Size optimization of space trusses using Big Bang–Big Crunch algorithm

A Hybrid Big Bang–Big Crunch (HBB–BC) optimization algorithm is employed for optimal design of truss structures. HBB–BC is compared to Big Bang–Big Crunch (BB–BC) method and other optimization methods including Genetic Algorithm, Ant Colony Optimization, Particle Swarm Optimization and Harmony Search. Numerical results demonstrate the efficiency and robustness of the HBB–BC method compared to other heuristic algorithms.     

Quadratic optimization on combinatorial sets in Rn

We consider the optimization of quadratic functions on the set of permutations in Rⁿ. Extremal properties of these functions are studied. Branch-and-bound methods are proposed for the solution of these optimization problems.Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 97–104, July–August, 1991.     

Two-point mid-range approximation enhanced recursive quadratic programming method

This research represents an attempt to combine good convergence properties of recursive quadratic programming methods with the benefits of mid-range approximations, initially developed in the field of structural optimization. In this paper, an optimization method based on Arora and coworkers PLBA (Pshenichny–Lim–Belegundu–Arora) algorithm is proposed in which, during the line search phase, cost and constraint functions are substituted by their two-point approximations using the Generalized Convex Approximation formulae of Chickermane and Gea. The results showed that the proposed optimization method preserves the reliability and accuracy of the recursive quadratic programming method while it might simultaneously reduce the computational effort for some problems. Therefore, the proposed optimization method may be taken as potentially suitable for general design optimization purposes.     

Solution of Euclidean combinatorial optimization problems by the method of construction of a lexicographic equivalence

A method of space partition based on an equivalence relation is considered. Based on a lexicographic exhaustive search for equivalence classes, algorithms are developed for solution of a new class of optimization problems, namely, linear conditional Euclidean problems of lexicographic combinatorial optimization.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 155–125, September–October 2004.     

α-concave functions and measures and their applications

Properties of functions arising in probability optimization problems are studied. Probability distribution functions are shown to have certain concavity properties under natural conditions. A calculus of these functions is constructed.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 77–88, November–December, 1991.     

Discrete approximations and optimal solutions of differential inclusions

The paper considers optimization of differential inclusions and convergence of discrete approximations. Necessary conditions of optimality are derived in terms of normal cones and Mordukhovich derivatives.Translated from Kibernetika, No. 1, pp. 76–79, 98, January–February, 1991.     

A Nonreducible System of Constraints of a Combinatorial Polyhedron in a Linear-Fractional Optimization Problem on Arrangements

A system of linear constraints is investigated. The system describes the domain of feasible solutions of a linear optimization problem to which a linear-fractional optimization problem on arrangements is reduced. A system of nonreducible constraints of a polyhedrom is established for the linear-fractional optimization problem on arrangements.__________Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 107–116, March–April 2005.     

Program reduction allowing for additional specifications

An optimization method for programs with procedures is proposed. The method is based on invariant assertions for program variables, which are viewed as the context of procedure call operators.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 57–67, September–October, 1991.     

Stochastic quasigradient method for optimizing the parameters of dynamic systems

Two-stage stochastic optimization of dynamic system parameters is considered. It is shown that the original optimization problem can be approximated with any degree of accuracy by a finite-dimensional minimax stochastic problem. An Arrow—Hurwicz type stochastic quasigradient algorithm is proposed for solving such problems.Translated from Kibernetika, No. 4, pp. 104–107, 130, July–August, 1990.     

Mixed integer vector optimization: Stability issues

Stability of the vector optimization problem with mixed (integer and continuous) variables is considered. Conditions for stability by vector criterion are derived for the mixed integer problem.Translated from Kibernetika, No. 1, pp. 58–60, 89, January–February, 1991.     

Integrated optimization of the use of information and hardware resources in data processing systems with controllable message size

The paper considers integrated optimization of a single-server semi-Markov queue with input conflicts, controllable message size, and a finite buffer with different types of storage organization. The optimization is based on an additive performance criterion.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 45–53, November–December, 1991.     

Conceptual design of aeroelastic structures by topology optimization

A topology optimization methodology is presented for the conceptual design of aeroelastic structures accounting for the fluid–structure interaction. The geometrical layout of the internal structure, such as the layout of stiffeners in a wing, is optimized by material topology optimization. The topology of the wet surface, that is, the fluid–structure interface, is not varied. The key components of the proposed methodology are a Sequential Augmented Lagrangian method for solving the resulting large-scale parameter optimization problem, a staggered procedure for computing the steady-state solution of the underlying nonlinear aeroelastic analysis problem, and an analytical adjoint method for evaluating the coupled aeroelastic sensitivities. The fluid–structure interaction problem is modeled by a three-field formulation that couples the structural displacements, the flow field, and the motion of the fluid mesh. The structural response is simulated by a three-dimensional finite element method, and the aerodynamic loads are predicted by a three-dimensional finite volume discretization of a nonlinear Euler flow. The proposed methodology is illustrated by the conceptual design of wing structures. The optimization results show the significant influence of the design dependency of the loads on the optimal layout of flexible structures when compared with results that assume a constant aerodynamic load.     

On-line optimization of the Tennessee Eastman challenge problem

On-line, optimal steady state operating conditions were determined for the six modes of operation (with and without disturbances) for the industrial recycle reactor problem proposed by Downs and Vogel (J.J. Downs, E.F. Vogel, A plant-wide industrial process control problem, Computers and Chemical Engineering 17 (1993) 245–255.). The optimization and modeling problem was formulated as a sequential solution of steady state material balances through the process. Optimal operating setpoints were obtained using NPSOL (P.E. Gill et al., User's Guide for NPSOL: A FORTRAN Package for Nonlinear Programming, Technical Report SOL86-2, Stanford University, CA, 1986.) and reactor feed material balances as equality, non-linear constraints. On-line optimization results, without disturbances, compared favorably with the results obtained by Ricker (N.L. Ricker, Optimal steady-state operation of the Tennessee Eastman challenge process, Computers and Chemical Engineering 19 (1995) 949–959.). The optimization objective function tended to be broad and flat around the optimal operating conditions for all six modes of operation. The on-line, steady state, optimization algorithm compared favorably with the more complicated optimization structure designed by Yan (M. Yan, N. L. Ricker, On-line optimization of the Tennessee Eastman challenge process, in: Proceedings of the 1997 American Control Conference.). However, the algorithm presented here required less computational effort and exhibited greater convergence reliability than the work of Yan. On-line optimization was performed every 8 h and required less than 5 min calculation time. Updated model parameters were calculated every minute and filtered using a first order filter with 15 min time constant. Net profit was introduced as a tool to compare economic performance of the plant operating under a knowledgeable operator and operating under an off-line/on-line optimization algorithm for all six modes of operation. For modes 1–3, operating at the setpoints generated by the optimization algorithm provided significant increases in production rate and net profit that amounted to a 16–45% decrease in product operating costs when compared to operation of the plant at the setpoints specified by an operator. By decreasing operating costs and increasing production rate while maintaining a specified G/H ratio, the optimization algorithm increased net profit by 9.3–0.5% for modes 4–6, respectively, when compared to knowledgeable operator optimization of the plant. Also for sustained disturbances, the optimization algorithm decreased the error in the desired G/H ratio and increased process stability when compared to knowledgeable operator optimization of the plant. On-line optimization provided a maximum 1% relative increase in production rate and 1.5% relative increase in net profit compared to off-line optimization for modes 4–6 only when certain sustained, disturbances occurred. The economic justification of on-line optimization over off-line optimization depends upon the type, magnitude, and frequency of the disturbances.     

An approach to automation of optimizing transformations of algorithms and programs

The paper describes the construction principles of the DIAMANT block — an interactive transformation machine. The functional capabilities of the block are demonstrated in application to formal transformation (optimization) of the shuttle sort algorithm as generated in the MUL'TIPROTSESSIST system.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 127–137, September–October, 1991.     

Optimization of parametrized control laws for technical systems with a discrete set of controls and discontinuous trajectories

The paper examines some basic concepts of analysis of control laws of technical systems, based on parametrized control algorithms, discrete intervals, and discontinuous control trajectories. Control optimization and determination of extremal state characteristics are considered.Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 167–169, July–August, 1992.     

Characterization of the convergence of stationary Fokker–Planck learning

The convergence properties of the stationary Fokker–Planck algorithm for the estimation of the asymptotic density of stochastic search processes is studied. Theoretical and empirical arguments for the characterization of convergence of the estimation in the case of separable and nonseparable nonlinear optimization problems are given. Some implications of the convergence of stationary Fokker–Planck learning for the inference of parameters in artificial neural network models are outlined.     

Minorant Methods of Stochastic Global Optimization

Generalizations of the branch and bound method and of the Piyavskii method for solution of stochastic global optimization problems are considered. These methods employ the concept of a tangent minorant of an objective function as a source of global information about the function. Calculus of tangent minorants is developed.__________Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 56–70, March–April 2005.     

Large clustering problems in a fuzzy setting

The clustering of a large discrete set of objects is considered as a combinatorial optimization problem in a fuzzy setting.Translated from Kibernetika, No. 1, pp. 116–121, January–February, 1991.     

Normalized convergence of random variables

The properties of a new type of convergence of sequences of random variables are considered. Normalized convergence occupies an intermediate position between convergence in the mean and convergence in probability. It is relevant for studying the rate of convergence of stochastic iterative optimization algorithms and statistical methods of stochastic programming.Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 84–92, May–June, 1992.     

Recurrent fuzzy network design using hybrid evolutionary learning algorithms

This paper proposes a recurrent fuzzy network design using the hybridization of a multigroup genetic algorithm and particle swarm optimization (R-MGAPSO). The recurrent fuzzy network designed here is the Takagi–Sugeno–Kang (TSK)-type recurrent fuzzy network (TRFN), in which each fuzzy rule comprises spatial and temporal sub-rules. Both the number of fuzzy rules and the parameters in a TRFN are designed simultaneously by R-MGAPSO. In R-MGAPSO, the techniques of variable-length individuals and the local version of particle swarm optimization are incorporated into a genetic algorithm, where individuals with the same length constitute the same group, and there are multigroups in a population. Population evolution consists of three major operations: elite enhancement by particle swarm optimization, sub-rule alignment-based crossover, and mutation. To verify the performance of R-MGAPSO, dynamic plant and a continuous-stirred tank reactor controls are simulated. R-MGAPSO performance is also compared with genetic algorithms in these simulations.