Software For Nonlinearly Constrained Optimization

Leyffer, Sven; Mahajan, Ashutosh

doi:10.1002/9780470400531.eorms0570

Cited by 15 publications

(11 citation statements)

References 38 publications

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“…These three optimization methods all have MATLAB interfaces, are popular, and have been extensively benchmarked in the optimization community, see e.g. (Benson et al 2002;Leyffer and Mahajan 2010). Moreover, IPOPT and SNOPT have already used for certain topology optimization problems in e.g.…”

Section: Chosen Optimization Methodsmentioning

confidence: 99%

Benchmarking optimization solvers for structural topology optimization

Labanda

Stolpe

2015

Struct Multidisc Optim

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The purpose of this article is to benchmark different optimization solvers when applied to various finite element based structural topology optimization problems. An extensive and representative library of minimum compliance, minimum volume, and mechanism design problem instances for different sizes is developed for this benchmarking. The problems are based on a material interpolation scheme combined with a density filter. Different optimization solvers including Optimality Criteria (OC), the Method of Moving Asymptotes (MMA) and its globally convergent version GCMMA, the interior point solvers in IPOPT and FMINCON, and the sequential quadratic programming method in SNOPT, are benchmarked on the library using performance profiles. Whenever possible the methods are applied to both the nested and the Simultaneous Analysis and Design (SAND) formulations of the problem. The performance profiles conclude that general solvers are as efficient and reliable as classical structural topology optimization solvers. Moreover, the use of the exact Hessians in SAND formulations, generally produce designs with better objective function values. However, with the benchmarked implementations solving SAND formulations consumes more computational time than solving the corresponding nested formulations.

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Section: Chosen Optimization Methodsmentioning

confidence: 99%

Benchmarking optimization solvers for structural topology optimization

Labanda

Stolpe

2015

Struct Multidisc Optim

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“…In the first case, SAC uses the quadratic tracking cost (31) with Q = Diag[ 0, 10, 0, 0 ], P = Diag[ 10, 0, 0, 0 ], and applies R = Diag [ 1,1 ] with T = 0.5 s, γ = −10, and feedback sampling at 100 Hz. 29 In this scenario, SAC is set to minimize error between the trajectory of the ball and a desired state a meter to the right of its starting position and one meter above the ground, x d = ( 1 m, 1 m, 0, 0 ). The 10 s closed-loop tracking results included in Fig.…”

Section: B Control Of a Bouncing Ballmentioning

confidence: 99%

“…Without the jump terms in the adjoint simulation (from reset map Π q,q ), the mode insertion gradient (4) does not 28 The first term ofρ is always 1 and can be stripped to obtain an unappended hybrid adjoint, ρ, which applies to unappended dynamics as in (4) when the incremental cost does not depend on the control (as in (3)). 29 The hybrid examples specify SAC with parameters that cause it to skip the (optional) control search process in Section II-C as it is unnecessary in these cases and complicates analysis. (Fig.…”

Section: B Control Of a Bouncing Ballmentioning

confidence: 99%

Sequential Action Control: Closed-Form Optimal Control for Nonlinear and Nonsmooth Systems

2016

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This paper presents a new model-based algorithm that computes predictive optimal controls on-line and in closed loop for traditionally challenging nonlinear systems. Examples demonstrate the same algorithm controlling hybrid impulsive, underactuated, and constrained systems using only high-level models and trajectory goals. Rather than iteratively optimize finite horizon control sequences to minimize an objective, this paper derives a closed-form expression for individual control actions, i.e., control values that can be applied for short duration, that optimally improve a tracking objective over a long time horizon. Under mild assumptions, actions become linear feedback laws near equilibria that permit stability analysis and performance-based parameter selection. Globally, optimal actions are guaranteed existence and uniqueness. By sequencing these actions on-line, in receding horizon fashion, the proposed controller provides a min-max constrained response to state that avoids the overhead typically required to impose control constraints. Benchmark examples show the approach can avoid local minima and outperform nonlinear optimal controllers and recent, case-specific methods in terms of tracking performance, and at speeds orders of magnitude faster than traditionally achievable.3 are nonlinear in state x : R → R n . Though these methods apply more broadly, we derive controls for the case where (1) is linear with respect to the control, u : R → R m , satisfying control-affine form, f (t, x(t), u(t)) = g(t, x(t)) + h(t, x(t)) u(t) .(2)The time dependence in (1) and (2) will be dropped for brevity. The prediction phase simulates motion resulting from some choice of nominal control, u = u 1 . Thus, the nominal predicted motion corresponds to, u 1 (t)).Although the nominal control may be chosen arbitrarily, all examples here use a null nominal control, u 1 = 0. Hence, in the SLIP example, SAC seeks actions that improve performance relative to doing nothing, i.e., letting the SLIP fall.With l 1 : R n → R and m : R n → R, the cost functional,

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“…A set of techniques non-linear mathematical programming and software are shown in [26,16], focusing on the contrasting strategies of local optimization and global optimization [2]. In the last years, several metaheuristic methods have been 186 r.mora-j.ramírez-e.rincón-a.ponsich-o.herrera-p.lara proposed for approaching CNOP problems e.g: an evolutionary algorithm based on homomorphous mappings proposed in [23], in [18] is put forward an adaptation of particle swarm optimization, a cultural algorithm is proposed in [24] and in [39] is presented the anti-culture population algorithm, among others.…”

Section: Introductionmentioning

confidence: 99%

An optimization algorithm inspired by musical composition in constrained optimization problems

Mora-Gutiérrez

García

Rodríguez

et al. 2013

RMTA

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Many real-world problems can be expressed as an instance of the constrained nonlinear optimization problem (CNOP). This problem has a set of constraints specifies the feasible solution space. In the last years several algorithms have been proposed and developed for tackling CNOP. In this paper, we present a cultural algorithm for constrained optimization, which is an adaptation of “Musical Composition Method” or MCM, which was proposed in [33] by Mora et al. We evaluated and analyzed the performance of MCM on five test cases benchmark of the CNOP. Numerical results were compared to evolutionary algorithm based on homomorphous mapping [23], Artificial Immune System [9] and anti-culture population algorithm [39]. The experimental results demonstrate that MCM significantly improves the global performances of the other tested metaheuristics on same of benchmark functions.

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Software For Nonlinearly Constrained Optimization

Cited by 15 publications

References 38 publications

Benchmarking optimization solvers for structural topology optimization

Benchmarking optimization solvers for structural topology optimization

Sequential Action Control: Closed-Form Optimal Control for Nonlinear and Nonsmooth Systems

An optimization algorithm inspired by musical composition in constrained optimization problems

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