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Abstract: In this paper, we focus on the proposed algorithms to solve a linear programming problem with the convex combination of the max–min and the max–average composition and the max–star composition, respectively. They have been proposed by Ghodousian and Khorram [A. Ghodousian, E. Khorram, Solving a linear programming problem with the convex combination of the max–min and the max–average fuzzy relation equations, Appl. Math. Comput. 180 (2006) 411–418] and Khorram et al. [E. Khorram, A. Ghodousian, A. Abbasi Molai, Solving linear optimization problems with max–star composition equation constraints, Appl. Math. Comput. 179 (2006) 654–661], respectively. Firstly, we show that the “Tabular method algorithm” in the first paper and the “First procedure” in the second paper may not lead to the optimal solutions of the two models in some cases. Secondly, we generalize the proposed algorithm by Abbasi Molai and Khorram [A. Abbasi Molai, E. Khorram, A modified algorithm for solving the proposed models by Ghodousian and Khorram and Khorram and Ghodousian, Appl. Math. Comput. 190 (2007) 1161–1167] to solve the two models. In fact, it modifies the presented algorithms in the two papers. Finally, some numerical examples are given to illustrate the purposes. [Copyright &y& Elsevier]

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]

Abstract: In this paper, a filled function with one-parameter is proposed for solving unconstrained global optimization problems. This filled function is modified from the previously reported one (see paper [Y.J. Yang, Y.L. Shang, A new filled function method for unconstrained global optimization, Applied Mathematics and Computations 173 (1) (2006) 501–512]). The properties of the filled function are discussed in this paper. An algorithm for unconstrained global optimization is developed from this new filled function. The computational results show that this algorithm is efficient and reliable. [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]

Abstract: This paper presents results of research into the use of the Bellman-Zadeh approach to decision making in a fuzzy environment for solving multiobjective optimization problems. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. The use of the Bellman-Zadeh approach has served as a basis for solving a problem of multiobjective allocation of resources (or their shortages) and developing a corresponding adaptive interactive decision-making system (AIDMS1). Its calculating kernel permits one to solve maxmin problems using an algorithm based on a nonlocal search (modification of the Gelfand''s and Tsetlin''s “long valley” method). The AIDMS1 includes procedures for considering linguistic variables to reflect conditions that are difficult to formalize as well as procedures for constructing and correcting vectors of importance factors for goals. The use of these procedures permits one to realize an adaptive approach to processing information of a decision maker to provide successive improving of the solution quality. C++ windows of the AIDMS1 are presented for input, output, and special possibilities related to considering linguistic variables and constructing and correcting vectors of importance factors. The results of the paper are universally applicable and are already being used to solve power engineering problems. [Copyright &y& Elsevier]

Abstract: In this paper, a new definition of the filled function is given, it is different from the primary definition which was given by Ge in paper [R.P. Ge, A filled function method for finding a global minimzer of a function of several variables, Math. Program. 46 (1990) 191–204]. Based on the definition, a new filled function is proposed, and it has better properties. An algorithm for unconstrained global optimization is developed from the new filled function. The implementation of the algorithm on several test problems is reported with satisfactory numerical results. [Copyright &y& Elsevier]

This paper considers the simultaneous fault detection and control (SFDC) problem. This problem is formulated as a mixed H2/H∞ optimization problem and its solution is presented in terms of two coupled Riccati equations. This solution yields controller/detector systems of modest complexity. An easily implementable design algorithm summarizes the methodology presented in the paper. [Copyright &y& Elsevier]

Abstract: This paper presents an impulsive optimal control model for solving the optimal designing problem of the trajectory of horizontal wells. We take fully into account the effect of unknown disturbances in drilling. The optimal control problem can be converted into a nonlinear parametric optimization by integrating the state equation. We discuss here that the locally optimal solution depends in a continuous way on the parameters (disturbances) and utilize this property to propose a revised Hooke–Jeeves algorithm. The uniform design technique is incorporated into the revised Hooke–Jeeves algorithm to handle the multimodal objective function. The numerical simulation is in accordance with theoretical results. The numerical results illustrate the validity of the model and efficiency of the algorithm. [Copyright &y& Elsevier]

Abstract: Particle swarm optimization (PSO) as an efficient and powerful problem-solving strategy has been widely used, but appropriate adjustment of its parameters usually requires a lot of time and labor. So a co-evolving framework is proposed to improve the robustness of the PSO. In this paper, within this framework the fuzzy rules for the manipulation of the inertia weights are co-evolved with the particles. And the simulation results on a suite of test functions show that the use of this co-evolving framework improves the performance of the PSO, especially the robustness against the dimensional variation of the test functions. [Copyright &y& Elsevier]

Abstract: In this paper, we combine the new global optimization method proposed by Qu et al. [S.J. Qu, K.C. Zhang, Y. Ji, A global optimization algorithm using parametric linearization relaxation, Appl. Math. Comput. 186 (2007) 763–771] with a suitable deleting technique to propose a new accelerating global optimization algorithm for solving the non-convex quadratic optimization problems with non-convex quadratic constraints (NQP). This technique offers a possibility to cut away a large part of the currently investigated region in which the global optimal solution of NQP does not exist, and can be seen as an accelerating device for the global optimization algorithm of the NQP problems. Compared with the method in Qu et al. (2007), numerical results show that the computational efficiency is obviously improved by using this new technique in the number of iterations, the required list length and the overall execution time of the algorithm. [Copyright &y& Elsevier]

Abstract: We consider the classical limit analysis problem of frame structures made up of rigid perfectly plastic members and involving some supports in unilateral frictional contact with the ground. A direct formulation as a mixed complementarity problem (MCP) is used. For the Coulomb case, which forms the focus of this paper, the corresponding MCP may admit multiple upper bound collapse load solutions. In order to identify the least upper bound solution, we propose two algorithms. The first one attempts to enumerate the possible multiple solutions, or at least map the solution space if the solutions are connected. The second scheme tries to find the least upper bound by directly formulating and solving a single nonconvex optimization problem, known in the literature as a mathematical program with equilibrium constraints (MPEC). Two simple examples are provided to illustrate application of these approaches. They also serve to highlight some key features of such structures. [Copyright &y& Elsevier]

Abstract: The method of successive averages is often used in iterative algorithms for solving various mathematical problems, and travel forecasting models in particular. In each iteration of these algorithms the current solution is averaged with an alternative solution generated by the algorithm. If the problem has an equivalent convex optimization formulation with a computable objective function, a line search can be used to determine the weight applied to the alternative solution, referred to as the step size. In the absence of a convex optimization formulation, the typical approach is to set the step size according to a predetermined sequence that is decreasing towards zero, such as 1/k where k is the iteration index. In this paper, we examine the use of a constant step size in the method of successive averages. A theoretical derivation shows that if the alternative solution generated by the algorithm is a linear function of the current solution, then using a constant step size is advantageous and substantially superior to using a sequence of decreasing step sizes. We conjecture that similar results may be expected in nonlinear differentiable problems as well. Numerical results are presented for a travel forecasting model that combines user-equilibrium route choice with an origin-destination-mode (ODM) choice model. The proposed algorithm is based on origin-based assignment, in conjunction with successive averaging of constant step sizes for the differentiable ODM model. The results show that a properly chosen constant step size leads to excellent convergence for both convex and non-convex models. A general strategy for choosing step sizes without a-priori knowledge is presented as well. [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: Consider the problem of computing the smallest enclosing ball of a set of m balls in . This problem arises in many applications such as location analysis, military operations, and pattern recognition, etc. In this paper, we reformulate this problem as an unconstrained convex optimization problem involving the maximum function max{0, t}, and then develop a simple algorithm particularly suitable for problems in high dimensions. This algorithm could efficiently handle problems of dimension n up to 10,000 under a moderately large m, as well as problems of dimension m up to 10,000 under a moderately large n. Numerical results are given to show the efficiency of algorithm. [Copyright &y& Elsevier]

Abstract: Given a set of positive numbers, the max–min partition problem asks for a k-partition such that the minimum part is maximized. The min–ratio partition problem has the similar definition but the objective is to minimize the ratio of the maximum to the minimum parts. In this paper, we analyze the performances of the longest processing time (LPT) algorithm for the two problems. We show that the tight bounds of the LPT are, respectively and . [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]

Let G=(V,E,w) be an undirected graph with positive edge lengths and S⊂V a set of k specified sources. The k-source maximum eccentricity spanning tree is a spanning tree T minimizing the maximum distance from a source to a vertex, i.e., maxs∈S {maxv∈V{dT(s,v)}}, where dT(s,v) is the length of the path between s and v in T. In this paper, we propose an O(|V|2 log |V|+|V| |E|) time algorithm, which improves the previous result on the problem. [Copyright &y& Elsevier]

Abstract: This paper proposes a rank-one modified fitting algorithm. The main feature of the approach is that the update formula for the deflection matrix in an iteration is deduced from a quadratic fitting function, not from the traditional quasi-Newton equation. Under some mild assumptions, the algorithm is globally and linearly convergent. [Copyright &y& Elsevier]