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Engineering optimization relies routinely on deterministic computer based design evaluations, typically comprising geometry creation, mesh generation and numerical simulation. Simple optimization routines tend to stall and require...
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Engineering optimization relies routinely on deterministic computer based design evaluations, typically comprising geometry creation, mesh generation and numerical simulation. Simple optimization routines tend to stall and require user intervention if a failure occurs at any of these stages. This motivated us to develop an optimization strategy based on surrogate modelling, which penalizes the likely failure regions of the design space without prior knowledge of their locations. A Gaussian process based design improvement expectation measure guides the search towards the feasible global optimum.
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In the paper, a necessary and sufficient criterion it provided such that any local optimal solution is also global in a not necessarily differentiable constrained optimization problem. This criterion is compared to others earlier
In the paper, a necessary and sufficient criterion it provided such that any local optimal solution is also global in a not necessarily differentiable constrained optimization problem. This criterion is compared to others earlier appeared in the literature, which are sufficient but not necessary for a local optimal solution to be global. The importance of the established criterion is illustrated by suitable examples of nonconvex optimization problems presented in the paper.
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This article introduces a new global optimization procedure called LARES. LARES is based on the concept of an artificial chemical process (ACP), a new paradigm which is described in this article. The algorithm's performance was st...
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This article introduces a new global optimization procedure called LARES. LARES is based on the concept of an artificial chemical process (ACP), a new paradigm which is described in this article. The algorithm's performance was studied using a test bed with a wide spectrum of problems including random multi-modal random problem generators, random LSAT problem generators with various degrees of epistasis, and a test bed of real-valued functions with different degrees of multi-modality, discontinuity and flatness. In all cases studied, LARES performed very well in terms of robustness and efficiency.
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A novel class of hybrid global optimization methods for application to the structure prediction in protein-folding problem is introduced. These optimization methods take the form of a hybrid between a deterministic global optimiza...
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A novel class of hybrid global optimization methods for application to the structure prediction in protein-folding problem is introduced. These optimization methods take the form of a hybrid between a deterministic global optimization algorithm the αBB, and a stochastically based method, conformational space annealing (CSA), and attempt to combine the beneficial features of these two algorithms. The αBB method as previously extant exhibits consistency, as it guarantees convergence to the global minimum for twice-continuously differentiable constrained nonlinear programming problems, but can benefit from improvements in the computational front. Computational studies for met-enkephalin demonstrate the promise for the proposed hybrid global optimization method.
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Multiplicative programming problems with exponent (MPE) have many practical applications in various fields. In this paper, a method for accelerating global optimization is proposed for a class of multiplicative programming problem...
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Multiplicative programming problems with exponent (MPE) have many practical applications in various fields. In this paper, a method for accelerating global optimization is proposed for a class of multiplicative programming problems with exponent under multiplicative constraints using a Suitable deleting technique. This technique offers the possibility of cutting away a large part of the currently investigated region in which the globally optimal solution of the WE does not exist. The deleting technique can accelerate the convergence of the proposed global optimization algorithm. Two numerical examples are given to illustrate the feasibility of the deleting technique. (C) 2008 Elsevier B.V. All rights reserved.
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In this paper, we develop a new theoretical framework by means of the absorbing Markov process theory for analyzing some stochastic globla optimization algorithms. Applying the framework tot he pure random search, we prove that th...
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In this paper, we develop a new theoretical framework by means of the absorbing Markov process theory for analyzing some stochastic globla optimization algorithms. Applying the framework tot he pure random search, we prove that the pure random search converges to the global minimum in probability and its time has geometry distri- bution. We also analyze the pure adaptive search by this framework and turn out that the pure adaptive search con- verges to the global minimum in probability and its time has Poisson distribution.
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In this paper, the improvement of pure random search is studied. By taking some information of the function to be minimized in- to consideration, the authors propose two stochastic global optimization algorithms. Some numerical ex...
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In this paper, the improvement of pure random search is studied. By taking some information of the function to be minimized in- to consideration, the authors propose two stochastic global optimization algorithms. Some numerical experiments for the new stochastic global optimization algorithms are presented for a class of test problems.
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This paper presents a new stochastic algorithm for box--constrained global optimization problem. Bacause the level set of objective function is always not known, the authors designed a region containing the current minimum Point t...
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This paper presents a new stochastic algorithm for box--constrained global optimization problem. Bacause the level set of objective function is always not known, the authors designed a region containing the current minimum Point to replace it, and in order to fit the level set well, this region would be walking and contracting in the running process. Thus, the new algorithm is named as region's walk and con- traction(RWC). Some numerical experiments for the RWC were conducted, which indicate good property of the algorithm.
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We study non-convex optimization problems over simplices. We show that for a large class of objective functions, the convex approximation obtained from the Reformulation-Linearization Technique (RLT) admits optimal solutions that ...
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We study non-convex optimization problems over simplices. We show that for a large class of objective functions, the convex approximation obtained from the Reformulation-Linearization Technique (RLT) admits optimal solutions that exhibit a sparsity pattern. This characteristic of the optimal solutions allows us to conclude that (i) a linear matrix inequality constraint, which is often added to tighten the relaxation, is vacuously satisfied and can thus be omitted, and (ii) the number of decision variables in the RLT relaxation can be reduced from O(n(2)) to O(n). Taken together, both observations allow us to reduce computation times by up to several orders of magnitude. Our results can be specialized to indefinite quadratic optimization problems over simplices and extended to non-convex optimization problems over the Cartesian product of two simplices as well as specific classes of polyhedral and non-convex feasible regions. Our numerical experiments illustrate the promising performance of the proposed framework.
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In this paper we present necessary conditions for global optimality for polynomial problems with box or bivalent constraints using separable polynomial relaxations. We achieve this by first deriving a numerically checkable charact...
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In this paper we present necessary conditions for global optimality for polynomial problems with box or bivalent constraints using separable polynomial relaxations. We achieve this by first deriving a numerically checkable characterization of global optimality for separable polynomial problems with box as well as bivalent constraints. Our necessary optimality conditions can be numerically checked by solving semi-definite programming problems. Then, by employing separable polynomial under-estimators, we establish sufficient conditions for global optimality for classes of polynomial optimization problems with box or bivalent constraints. We construct underestimators using the sum of squares convex (SOS-convex) polynomials of real algebraic geometry. An important feature of SOS-convexity that is generally not shared by the standard convexity is that whether a polynomial is SOS-convex or not can be checked by solving a semidefinite programming problem. We illustrate the versatility of our optimality conditions by simple numerical examples.
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