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ENHANCED COLLABORATIVE OPTIMIZATION: A DECOMPOSITIONBASED METHOD FOR MULTIDISCIPLINARY DESIGN
, 2008
"... Astute choices made early in the design process provide the best opportunity for reducing the life cycle cost of a new product. Optimal decisions require reasonably detailed disciplinary analyses, which pose coordination challenges. These types of complex multidisciplinary problems are best addresse ..."
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Astute choices made early in the design process provide the best opportunity for reducing the life cycle cost of a new product. Optimal decisions require reasonably detailed disciplinary analyses, which pose coordination challenges. These types of complex multidisciplinary problems are best addressed through the use of decompositionbased methods, several of which have recently been developed. Two of these methods are collaborative optimization (CO) and analytical target cascading (ATC). CO was conceived in 1994 in response to multidisciplinary design needs in the aerospace industry. Recent progress has led to an updated version, enhanced collaborative optimization (ECO), that is introduced in this paper. ECO addresses many of the computational challenges inherent in CO, yielding significant computational savings and more robust solutions. ATC was formalized in 2000 to address needs in the automotive industry. While ATC was originally developed for objectbased decomposition, it is also applicable to multidisciplinary design problems. In this paper, both methods are applied to a set of test cases. The goal is to introduce the ECO methodology by comparing and contrasting it with ATC, a method familiar within the mechanical engineering design community. Comparison of ECO and ATC is not intended to establish the computational superiority of either method. Rather, these two methods are compared as a means of highlighting several promising approaches to the coordination of distributed design problems.
M.Pedram “Gate sizing with controlled Displacement
 in Proceedings of international symposium on physical design
"... Abstract In this paper, we present an algorithm for gate sizing with controlled displacement to improve the overall circuit timing. We use a pathbased delay model to capture the timing constraints in the circuit. To reduce the problem size and improve the solution convergence, we iteratively ident ..."
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Abstract In this paper, we present an algorithm for gate sizing with controlled displacement to improve the overall circuit timing. We use a pathbased delay model to capture the timing constraints in the circuit. To reduce the problem size and improve the solution convergence, we iteratively identify and optimize the kmost critical paths in the circuit and their neighboring cells. All the operations are formulated and solved as mathematical programming problems by using efficient solution techniques. Experimental results on a set of benchmark circuits demonstrate the effectiveness of our approach compared to the conventional approaches, which separate gate sizing from gate placement. 1
Geometric Programming for Aircraft Design Optimization
 53rd AIAA Structures, Structural Dynamics, and Materials Conference
, 2012
"... We propose formulating conceptualstage aircraft design problems as geometric programs (GPs), which are a specific type of convex optimization problem. Recent advances in convex optimization offer significant advantages over the general nonlinear optimization methods typically used in aircraft desi ..."
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We propose formulating conceptualstage aircraft design problems as geometric programs (GPs), which are a specific type of convex optimization problem. Recent advances in convex optimization offer significant advantages over the general nonlinear optimization methods typically used in aircraft design. Modern GP solvers are extremely fast, even on large problems, require no initial guesses or tuning of solver parameters, and guarantee globally optimal solutions. These benefits come at a price: all objective and constraint functions – the mathematical models that describe aircraft design relations – must be expressed within the restricted functional forms of GP. Perhaps surprisingly, this restricted set of functional forms appears again and again in prevailing physicsbased models for aircraft systems. Moreover, we show that for various models that cannot be manipulated algebraically into the forms required by GP, we can often fit compact GP models which accurately approximate the original models. The speed and reliability of GP solution methods makes them a promising approach for conceptualstage aircraft design problems. Nomenclature A = aspect ratio b = wing span [m] CD = total drag coefficient C f = skin friction coefficient CL = lift coefficient CDp = profile drag coefficient CDA0 = nonwing drag area [m2] D = drag force [N] e = Oswald efficiency factor g = gravitational constant, 9.8m/s2 hfuel = fuel heating value [J/kg] h̄rms = root mean square spar box height Ir = root area moment of inertia [m4] Īcap = area moment of inertia per chord4 k = pressure drag form factor L = lift force [N] L ′ = lift force per unit span [N/m] Mr = root moment [N·m] ṁfuel = fuel mass flow rate [kg/s] M̄r = root moment per chord, Mr/cr Nlift = ultimate load factor p = ≡ 1 + 2λ Pfuel = fuel power, ṁfuelhfuel [W] Pmax = max engine output power [W] q = ≡ 1 + λ R = range [m]
ABSTRACT* FLEXIBLE DATA FUSION ( & FISSION)
"... An approach is described for developing methods for "data fusion": given how events A & B occurring by themselves influence some measure, estimate the influence (on that measure) of A and B occurring together. An example is "combine the effects of evidence on the belie ..."
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An approach is described for developing methods for &quot;data fusion&quot;: given how events A & B occurring by themselves influence some measure, estimate the influence (on that measure) of A and B occurring together. An example is &quot;combine the effects of evidence on the belief (likelihood) of some hypothesis.&quot; This approach also deals with the opposite problem of estimating the effects on a measure of A and B by themselves when only their combined effects are known: data fission. The methods developed will both 1) try to make intuitive estimations at information not given, and 2) not conflict with any information given (unless it is inconsistent). 1.
Robustness of Posynomial Geometric Programming Optima
 Mathematical Programming
, 1999
"... This paper develops a simple bounding procedure for the optimal value of a posynomial geometric programming (GP) problem when some of the coefficients for terms in the problem's objective function are estimated with error. The bound may be computed even before the problem is solved and it is s ..."
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This paper develops a simple bounding procedure for the optimal value of a posynomial geometric programming (GP) problem when some of the coefficients for terms in the problem's objective function are estimated with error. The bound may be computed even before the problem is solved and it is shown analytically that the optimum value is very insensitive to errors in the coefficients; for example, a 20% error could cause the optimum to be wrong by no more than 1.67%. Key Words: Geometric Programming, Posynomials, Sensitivity Analysis *Corresponding Author Address: Department of Industrial Engineering 1048 Benedum Hall University of Pittsburgh Pittsburgh, PA 15261 email: rajgopal@engrng.pitt.edu fax: (412) 6249831 1 Introduction Geometric Programming (GP) is a technique for solving certain classes of algebraic nonlinear optimization problems. Since its original development by Duffin, Peterson and Zener (1967) at the Westinghouse R & D Center, it has been studied extensively and...
Two modified differential evolution algorithms and their applications to engineering design problems
, 2009
"... Abstract. Differential Evolution (DE) is a stochastic, population based search technique, which can be classified as an Evolutionary Algorithm (EA) using the concepts of selection crossover and reproduction to guide the search. It has emerged as a powerful tool for solving optimization problems in t ..."
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Abstract. Differential Evolution (DE) is a stochastic, population based search technique, which can be classified as an Evolutionary Algorithm (EA) using the concepts of selection crossover and reproduction to guide the search. It has emerged as a powerful tool for solving optimization problems in the past few years. However, the convergence rate of DE still does not meet all the requirements, and attempts to speed up differential evolution are considered necessary. In order to improve the performance of DE, We propose two versions of (DE) called Differential Evolution with Parent Centric Crossover (DEPCX) and Differential Evolution with probabilistic Parent Centric Crossover (Pro. DEPCX). The proposed algorithms are validated on a test bed of seven real life, nonlinear engineering design problems and numerical results are compared with original differential evolution (DE). Empirical analysis of the results indicates that the proposed schemes enhance the performance of basic DE in terms of convergence rate without compromising with the quality of solution.
jpvQeecs.berkeley.edu
"... We present a method for designing operational amplifiers using reversed geometric programming, which is an extension of geometric programming that allows both convex and nonconvex constraints. Adding a limited set of nonconvex constraints can improve the accuracy of convex equationbased optimizati ..."
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We present a method for designing operational amplifiers using reversed geometric programming, which is an extension of geometric programming that allows both convex and nonconvex constraints. Adding a limited set of nonconvex constraints can improve the accuracy of convex equationbased optimization, without compromising global optimality. These constraints allow increased accuracy for critical modeling equations, such as the relationship between gm and Ips. To demonstrate the design methodology, a foldedcascode amplifier is designed in a 0.18'pm technology for varying speed requirements and is compared with simnlations and designs obtained from geometric programming. Categories and Subject Descriptors:
= approximate Hessian
"... Modelbased decomposition is a powerful tool for breaking design problems into smaller subproblems, establishing hierarchical structure, and analyzing the interrelations in engineering design problems. However, the theoretical foundation for solving decomposed nonlinear optimization problems require ..."
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Modelbased decomposition is a powerful tool for breaking design problems into smaller subproblems, establishing hierarchical structure, and analyzing the interrelations in engineering design problems. However, the theoretical foundation for solving decomposed nonlinear optimization problems requires further work. We show that the formulation of the coordination problem is critical in quickly identifying the correct active constraints and that solving subproblems independently may hinder the local convergence of algorithms tailored to hierarchical coordination.Yet hierarchical decomposition algorithms can have excellent global convergence properties and can be expected to exhibit superior improvement in the ® rst few iterations when compared to the undecomposed case. Based on these insights, a generic sequentially decomposed programming(SDP) algorithmis outlined. SDP has two phases: far from the solution ( ® rst phase) decomposition is used; close to the solution (second phase) subproblems are not solved separately. The generic SDP is applied to sequential quadratic programming (SQP) to de ® ne an SDP ± SQP implementation. A global convergence proof and a simple example are given.
1Interference Management in Cognitive Radio Systems with Feasibility Detection
"... Abstract—In this paper, we consider a cognitive radio system with N secondary user (SU) pairs sharing spectrum with a pair of primary users (PU). The SU power allocation problem is formulated as a capacity maximisation problem under PU and SU quality of service and SU peak power constraints. We show ..."
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Abstract—In this paper, we consider a cognitive radio system with N secondary user (SU) pairs sharing spectrum with a pair of primary users (PU). The SU power allocation problem is formulated as a capacity maximisation problem under PU and SU quality of service and SU peak power constraints. We show our problem formulation is a geometric program and can be solved with convex optimisation techniques. We examine the effect of PU transmissions in our formulations. Solutions for both lowand high signaltointerferenceandnoise ratio (SINR) scenarios are provided. We show that including the PU capacity in the optimisation problem in some circumstances leads to increased PU performance while not significantly degrading SU capacity. In a practical wireless communications system, accurate channel state information (CSI) is not often available hence we formulate power allocation problems with both perfect and imperfect CSI and analyse the performance loss incurred due to imperfect CSI. Furthermore, we present a novel method of detecting and removing infeasible SU quality of service constraints from the SU power allocation problem that results in considerably improved SU performance. Cumulative distribution functions of capacity for various Rayleigh fading channels are presented. I.