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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: 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: 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: 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]