linearized elasticity. • Multi-material topology optimization based on topological derivatives. • Arbitrary number of materials. • Local topological optimality condition for multi-material design. • Application to structural optimization. [ABSTRACT FROM AUTHOR]

DSCTool is a statistical tool for comparing performance of stochastic optimization algorithms on a single benchmark function (i.e. single-problem analysis) or a set of benchmark functions (i.e., multiple-problem analysis). DSCTool implements a recently proposed approach, called Deep Statistical Comparison (DSC), and its variants. DSC ranks optimization algorithms by comparing distributions of obtained solutions for a problem instead of using a simple descriptive statistic such as the mean or the median. The rankings obtained for an individual problem give the relations between the performance of the applied algorithms. To compare optimization algorithms in the multiple-problem scenario, an appropriate statistical test must be applied to the rankings obtained for a set of problems. The main advantage of DSCTool are its REST web services, which means all its functionalities can be accessed from any programming language. In this paper, we present the DSCTool in detail with examples for its usage. • DSCTool - a statistical tool for comparing stochastic optimization algorithms. • REST web services implementation allows access from any programming language. • Identification of statistical and practical significance. • Understanding of exploitation and exploration powers of single-objective algorithms. • Ranking of multi-objective algorithms using an ensemble of quality indicators. [ABSTRACT FROM AUTHOR]

Inspired by the mechanism of generation and restriction among five elements in Chinese traditional culture, we present a novel Multi-Objective Five-Elements Cycle Optimization algorithm (MOFECO). During the optimization process of MOFECO, we use individuals to represent the elements. At each iteration, we first divide the population into several cycles, each of which contains several individuals. Secondly, for every individual in each cycle, we judge whether to update it according to the force exerted on it by other individuals in the cycle. In the case of an update, a local or global update is selected by a dynamically adjustable probability P s ; otherwise, the individual is retained. Next, we perform combined mutation operations on the updated individuals, so that a new population contains both the reserved and updated individuals for the selection operation. Finally, the fast non-dominated sorting method is adopted on the current population to obtain an optimal Pareto solution set. The parameters' comparison of MOFECO is given by an experiment and also the performance of MOFECO is compared with three classic evolutionary algorithms Non-dominated Sorting Genetic Algorithm II (NSGA-II), Multi-Objective Particle Swarm Optimization algorithm (MOPSO), Pareto Envelope-based Selection Algorithm II (PESA-II) and two latest algorithms Knee point-driven Evolutionary Algorithm (KnEA) and Non-dominated Sorting and Local Search (NSLS) on solving test function sets Zitzler et al's Test suite (ZDT), Deb et al's Test suite (DTLZ), Walking Fish Group (WFG) and Many objective Function (MaF). The experimental results indicate that the proposed MOFECO can approach the true Pareto-optimal front with both better diversity and convergence compared to the five other algorithms. [ABSTRACT FROM AUTHOR]