Global Optimum

We consider the problem of minimizing the sum of a convex function and of p=1 fractions subject to convex constraints. The numerators of the fractions are positive convex functions, and the denominators are positive concave functions. Thus, each fraction is quasi-convex. We give a brief discussion of the problem and prove that in spite of its special structure, the problem

In this paper, a global optimum-based search strategy is proposed to alleviate the situation that the differential evolution (DE) usually sticks into a stagnation, especially on complex problems. It aims to reconstruct the balance between exploration and exploitation, and improve the search efficiency and solution quality of DE. The proposed method is activated by recording the number of recently consecutive unsuccessful global optimum updates. It takes the feedback from the global optimum, which makes the search strategy not only refine the current solution quality, but also have a change to find other promising space with better individuals. This search strategy is incorporated with various DE mutation strategies and DE variations. The experimental results indicate that the proposed method has remarkable performance in enhancing search efficiency and improving solution quality.

This paper describes how to tackle new challenging coastal engineering problems related to beach erosion with a shape optimization approach. The method modifies the shape of the sea bottom in order to reduce beach erosion effects. Global optimization is shown to be necessary as the related functionals have several local minima. We describe the physical model used, the proposed protection devices against beach erosion and real case applications. Copyright © 2007 John Wiley & Sons, Ltd.

The aim of this paper is to investigate from the numerical point of view the possibility of coupling the Hamilton-Jacobi-Bellman (HJB) equation and Pontryagin's Minimum Principle (PMP) to solve some control problems. A rough approximation of the value function computed by the HJB method is used to obtain an initial guess for the PMP method. The advantage of our approach over other initialization techniques (such as continuation or direct methods) is to provide an initial guess close to the global minimum. Numerical tests involving multiple minima, discontinuous control, singular arcs and state constraints are considered. The CPU time for the proposed method is less than four minutes up to dimension four, without code parallelization.

The primary objective of this study is to estimate the parameters of a constitutive model characterizing the rheological properties of a ferrous nanoparticle-based magnetorheological fluid. Constant shear rate rheometer measurements were carried out using suspensions of nanometer sized iron particles in hydraulic oil. These measurements provided shear stress vs. shear rate as a function of applied magnetic field. The MR fluid was characterized using both a Bingham-Plastic constitutive model and a Herschel-Bulkley constitutive model. Both these models have two regimes: a rigid pre-yield behavior for shear stress less than a field-dependant yield stress, and viscous behavior for higher shear rates. While the Bingham-Plastic model assumes linear post-yield behavior, the Herschel-Bulkley model uses a power law dependent on the dynamic yield shear stress, a consistency parameter and a flow behavior index. Determination of the model parameters is a complex problem due to the non-linearity of the model and the large amount of scatter in the experimentally observed data. Usual gradient-based numerical methods are not sufficient to determine the characteristic values. In order to estimate the rheological parameters, we have used a genetic algorithm and carried out global optimization. The obtained results provide a good fit to the data and support the choice of the Herschel-Bulkley fluid model.

In this study, an optimization procedure is proposed to minimize thickness (or weight) of laminated composite plates subject to in-plane loading. Fiber orientation angles and layer thickness are chosen as design variables. Direct search simulated annealing (DSA), which is a reliable global search algorithm, is used to search the optimal design. Static failure criteria are used to determine whether load bearing capacity is exceeded for a configuration generated during the optimization process. In order to avoid spurious optimal designs, both the Tsai–Wu and the maximum stress criteria are employed to check static failure. Numerical results are obtained and presented for different loading cases.

ABSTRACT Mutual dependence of articulatory parameters allows the reducing of codebook volume and helps to improve conditions for global optimum search. The initial approximations of articulatory vectors for the inverse problem solving are sampled along the trajectories of articulatory parameters in synthesized syllables. Piece-wise linear mapping of the space of articulatory parameters onto the space of acoustic parameters, the minimal value of cross-sectional area of the vocal tract and the Reynolds number accelerate the process of optimization over 100 times.

Abstract—This paper introduces a novel parameter automation strategy for the particle swarm algorithm and two further extensions to improve its performance after a predefined number of generations. Initially, to efficiently control the local search and convergence to the global optimum solution, time-varying acceleration coefficients (TVAC) are introduced in addition to the time-varying inertia weight factor in particle swarm optimization (PSO). From the basis of TVAC, two new strategies are discussed to improve the performance of the PSO. First, the concept of “mutation ” is introduced to the particle swarm optimization along with TVAC (MPSO-TVAC), by adding a small perturbation to a randomly selected modulus of the velocity vector of a random particle by predefined probability. Second, we introduce a novel particle swarm concept “self-organizing hierarchical particle swarm optimizer with TVAC (HPSO-TVAC). ” Under this method, only the “social ” part and the “cognitive ” part of th...

Based on previously developed Mode Pursuing Sampling (MPS) approach for continuous variables, a variation of MPS for discrete variable global optimization problems on expensive black-box functions is developed in this paper. The proposed method, namely, the discrete variable MPS (D-MPS) method, differs from its continuous variable version not only on sampling in a discrete space, but moreover, on a novel double-sphere strategy. The double-sphere strategy features two hyperspheres whose radii are dynamically enlarged or shrunk in control of, respectively, the degree of “exploration” and “exploitation” in the search of the optimum. Through testing and application to design problems, the proposed D-MPS method demonstrates excellent efficiency and accuracy as compared to the best results in literature on the test problems. The proposed method is believed a promising global optimization strategy for expensive black-box functions with discrete variables. The double-sphere strategy provide...