Method Of Feasible Directions Research Articles

Packing congruent hyperspheres into a hypersphere

The paper considers a problem of packing the maximal number of congruent nD hyperspheres of given radius into a larger nD hypersphere of given radius where n = 2, 3, . . . , 24. Solving the problem is reduced to solving a sequence of packing subproblems provided that radii of hyperspheres are variable. Mathematical models of the subproblems are constructed. Characteristics of the mathematical models are investigated. On the ground of the characteristics we offer a solution approach. For n ? 3 starting points are generated either in accordance with the lattice packing of circles and spheres or in a random way. For n > 3 starting points are generated in a random way. A procedure of perturbation of lattice packings is applied to improve convergence. We use the Zoutendijk feasible direction method to search for local maxima of the subproblems. To compute an approximation to a global maximum of the problem we realize a non-exhaustive search of local maxima. Our results are compared with the benchmark results for n = 2. A number of numerical results for 2 ? n ? 24 are given.

A New Rank-two Semidefinite Programming Relaxation Method for Multiuser Detection Problem

Based on the semidefinite programming relaxation model of the code division multiple access maximum likelihood multiuser detection problem, a detection strategy by the rank-two method is presented. The proposed method restricts the matrix variable in the semidefinite programming relaxation to be rank-two, and yields a quadratic objective function with simple quadratic constraints. A feasible direction method is used to solve the nonlinear programming. Coupled with randomized method, a suboptimal solution is obtained for the multiuser detection problem. Simulation results show that the bit error rate performances of a detection strategy based on the new rank-two method are almost similar to that of the detection strategy based on the semidefinite programming relaxation. Furthermore, average CPU time of the new rank-two method is at least 10 times lower than that of the semidefinite programming relaxation method, With the increasing of the users number, the average CPU time increasing rate of the new rank-two method is lower than that of the semidefinite programming relaxation method, especially for the large-scale detection problems. This approach provides good approximations to the optimal maximum likelihood performance.

Blindman-Walking Optimization Method

Optimization methods are all implemented with the hypothesis of unknowing the mathematic express of objective objection. Using the human analogy innovative method, the one-dimension blind-walking optimal method is proposed in this paper. The theory and the algorithm of this method includes halving, doubling, reversing probing step and verifying the applicability condition. Double-step is available to make current point moving to the extremum point. Half-step is available to accelerate convergence. In order to improve the optimization, the applicability condition decides whether update current point or not. The operation process, algorithmic flow chart and characteristic analysis of the method were given. Two optimization problems with unimodal or multimodal objective function were solved by the proposed method respectively. The simulation result shows that the proposed method is better than the ordinary method. The proposed method has the merit of rapid convergence, little calculation capacity, wide applicable range, etc. Taking the method as innovative kernel, the random research method, feasible direction method and complex shape method were improved. Taking the innovative content of this paper as innovative kernel, a monograph was published. The other innovations of the monograph are listed, such as applied algorithm of Karush-Kuhn-Tucker (KKT) qualifications on judging the restriction extremum point, the design step of computing software, the complementarity and derivation of Powell criterion, the method of keeping the complex shape not to deduce dimension and the analysis of gradual optimization characteristic, the reinforced wall of inner point punish function method, the analysis of problem with constrained monstrosity extremum point, the improvement of Newton method and the validation of optimization idea of blind walking repeatedly, the explanation of later-day optimization method, the conformity of seeking algorithm needing the objective function derivation, etc.

System Optimal Design Based on Neighborhood Cultivation Genetic Algorithm Combined with Modified Method of Feasible Directions

Parametric model of floating raft vibration isolation and shock resistance system was built. Optimization techniques of exploitation combined with exploration was brought forward with NCGA used in global and MMFD used in local optimization. Multi-objective optimization design frame was set up in the paper and the Pareto optimal sets were given. At last the method of deducing design variables from Pareto sets was brought forward.

Study on Q-RAM and Feasible Directions Based Methods for Resource Management in Phased Array Radar Systems

Our recent progress and results on optimal real-time resource allocation in phased array radar systems are reported. A previously proposed discrete resource allocation approach, the Quality of Service based Resource Allocation Model (Q-RAM), is analyzed and is observed to generate nonoptimal results. We identify the shortcomings of this method and first extend it using the Karush-Kuhn-Tucker (KKT) optimality conditions for the single resource type case. We obtain an algorithm that delivers a globally optimal solution. We later generalize this further for the multiple resource type case. The Q-RAM approach has its origins in the quality-of-service domain and is fundamentally limited to sampled cost functions. The availability of empirically obtained samples of convex tracking performance curves for phased array radar and the feasibility of continuous approximations to these samples lead our study to the consideration of well formulated alternative methods from the optimization literature belonging to the class of methods of feasible directions. In particular we successfully apply the gradient-projection algorithm for the more general multiple resource type case. Our experimental studies using simulated radar performance data (formulated as a calibration data set) show that superior performance can be obtained in achieving closeness to optimality, while also maintaining similar algorithm execution speeds. Performance can even be increased further if additional computational complexity can be tolerated. In particular improvements in closeness to optimality become significant for dense target scenarios with large number of targets.

열 변형과 목적형상을 고려한 선체구조의 형상 최적설계

In this paper, we develop a shape design optimization method for thermo-elasto- plasticity problems that is applicable to the welding or thermal deformation problems of ship structures. Shell elements and a programming language APDL in a commercial finite element analysis code, ANSYS, are employed in the shape optimiz ation. The point of developed method is to determine the design parameters such that the deformed shape after welding fits very well to a desired design. The geometric parameters of surfaces are selected as the design parameters. The modified method of feasible direction (MMFD) and finite difference sensitivity are used for the optimization alg orithm. Two numerical examples demonstrate that the developed shape design method is applicable to existing hull structures and effective for the structural design of ships. ※Keywords: Thermo-elastic-plastic analysis (열탄소성 해석), Welding deformation (용접 변형), Shape design optimization (형상 최적설계), Finite difference sensitiv ity (유한차분 민감도), Method of feasible direction (유용 방향법)

10.1007/s11470-008-2007-1

The convergence of the method of feasible directions is proved for the case of the smooth objective function and a constraint in the form of the difference of convex sets (the so-called preconvex set). It is shown that the method converges to the set of stationary points, which generally is narrower than the corresponding set in the case of a smooth function and smooth constraints. The scheme of the proof is similar to that proposed earlier by Karmanov.

Optimization Procedure for Improvement of Thermal Interruption Capability of Tandem-puffer Interrupting Chamber -90% SLF Interruption for the Rating of 63kA-50Hz-

63kA-50Hz 90% short line fault (L90) is severer than 50kA-60Hz L90 from the points of view of electric endurance and interruption window. Interruption criteria and an optimization method of the chamber design are discussed to improve thermal interruption capability with it. The combination of the SA (Simulated Annealing) and MMFD (Modified Method of Feasible Directions) is applied to the optimization procedure. The optimized chambers with superior electric reliability are designed at 63kA-50Hz to improve gas density at current zero in thermal volume. 63kA-50Hz L90 interruptions are performed with the new chamber. In addition, influence of gas blast angle of nozzle on L90 interruption is clarified.

Packing identical spheres into a cylinder

AbstractThe paper deals with the optimization problem of packing identical spheres into a cylinder of minimal height. A mathematical model of the problem is constructed and its characteristics are considered. On the ground of characteristics, a strategy of searching for an approximation to a global minimum is offered. The strategy includes a special search tree construction, a modification of the Zoutendijk method of feasible directions to calculate local minima, and a modification of the decremental neighborhood method to search for an approximation to a global minimum. Numerical examples and performance analysis of solutions are given. On the basis of the mathematical model and numerical experiment, a number of conclusions are drawn.

Minimum power requirement for a propeller-driven aircraft and optimum cycle parameters of turboprop engines

This article presents a methodology to design for optimal performance of turboprop engines matching the power requirements for propeller-driven aircrafts. First, the flight performance analyses were used to assess the relatively significant constraints, and then identify the feasible design space and the ideal design point by adopting KSOPT optimizing technique. Second, a multi-objective deterministic algorithm modified method of feasible direction was used for the Pareto approach optimization of the propulsion cycle for three configurations of turboprops. In this optimization problem the maximum specific power and the minimum power specific fuel consumption are the principal figures of merit. The obtained results were based on a created model from the published data of a particular aircraft. This methodology used in the preliminary design phase has shown its effectiveness in rapidly searching for the ideal match point and identifying a candidate turboprop engine, as well as in the development of a derivative engine.

Origin-Based Partial Linearization Method for the Stochastic User Equilibrium Traffic Assignment Problem

This paper proposes a modified origin-based partial linearization method for solving the logit-based stochastic user equilibrium traffic assignment problem formulated by a strictly convex minimization model in terms of origin-based link flows. As a feasible descent direction method, it first generates a feasible descent direction in terms of the origin-based link flows by Bell's second logit-based stochastic network loading algorithm without path enumeration, and it proceeds to improve the descent direction according to the Fukushima's strategy and the PARTAN technique which haven been successfully applied to accelerate convergence of the link-based Frank-Wolfe method for solving the deterministic user equilibrium traffic assignment problem. To tackle the numerical overflow or underflow issue of the exponential function calculation arising in the computerized logit-based stochastic network loading algorithms, this paper develops a scientific notation based engineering approach for large-scale problems. Two numerical examples are carried out to compare the proposed solution method with the conventional origin-based partial linearization method and the method of successive averages in computational time and accuracy of solution. DOI: 10.1061/ASCE0733-947X2010136:152 CE Database subject headings: Traffic assignment; Mathematical models; Algorithms; Equilibrium. Author keywords: Traffic assignment; Mathematical models; Algorithms.

Distributed Optimization for Model Predictive Control of Linear-Dynamic Networks

A linear-dynamic network consists of a directed graph in which the nodes represent subsystems and the arcs model dynamic couplings. The local state of each subsystem evolves according to discrete linear dynamics that depend on the local state, local control signals, and control signals of upstream subsystems. Such networks appear in the model predictive control (MPC) of geographically distributed systems such as urban traffic networks and electric power grids. In this correspondence, we propose a decomposition of the quadratic MPC problem into a set of local subproblems that are solved iteratively by a network of agents. A distributed algorithm based on the method of feasible directions is developed for the agents to iterate toward a solution of the subproblems. The local iterations require relatively low effort to arrive at a solution but at the expense of high communication among neighboring agents and with a slower convergence rate.

Multiobjective optimization of angle-ply laminated plates for maximum buckling load

This paper deals with multiobjective optimization of symmetrically angle-ply square laminated plates subjected to biaxial compressive and uniform thermal loads. The design objective is the maximization of the buckling load for weighted sum of the biaxial compressive and thermal loads. The design variable is the fiber orientations in the layers. The performance index is formulated as the weighted sum of individual objectives in order to obtain optimal solutions of the design problem. The first-order shear deformation theory (FSDT) is used in the mathematical formulation of buckling analysis of laminated plates. The modified feasible direction (MFD) method is used for optimization routine. For this purpose, a program based on FORTRAN is used. Finally, the effect of different weighting factors, number of layers, aspect ratios, load ratios and boundary conditions on the optimal design is investigated.

Acoustic design optimization for vibration of cylinder container coupled with interior acoustic field

Cylinder container is a thin cylindrical shell sealed by a top and bottom plate. The internal noise reduction of the cylinder container is very important for vehicle, ship and other projects. A finite element model of the cylinder container vibration coupled with internal acoustic field is set up and the acoustic response feature is determined. Then, two optimization models are adopted: (1) the acoustic response is taken as the object function and the structure weight is taken as constraints; (2) the structure weight is taken as the object function and the acoustic response is taken as constraints. The design variables are thickness distribution for shell, bottom plate and top plate. The optimization problem is solved by the feasible direction method and a 30 dB reduction of the pressure level is achieved for optimum designs. The results show the effectiveness of the method.

A CONTINUATION APPROACH USING NCP FUNCTION FOR SOLVING MAX-CUT PROBLEM

A continuous approach using NCP function for approximating the solution of the max-cut problem is proposed. The max-cut problem is relaxed into an equivalent nonlinearly constrained continuous optimization problem and a feasible direction method without line searches is presented for generating an optimal solution of the relaxed continuous optimization problem. The convergence of the algorithm is proved. Numerical experiments and comparisons on some max-cut test problems show that we can get the satisfactory solution of max-cut problems with less computation time. Furthermore, this is the first time that the feasible direction method is combined with NCP function for solving max-cut problem, and similar idea can be generalized to other combinatorial optimization problems.

Design of time-limited pulses

An approach for designing time-limited transmit pulses is proposed. In the approach, a time-limited pulse is represented by a weighted sum of cosine functions whose frequencies are integer multiples of one over the time duration of the transmit pulse. The weighting coefficients are derived to minimize the mean square error of received symbols for a given symbol timing offset, while restricting the out-of-band energy to a predefined level. The minimization is numerically performed by using the Zoutendijk's feasible direction method. Performance comparison results are presented showing that the pulses derived by this approach not only have smaller mean square errors, but also smaller symbol error probabilities for BPSK signaling compared to the time-truncated versions of conventional square-root Nyquist pulses.

Gate Sizing by Lagrangian Relaxation Revisited

In this paper, we formulate the generalized convex sizing (GCS) problem that unifies the sizing problems and applies to sequential circuits with clock-skew optimization. We revisit the approach to solve the sizing problem by Lagrangian relaxation, point out several misunderstandings in the previous paper, and extend the approach to handle general convex delay functions in the GCS problems. We identify a class of proper GCS problems whose objective functions in the simplified dual problem are differentiable and transform the simultaneous sizing and clock-skew optimization problem into a proper GCS problem. We design an algorithm based on the method of feasible directions and min-cost network flow to solve proper GCS problems. The algorithm will provide evidences for infeasible GCS problems according to a condition derived by us. Experimental results confirm the efficiency and the effectiveness of our algorithm when the Elmore delay model is used.

Aerodynamic/Structural Optimization of a Training Aircraft Wing

This paper presents a coupled aerodynamic/structural optimization model for a light training, low subsonic aircraft wing. Four optimization strategies have been developed and tested. The first was based on minimization of the total weight of the main wing structure subject to strength, stiffness and aeroelastic constraints. The second strategy considered maximization of the critical flight speed at which divergence occurs, while the third one focused on minimization of the wing drag/lift ratio as a measure of improving aerodynamic efficiency without violating structural weight requirements. The last strategy was based on minimization of the power consumption, which has worked very well and shown balanced improvements in both the aerodynamic and structural efficiencies of the wing under the imposed design constraints. The aerodynamic variables are chosen to be the wing aspect and chord taper ratios, while the structural variables encompassed spar locations, spar flange cross-sectional areas, shear webs and covering skin thicknesses of the main wing box section. The optimization problem has been formulated as a nonlinear mathematical programming problem solved by invoking the MATLab optimization Toolbox routines, which implements the method of feasible directions. Structural, aerodynamic and aeroelastic analyses assumed slender one-dimensional configuration. It makes use of the quasi-steady strip theory in evaluating aerodynamic loads and the classical engineering theories of bending and torsion in calculating stresses and deformations. Results have shown that the approach implemented inthis study can be efficient in producing improved designs in a reasonable computer time. The proposed model has succeeded in arriving at the optimum solutions showing significant improvements in the needed design goals as compared with a baseline wing design.

Optimizing Fiber Direction in Perforated Orthotropic Media to Reduce Stress Concentration

Structures often consist of composite members containing holes or notches. Since stress concentrations associated with such geometric discontinuities can decrease strength, there is desire to minimize stress concentrations. This article demonstrates ability to reduce tensile stress concentrations in perforated composites by synergizing a finite-element program with a feasible-direction method to optimize fiber directions locally, i.e., form a functionally graded material. Optimization is conducted under constraints on the maximum stress in the structure. In addition to reducing the tensile stress concentration beyond that achieved by previous methods, the current approach is compatible with contemporary processing techniques.

Frequency optimization of laminated general quadrilateral and trapezoidal thin plates

This paper deals with frequency optimization of symmetrically laminated angle-ply general quadrilateral and trapezoidal thin plates. The objective function is to maximize the fundamental frequency of the quadrilateral and trapezoidal laminated plates and the fibre orientation is considered as design variable. The mathematical formulation is based on the classical laminated plate theory (CLPT) for the frequency analysis. The modified feasible direction (MFD) method is used as the optimization routine. Therefore, a program based on FORTRAN is used. Finally, the significant effects of aspect ratios, boundary conditions, taper ratios and unsymmetric trapezoidal plates on the optimal results are investigated and the results are compared.