Modeling and Solution Strategies for Unconstrained Stochastic Optimization Problems

We review some modeling alternatives for handling risk in decision making processes for unconstrained stochastic optimization problems. Solution strategies are discussed and compared

Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control

Constrained optimization of high-dimensional numerical problems plays an important role in many scientific and industrial applications. Function evaluations in many industrial applications are severely limited and no analytical information about objective function and constraint functions is available. For such expensive black-box optimization tasks, the constraint optimization algorithm COBRA was proposed, making use of RBF surrogate modeling for both the objective and the constraint functions. COBRA has shown remarkable success in solving reliably complex benchmark problems in less than 500 function evaluations. Unfortunately, COBRA requires careful adjustment of parameters in order to do so. In this work we present a new self-adjusting algorithm SACOBRA, which is based on COBRA and capable to achieve high-quality results with very few function evaluations and no parameter tuning. It is shown with the help of performance profiles on a set of benchmark problems (G-problems, MOPTA08) that SACOBRA consistently outperforms any COBRA algorithm with fixed parameter setting. We analyze the importance of the several new elements in SACOBRA and find that each element of SACOBRA plays a role to boost up the overall optimization performance. We discuss the reasons behind and get in this way a better understanding of high-quality RBF surrogate modeling

Particle algorithms for optimization on binary spaces

We discuss a unified approach to stochastic optimization of pseudo-Boolean objective functions based on particle methods, including the cross-entropy method and simulated annealing as special cases. We point out the need for auxiliary sampling distributions, that is parametric families on binary spaces, which are able to reproduce complex dependency structures, and illustrate their usefulness in our numerical experiments. We provide numerical evidence that particle-driven optimization algorithms based on parametric families yield superior results on strongly multi-modal optimization problems while local search heuristics outperform them on easier problems

Parallel Deterministic and Stochastic Global Minimization of Functions with Very Many Minima

The optimization of three problems with high dimensionality and many local minima are investigated under five different optimization algorithms: DIRECT, simulated annealing, Spall’s SPSA algorithm, the KNITRO package, and QNSTOP, a new algorithm developed at Indiana University

A hybrid EKF and switching PSO algorithm for joint state and parameter estimation of lateral flow immunoassay models

This is the post-print version of the Article. The official published can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, a hybrid extended Kalman filter (EKF) and switching particle swarm optimization (SPSO) algorithm is proposed for jointly estimating both the parameters and states of the lateral flow immunoassay model through available short time-series measurement. Our proposed method generalizes the well-known EKF algorithm by imposing physical constraints on the system states. Note that the state constraints are encountered very often in practice that give rise to considerable difficulties in system analysis and design. The main purpose of this paper is to handle the dynamic modeling problem with state constraints by combining the extended Kalman filtering and constrained optimization algorithms via the maximization probability method. More specifically, a recently developed SPSO algorithm is used to cope with the constrained optimization problem by converting it into an unconstrained optimization one through adding a penalty term to the objective function. The proposed algorithm is then employed to simultaneously identify the parameters and states of a lateral flow immunoassay model. It is shown that the proposed algorithm gives much improved performance over the traditional EKF method.This work was supported in part by the International Science and Technology Cooperation Project of China under Grant 2009DFA32050, Natural Science Foundation of China under Grants 61104041, International Science and Technology Cooperation Project of Fujian Province of China under Grant 2009I0016

A dynamic programming approach to constrained portfolios

This paper studies constrained portfolio problems that may involve constraints on the probability or the expected size of a shortfall of wealth or consumption. Our first contribution is that we solve the problems by dynamic programming, which is in contrast to the existing literature that applies the martingale method. More precisely, we construct the non-separable value function by formalizing the optimal constrained terminal wealth to be a (conjectured) contingent claim on the optimal non-constrained terminal wealth. This is relevant by itself, but also opens up the opportunity to derive new solutions to constrained problems. As a second contribution, we thus derive new results for non-strict constraints on the shortfall of inter¬mediate wealth and/or consumption