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Abstract: The aim of this short note is to show on a numerical example that one of the two optimization algorithms proposed in [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886] may not lead to the optimal solution in some cases. Besides it will be pointed out that the other algorithm (correct, but unfortunately ineffective for larger problems) proposed in [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886] can be extended to a wider class of non-convex optimization problems. [Copyright &y& Elsevier]

In this paper, the hybrid model of Edge Potential Function (EPF) and Simulated Annealing Pigeon-inspired Optimization (SAPIO) algorithm is proposed to accomplish the target detection task for Unmanned Aerial Vehicles (UAVs) at low altitude. EPF can be calculated from the edge map of the original image and provide a kind of attractive pattern for the given target, which is conventionally exploited by the optimization algorithms. Pigeon-inspired Optimization (PIO) is a novel bio-inspired computation algorithm, which was inspired from the homing characteristics of pigeons. In this paper, the simulated annealing mechanism is adopted in our SAPIO algorithm for maximizing the value of EPF. A series of comparative experiments with standard Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Artificial Bee Colony Optimization (ABC) and PIO algorithms demonstrate the robustness and effectiveness of our SAPIO algorithm. Meanwhile, the proposed approach can guarantee accurate target matching. [ABSTRACT FROM AUTHOR]

Abstract: This paper aims at the automatic design and cost minimization of reinforced concrete vaults used in road construction. This paper presents three heuristic optimization methods: the multi-start global best descent local search (MGB), the meta-simulated annealing (SA) and the meta-threshold acceptance (TA). Penalty functions are used for unfeasible solutions. The structure is defined by 49 discrete design variables and the objective function is the cost of the structure. All methods are applied to a vault of 12.40m of horizontal free span, 3.00m of vertical height of the lateral walls and 1.00m of earth cover. This paper presents two original moves of neighborhood search and an algorithm for the calibration of SA-TA algorithms. The MGB algorithm appears to be more efficient than the SA and the TA algorithms in terms of mean results. However, the SA outperforms MGB and TA in terms of best results. The optimization method indicates savings of about 10% with respect to a traditional design. [Copyright &y& Elsevier]

Abstract: In this paper, we focus on the proposed algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max-prod composition that it has been proposed by Ghodousian and Khorram [A. Ghodousian, E. Khorram, An algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max-prod composition, Appl. Math. Comput. 178 (2006) 502–509]. Firstly, we show that the algorithm may not lead to the optimal solution in some cases. Secondly, we propose a new algorithm for solving the presented model by Ghodousian and Khorram (2006), as mentioned above. In fact, it modifies the presented algorithm in the Ghodousian and Khorram’s paper. Also, this algorithm is extended to the presented model by Khorram and Ghodousian [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886.] with max-av composition. Finally, some numerical examples are given for illustrating the purposes. [Copyright &y& Elsevier]

Linear Discriminant Analysis (LDA) is a standard tool for classification and dimension reduction in many applications. However, the problem of high dimension is still a great challenge for the classical LDA. In this paper we consider the supervised pattern classification in the high dimensional setting, in which the number of features is much larger than the number of observations and present a novel approach to the sparse optimal scoring problem using the zero-norm. The difficulty in treating the zero-norm is overcome by using appropriate continuous approximations such that the resulting problems are solved by alternating schemes based on DC (Difference of Convex functions) programming and DCA (DC Algorithms). The experimental results on both simulated and real datasets show the efficiency of the proposed algorithms compared to the five state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Multi-modal optimization is concerned with locating multiple optima in one single run. Finding multiple solutions to a multi-modal optimization problem is especially useful in engineering, as the best solution may not always be the best realizable due to various practical constraints. To compare the performances of multi-modal optimization algorithms, multi-modal benchmark problems are always required. In this paper, 15 novel scalable multi-modal and real parameter benchmark problems are proposed. Among these 15 problems, 8 are extended simple functions while the rest are composition functions. These functions coordinate rotation and shift operations to create linkage among different dimensions and to place the optima at different locations, respectively. Four typical niching algorithms are used to solve the proposed problems. As shown by the experimental results, the proposed problems are challenging to these four recent algorithms. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) has been proved to be a powerful data representation method, and has shown success in applications such as data representation and document clustering. However, the non-negative constraint alone is not able to capture the underlying properties of the data. In this paper, we present a framework to enforce general subspace constraints into NMF by augmenting the original objective function with two additional terms. One on constraints of the basis, the other on preserving the structural properties of the original data. This framework is general as it can be used to regularize NMF with a wide variety of subspace constraints that can be formulated into a certain form such as PCA, Fisher LDA and LPP. In addition, we present an iterative optimization algorithm to solve the general subspace constrained non-negative matrix factorization (GSC NMF). We show that the resulting subspace has enriched representation power as shown in our experiments. [ABSTRACT FROM AUTHOR]

The bilevel problem is usually much more difficult to solve than the single level problem. If the bilevel problem can be transformed into a single level problem, it will be much easier for one to design effective algorithms. In this paper, a novel penalty function method for semivectorial bilevel programming problem is proposed. First, based on Benson’s method and dual theory of linear programming, the semivectorial bilevel programming problem is transformed into a single level optimization problem by setting the dual gap of the lower level problem to zero; then the transformed problem is further relaxed in order to make the transformed problem solving easier; furthermore, a twice differentiable function called dual gap indicator is designed and a penalty function is constructed by using the dual gap indicator as the penalty term for the relaxed transformed problem. Based on all these, a new penalty function method is proposed, and the solution of the penalty problem can be proved to be the solution of the original problem under mild conditions. Finally, numerical examples are provided to demonstrate the good performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a novel optimization algorithm inspired by the ions motion in nature. In fact, the proposed algorithm mimics the attraction and repulsion of anions and cations to perform optimization. The proposed algorithm is designed in such a way to have the least tuning parameters, low computational complexity, fast convergence, and high local optima avoidance. The performance of this algorithm is benchmarked on 10 standard test functions and compared to four well-known algorithms in the literature. The results demonstrate that the proposed algorithm is able to show very competitive results and has merits in solving challenging optimization problems. [ABSTRACT FROM AUTHOR]

This paper presents a modified version of the water cycle algorithm (WCA). The fundamental concepts and ideas which underlie the WCA are inspired based on the observation of water cycle process and how rivers and streams flow to the sea. New concept of evaporation rate for different rivers and streams is defined so called evaporation rate based WCA (ER-WCA), which offers improvement in search. Furthermore, the evaporation condition is also applied for streams that directly flow to sea based on the new approach. The ER-WCA shows a better balance between exploration and exploitation phases compared to the standard WCA. It is shown that the ER-WCA offers high potential in finding all global optima of multimodal and benchmark functions. The WCA and ER-WCA are tested using several multimodal benchmark functions and the obtained optimization results show that in most cases the ER-WCA converges to the global solution faster and offers more accurate results than the WCA and other considered optimizers. Based on the performance of ER-WCA on a number of well-known benchmark functions, the efficiency of the proposed method with respect to the number of function evaluations (computational effort) and accuracy of function value are represented. [ABSTRACT FROM AUTHOR]

The fuzzy 2-partition entropy approach has been widely used to select threshold value for image segmenting. This approach used two parameterized fuzzy membership functions to form a fuzzy 2-partition of the image. The optimal threshold is selected by searching an optimal combination of parameters of the membership functions such that the entropy of fuzzy 2-partition is maximized. In this paper, a new fuzzy 2-partition entropy thresholding approach based on the technology of the Big Bang–Big Crunch Optimization (BBBCO) is proposed. The new proposed thresholding approach is called the BBBCO-based fuzzy 2-partition entropy thresholding algorithm. BBBCO is used to search an optimal combination of parameters of the membership functions for maximizing the entropy of fuzzy 2-partition. BBBCO is inspired by the theory of the evolution of the universe; namely the Big Bang and Big Crunch Theory. The proposed algorithm is tested on a number of standard test images. For comparison, three different algorithms included Genetic Algorithm (GA)-based, Biogeography-based Optimization (BBO)-based and recursive approaches are also implemented. From experimental results, it is observed that the performance of the proposed algorithm is more effective than GA-based, BBO-based and recursion-based approaches. [ABSTRACT FROM AUTHOR]

In this paper, we study the optimal solution of minimizing a linear objective function subject to the fuzzy relation inequalities with addition–min composition. We first discuss some properties about the minimal solutions of fuzzy relation inequalities with addition–min composition, and define the pseudo-minimal indexes of this system. Next we give an algorithm to get the set of the pseudo-minimal indexes, which is called PMI algorithm. Finally, we obtain an algorithm for this optimization system by utilizing these concepts and results. The example is provided to show that our algorithm is simple and convenient. [ABSTRACT FROM AUTHOR]

Abstract: Recently, Gandomi and Alavi proposed a meta-heuristic optimization algorithm, called Krill Herd (KH), for global optimization [Gandomi AH, Alavi AH. Krill Herd: A New Bio-Inspired Optimization Algorithm. Communications in Nonlinear Science and Numerical Simulation, 17(12), 4831–4845, 2012.]. This paper represents an optimization method to global optimization using a novel variant of KH. This method is called the Stud Krill Herd (SKH). Similar to genetic reproduction mechanisms added to KH method, an updated genetic reproduction schemes, called stud selection and crossover (SSC) operator, is introduced into the KH during the krill updating process dealing with numerical optimization problems. The introduced SSC operator is originated from original Stud genetic algorithm. In SSC operator, the best krill, the Stud, provides its optimal information for all the other individuals in the population using general genetic operators instead of stochastic selection. This approach appears to be well capable of solving various functions. Several problems are used to test the SKH method. In addition, the influence of the different crossover types on convergence and performance is carefully studied. Experimental results indicate an instructive addition to the portfolio of swarm intelligence techniques. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate a discriminative visual dictionary learning method for boosting the classification performance. Tied to the K-means clustering philosophy, those popular algorithms for visual dictionary learning cannot guarantee the well-separation of the normalized visual word frequency vectors from distinctive classes or large label distances. The rationale of this work is to harness sample label information for learning visual dictionary in a supervised manner, and this target is then formulated as an objective function, where each sample element, e.g., SIFT descriptor, is expected to be close to its assigned visual word, and at the same time the normalized aggregative visual word frequency vectors are expected to possess the property that kindred samples shall be close to each other while inhomogeneous samples shall be far away. By relaxing the hard binary constraints to soft nonnegative ones, a multiplicative nonnegative update procedure is proposed to optimize the objective function along with theoretic convergence proof. Extensive experiments on classification tasks (i.e., natural scene and sports event classifications) all demonstrate the superiority of this proposed framework over conventional clustering based visual dictionary learning. [Copyright &y& Elsevier]

Abstract: This paper presents a fast simulated annealing framework for combining multiple clusterings based on agreement measures between partitions, which are originally used to evaluate a clustering algorithm. Although we can follow a greedy strategy to optimize these measures as the objective functions of clustering ensemble, it may suffer from local convergence and simultaneously incur too large computational cost. To avoid local optima, we consider a simulated annealing optimization scheme that operates through single label changes. Moreover, for the measures between partitions based on the relationship (joined or separated) of pairs of objects, we can update them incrementally for each label change, which ensures that our optimization scheme is computationally feasible. The experimental evaluations demonstrate that the proposed framework can achieve promising results. [Copyright &y& Elsevier]

Abstract: In this paper, the strictly convex quadratic program (QP) arising in model predictive control (MPC) for constrained linear systems is reformulated as a system of piecewise affine equations. A regularized piecewise smooth Newton method with exact line search on a convex, differentiable, piecewise-quadratic merit function is proposed for the solution of the reformulated problem. The algorithm has considerable merits when applied to MPC over standard active set or interior point algorithms. Its performance is tested and compared against state-of-the-art QP solvers on a series of benchmark problems. The proposed algorithm is orders of magnitudes faster, especially for large-scale problems and long horizons. For example, for the challenging crude distillation unit model of with 252 states, 32 inputs, and 90 outputs, the average running time of the proposed approach is 1.57 ms. [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: We consider a class of global optimization problems, in which the objective function is Lebesgue integrable. In this paper, we present a sufficient and necessary condition for computing the essential infimum. This optimality condition can be used to design algorithms for solving the global optimization problem. [Copyright &y& Elsevier]

Abstract: In this paper, a new filled function which has better properties is proposed for identifying a global minimum point for a general class of nonlinear programming problems within a closed bounded domain. An algorithm for unconstrained global optimization is developed from the new filled function. Theoretical and numerical properties of the proposed filled function are investigated. The implementation of the algorithm on seven test problems is reported with satisfactory numerical results. [Copyright &y& Elsevier]

Abstract: In this paper, a numerical research on the sensitivity of nonmonotone trust region algorithms to their parameters is presented. We compare the numerical efficiency of two classes of nonmonotone trust region (NTR) algorithms in the context of unconstrained optimization. We examine the sensitivity of the algorithms to the parameters related to the nonmonotone technique and the initial trust region radius. We show that the numerical efficiency of nonmonotone trust region algorithms can be improved by choosing appropriate parameters. Based on extensive numerical tests, some efficient ranges of these parameters for nonmonotone trust region algorithms are recommended. [Copyright &y& Elsevier]

1 A dual fitness value chaotic particle swarm optimization algorithm with equality constraints handling is proposed. 2 Equality constraints are solved by parametric equations and inequality constraints are handled by dual fitness evaluation criteria. 3 The chaotic-Cat-mapping-based mutation is implemented to ensure the diversity of particles. 4 Several mathematical test functions are utilized to illustrate the effectiveness of the proposed algorithm. 5 An application in a combined bidding model is implemented. Particle swarm optimization (PSO) is a widely used intelligent optimization algorithm. The premature convergence and the constraint handling, however, remain problems for the global optimization searching. In this paper, a dual fitness value chaotic PSO algorithm with equality constraint handling (EDFC-PSO) is proposed. The particle mutation process based on the chaotic Cat mapping is introduced to increase the diversity of particles. Equality constraints are solved by parametric equations, and inequality constraints are considered using the dual fitness value. The proposed EDFC-PSO algorithm is tested by several test functions and then compared with other algorithms. Further, the performance of the proposed algorithm is validated by a combined bidding model of a power system. Our EDFC-PSO algorithm has equality constraints satisfied and enhances the global searching capability in both the test functions and the engineering model. [Display omitted]. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we modify the concept of cut-peak function given in Wang et al. [Y. Wang, W. Fang, T. Wu, A deterministic algorithm of global optimization using cut-peak functions, Technique Report, in: The Conference of Mathematical Programming of China, 2006], and then propose a revised cut-peak function algorithm for solving box constrained continuous optimization problems. The smoothing technique is used to overcome the difficulty arising from the non-smoothness of the constructed function. By using the exterior penalty function method we find iteratively a better minimizer from the current local minimizer till a global minimizer of the concerned problem is found. Some preliminary numerical results are reported. [Copyright &y& Elsevier]

Abstract: This paper presents an affine scaling reduced preconditional conjugate gradient path approach in association with nonmonotonic interior backtracking line search technique for the linear constrained optimization. Employing the affine scaling preconditional conjugate gradient to form the curvilinear path and using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The nonmonotone criterion is used to speed up the convergence progress in the contours of objective function with large curvature. Theoretical analysis are given which prove that the proposed algorithm is globally convergent and has a local superlinear convergence rate under some reasonable conditions. [Copyright &y& Elsevier]

Abstract: Fuzzy sets as the feasible region for optimization problems is an interesting and on-going research topic [S.C. Fang, G. Li, Solving fuzzy relations equations with a linear objective function, Fuzzy Sets Syst. 103 (1999) 107–113 [7]; J. Lu, S.C. Fang, Solving nonlinear optimization problems with fuzzy relation constraints, Fuzzy Sets Syst. 119 (2001) 1–20 [16]; E. Khorram, A. Ghodpusian, Linear objective function optimization with fuzzy relation constraints regarding max-av composition, Appl. Math. Comput., in press, doi:10.1016/j.amc.2005.04.021]. In this paper, we focus on these kind problems in which the solutions region is the fuzzy relation equation with max-prod composition and the objective function is linear. Whereas, one of the major difficulties in such problems is non-convexity of the feasible region, it is preferable to study these regions in the first step. Hence, we have primarily investigated two methods and their relationship and then we have determined the feasible region via them. After determining the feasible set, we have given an algorithm to optimize the linear objective function on such these regions. Finally, we have presented two examples to illustrate the methods and algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, MPEC problems with linear complementarity constraints are considered. By means of Fischer–Burmeister function, the linear complementarity condition is transformed into a nonsmooth equation. Then, during the iteration, a corresponding smooth system approximates the nonsmooth equation. The smooth optimization is solved by SQP algorithm for standard constrained optimization. Global convergence and superlinear convergence rate are established under some suitable assumptions. Moreover, we conclude that the current iterate point is an exact stationary point of the MPEC problem when the proposed algorithm stops in finite iteration. [Copyright &y& Elsevier]

Abstract: Line search method is sometimes a useful and efficient technique for solving unconstrained optimization problems, especially for solving small and middle scale problems. However, A line search procedure is necessary at each iteration, leading to a significant amount of computation. In order to reduce the evaluations of objective functions and gradients, the line search procedure should be avoided in algorithm design. In this paper we propose a new descent method without line search for unconstrained optimization problems. The algorithm is required to estimate some parameters at each iteration. We analyze theoretically the global convergence of the new algorithm under mild conditions. These theoretical conclusions can help us in designing new efficient methods for optimization problems. [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]

• An improved Jaya algorithm (IJaya) using randomly initiated bounds based grid-oriented weight parameters is developed. • The introduced weight parameter acts as a varying coefficient for the whole population updation equation for Jaya algorithm (JA). • The proposed weight parameter helps to maintain diversity among the population, thus overall improves the exploration and exploitation capabilities of JA. • The proposed IJaya mitigates the complexity of parameter tuning as there is no need to set specific limits for the parameter bounds. • The proposed IJaya outperforms other JA variants and is very competitive with other metaheuristic algorithms. Jaya algorithm (JA) is a single-step metaheuristic optimization technique that is free from algorithm-specific parameters. Regardless of its simplicity, JA proved its effective performance against the variety of optimization algorithms (Du et al., 2018). However, like other swarm-based optimization techniques, the JA also suffers from the inadequacies of slow or premature convergence (Farah and Belazi, 2018). In this study, an improved variant of JA (IJaya) is proposed whose functioning depends on the randomly initiated bounds based grid-oriented weight parameters. Initially, aiming to balance the global exploration and local exploitation capabilities of JA, a dynamic weight parameter is introduced as a varying coefficient for the entire solution updating expression of JA. Then, to maintain the population diversity and to mitigate the complexity of parameter tuning, the introduced weight parameter is dealt with the randomly selected parameter bounds based grid-search mechanism. The proposed IJaya algorithm is benchmarked on well-known 15 unconstrained mathematical test functions, and its performance is analyzed against the standard JA, one modified variant of JA, some well-known state-of-the-art, and few newly introduced optimization algorithms. Furthermore, the non-parametric Friedman and Quade rank tests are also conducted which confirmed the superiority of proposed IJaya both in convergence rate and solution quality. The paper also presents the results obtained by IJaya in two classical structural design problems (a cantilever beam and a 3-bar truss) and a real-world electrical power engineering problem. Numerical results clearly prove the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]