Adjustable robust treatment-length optimization in radiation therapy

Adjustable Robust Multistage Optimization

Format (5.1.1) covers all uncertain optimization problems considered so far; moreover, in these latter problems the objective f and the right hand side F of the constraints always were bi-affine in x, ζ, (that is, affine in x when ζ is fixed, and affine in ζ, x being fixed), and K was a “simple” convex cone (a direct product of nonnegative rays/Lorentz cones/Semidefinite cones, depending on whe...

Adjustable Robust Optimization via Fourier-Motzkin Elimination

We demonstrate how adjustable robust optimization (ARO) problems with fixed recourse can be casted as static robust optimization problems via Fourier-Motzkin elimination (FME). Through the lens of FME, we characterize the structures of the optimal decision rules for a broad class of ARO problems. A scheme based on a blending of classical FME and a simple Linear Programming technique that can ef...

Dynamic programming approach to adjustable robust optimization

In this paper we consider the adjustable robust approach to multistage optimization, for which we derive dynamic programming equations. We also discuss this from a point of view of risk averse stochastic programming. As an example we consider a robust formulation of the classical inventory model and show that, similar to the risk neutral case, a basestock policy is optimal.

Robust optimization with time-dependent uncertainty in radiation therapy

Robust Optimization of Adjustable Control Factors Using Particle Swarm Optimization

Most conventional robust design methods assume design solutions are fixed values. Using these methods, designers set each control factor to a fixed value to maximize the robustness of objective characteristics. However, fluctuations in the objective characteristic often exceed the allowable range in a design problem. Consequently, obtaining sufficient robustness is difficult using conventional ...