An adaptive population importance sampler

Monte Carlo (MC) methods are widely used in signal processing, machine learning and communications for statistical inference and stochastic optimization. A well-known class of MC methods is composed of importance sampling and its adaptive extensions (e.g., population Monte Carlo). In this work, we introduce an adaptive importance sampler using a population of proposal densities. The novel algorithm provides a global estimation of the variables of interest iteratively, using all the samples generated. The cloud of proposals is adapted by learning from a subset of previously generated samples, in such a way that local features of the target density can be better taken into account compared to single global adaptation procedures. Numerical results show the advantages of the proposed sampling scheme in terms of mean absolute error and robustness to initialization.

Orthogonal MCMC algorithms

Monte Carlo (MC) methods are widely used in signal processing, machine learning and stochastic optimization. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In this work, we introduce a novel parallel interacting MCMC scheme, where the parallel chains share information using another MCMC technique working on the entire population of current states. These parallel ?vertical? chains are led by random-walk proposals, whereas the ?horizontal? MCMC uses a independent proposal, which can be easily adapted by making use of all the generated samples. Numerical results show the advantages of the proposed sampling scheme in terms of mean absolute error, as well as robustness w.r.t. to initial values and parameter choice.

Cross-validated maximum likelihood enhances crystallographic simulated annealing refinement

Recently, the target function for crystallographic refinement has been improved through a maximum likelihood analysis, which makes proper allowance for the effects of data quality, model errors, and incompleteness. The maximum likelihood target reduces the significance of false local minima during the refinement process, but it does not completely eliminate them, necessitating the use of stochastic optimization methods such as simulated annealing for poor initial models. It is shown that the combination of maximum likelihood with cross-validation, which reduces overfitting, and simulated annealing by torsion angle molecular dynamics, which simplifies the conformational search problem, results in a major improvement of the radius of convergence of refinement and the accuracy of the refined structure. Torsion angle molecular dynamics and the maximum likelihood target function interact synergistically, the combination of both methods being significantly more powerful than each method individually. This is demonstrated in realistic test cases at two typical minimum Bragg spacings (dmin = 2.0 and 2.8 Å, respectively), illustrating the broad applicability of the combined method. In an application to the refinement of a new crystal structure, the combined method automatically corrected a mistraced loop in a poor initial model, moving the backbone by 4 Å.

Estratégias de comercialização e investimento, com ênfase em energias renováveis, suportadas por modelos de otimização especializados para avaliação estocástica de risco x retorno.

A comercialização de energia elétrica de fontes renováveis, ordinariamente, constitui-se uma atividade em que as operações são estruturadas sob condições de incerteza, por exemplo, em relação ao preço \"spot\" no mercado de curto prazo e a geração de energia dos empreendimentos. Deriva desse fato a busca dos agentes pela formulação de estratégias e utilização de ferramentais para auxiliá-los em suas tomadas de decisão, visando não somente o retorno financeiro, mas também à mitigação dos riscos envolvidos. Análises de investimentos em fontes renováveis compartilham de desafios similares. Na literatura, o estudo da tomada de decisão considerada ótima sob condições de incerteza se dá por meio da aplicação de técnicas de programação estocástica, que viabiliza a modelagem de problemas com variáveis randômicas e a obtenção de soluções racionais, de interesse para o investidor. Esses modelos permitem a incorporação de métricas de risco, como por exemplo, o Conditional Value-at-Risk, a fim de se obter soluções ótimas que ponderem a expectativa de resultado financeiro e o risco associado da operação, onde a aversão ao risco do agente torna-se um condicionante fundamental. O objetivo principal da Tese - sob a ótica dos agentes geradores, consumidores e comercializadores - é: (i) desenvolver e implementar modelos de otimização em programação linear estocástica com métrica CVaR associada, customizados para cada um desses agentes; e (ii) aplicá-los na análise estratégica de operações como forma de apresentar alternativas factíveis à gestão das atividades desses agentes e contribuir com a proposição de um instrumento conceitualmente robusto e amigável ao usuário, para utilização por parte das empresas. Nesse contexto, como antes frisado, dá-se ênfase na análise do risco financeiro dessas operações por meio da aplicação do CVaR e com base na aversão ao risco do agente. Considera-se as fontes renováveis hídrica e eólica como opções de ativos de geração, de forma a estudar o efeito de complementaridade entre fontes distintas e entre sites distintos da mesma fonte, avaliando-se os rebatimentos nas operações.

Application of the cross-entropy method to the buffer allocation problem in a simulation-based environment

The buffer allocation problem (BAP) is a well-known difficult problem in the design of production lines. We present a stochastic algorithm for solving the BAP, based on the cross-entropy method, a new paradigm for stochastic optimization. The algorithm involves the following iterative steps: (a) the generation of buffer allocations according to a certain random mechanism, followed by (b) the modification of this mechanism on the basis of cross-entropy minimization. Through various numerical experiments we demonstrate the efficiency of the proposed algorithm and show that the method can quickly generate (near-)optimal buffer allocations for fairly large production lines.

A New Algorithm for Monte Carlo for American Options

2000 Mathematics Subject Classification: 91B28, 65C05.

Metodologia de otimização estocástica para coordenação eólico-fotovoltaica

Esta dissertação incide sobre o tema da coordenação entre sistemas eólicos e fotovoltaicos que participam no mercado de eletricidade. A incerteza da potência eólica e fotovoltaica é uma caraterística predominante nesta coordenação, devendo ser considerada no planeamento ótimo de sistemas eólico-fotovoltaicos. A fim de modelizar a incerteza é apresentada uma metodologia de otimização estocástica baseada em programação linear para maximizar o lucro esperado de uma empresa produtora de energia elétrica que participa no mercado diário. A coordenação entre sistemas eólicos e fotovoltaicos visa mitigar os desequilíbrios de energia, resultantes das ofertas horárias submetidas no mercado diário e, consequentemente, reduzir as penalizações financeiras. Os resultados da coordenação entre um sistema eólico e um sistema fotovoltaico são comparados com os resultados obtidos para a operação não coordenada. Estes resultados permitem concluir que a metodologia desenvolvida aplicada à coordenação apresenta um lucro esperado superior ao lucro obtido para a operação não coordenada; Abstract Stochastic Optimization Methodology for Wind-Photovoltaic Coordination This dissertation focuses on the issue of coordination between wind and photovoltaic systems participating in electricity markets. The uncertainty of wind and photovoltaic power is a main characteristic of these systems, which must be included in the optimal scheduling of the coordination of wind with photovoltaic systems. In order to model the uncertainty is presented a stochastic approach based on linear programming to maximize the profit of a wind photovoltaic power producer which participates in electricity markets. The coordination of wind with photovoltaic systems aims to mitigate the energy deviations, as a result of the participation in day-ahead market and therefore reducing economic penalties. The results obtained by the coordination are compared to results obtained by the separated operation of wind and photovoltaic systems. The results allow concluding that the proposed approach applied to the coordination presents an expected profit higher than the expected profit without coordination.

Coordinated Scheduling of Wind-Thermal Gencos in Day-Ahead Markets

This paper presents a stochastic mixed-integer linear programming approach for solving the self-scheduling problem of a price-taker thermal and wind power producer taking part in a pool-based electricity market. Uncertainty on electricity price and wind power is considered through a set of scenarios. Thermal units are modeled by variable costs, start-up costs and technical operating constraints, such as: ramp up/down limits and minimum up/down time limits. An efficient mixed-integer linear program is presented to develop the offering strategies of the coordinated production of thermal and wind energy generation, aiming to maximize the expected profit. A case study with data from the Iberian Electricity Market is presented and results are discussed to show the effectiveness of the proposed approach.

Asset liability modelling and pension schemes: the application of robust optimization to USS

This paper uses a novel numerical optimization technique - robust optimization - that is well suited to solving the asset-liability management (ALM) problem for pension schemes. It requires the estimation of fewer stochastic parameters, reduces estimation risk and adopts a prudent approach to asset allocation. This study is the first to apply it to a real-world pension scheme, and the first ALM model of a pension scheme to maximise the Sharpe ratio. We disaggregate pension liabilities into three components - active members, deferred members and pensioners, and transform the optimal asset allocation into the scheme’s projected contribution rate. The robust optimization model is extended to include liabilities and used to derive optimal investment policies for the Universities Superannuation Scheme (USS), benchmarked against the Sharpe and Tint, Bayes-Stein, and Black-Litterman models as well as the actual USS investment decisions. Over a 144 month out-of-sample period robust optimization is superior to the four benchmarks across 20 performance criteria, and has a remarkably stable asset allocation – essentially fix-mix. These conclusions are supported by six robustness checks.

Efficient robust optimization based on polynomial chaos and tabu search algorithm

The study of robust design methodologies and techniques has become a new topical area in design optimizations in nearly all engineering and applied science disciplines in the last 10 years due to inevitable and unavoidable imprecision or uncertainty which is existed in real word design problems. To develop a fast optimizer for robust designs, a methodology based on polynomial chaos and tabu search algorithm is proposed. In the methodology, the polynomial chaos is employed as a stochastic response surface model of the objective function to efficiently evaluate the robust performance parameter while a mechanism to assign expected fitness only to promising solutions is introduced in tabu search algorithm to minimize the requirement for determining robust metrics of intermediate solutions. The proposed methodology is applied to the robust design of a practical inverse problem with satisfactory results.

Dynamic, convex, and robust optimization with Bayesian learning for response-guided dosing

Thesis (Ph.D.)--University of Washington, 2016-08

Robust scenario formulations for strategic supply chain optimization under uncertainty

Strategic supply chain optimization (SCO) problems are often modelled as a two-stage optimization problem, in which the first-stage variables represent decisions on the development of the supply chain and the second-stage variables represent decisions on the operations of the supply chain. When uncertainty is explicitly considered, the problem becomes an intractable infinite-dimensional optimization problem, which is usually solved approximately via a scenario or a robust approach. This paper proposes a novel synergy of the scenario and robust approaches for strategic SCO under uncertainty. Two formulations are developed, namely, naïve robust scenario formulation and affinely adjustable robust scenario formulation. It is shown that both formulations can be reformulated into tractable deterministic optimization problems if the uncertainty is bounded with the infinity-norm, and the uncertain equality constraints can be reformulated into deterministic constraints without assumption of the uncertainty region. Case studies of a classical farm planning problem and an energy and bioproduct SCO problem demonstrate the advantages of the proposed formulations over the classical scenario formulation. The proposed formulations not only can generate solutions with guaranteed feasibility or indicate infeasibility of a problem, but also can achieve optimal expected economic performance with smaller numbers of scenarios.

Robust integration of real time optimization with linear model predictive control

Here, we study the stable integration of real time optimization (RTO) with model predictive control (MPC) in a three layer structure. The intermediate layer is a quadratic programming whose objective is to compute reachable targets to the MPC layer that lie at the minimum distance to the optimum set points that are produced by the RTO layer. The lower layer is an infinite horizon MPC with guaranteed stability with additional constraints that force the feasibility and convergence of the target calculation layer. It is also considered the case in which there is polytopic uncertainty in the steady state model considered in the target calculation. The dynamic part of the MPC model is also considered unknown but it is assumed to be represented by one of the models of a discrete set of models. The efficiency of the methods presented here is illustrated with the simulation of a low order system. (C) 2010 Elsevier Ltd. All rights reserved.

Robust algorithms for solving stochastic partial differential equations

A robust semi-implicit central partial difference algorithm for the numerical solution of coupled stochastic parabolic partial differential equations (PDEs) is described. This can be used for calculating correlation functions of systems of interacting stochastic fields. Such field equations can arise in the description of Hamiltonian and open systems in the physics of nonlinear processes, and may include multiplicative noise sources. The algorithm can be used for studying the properties of nonlinear quantum or classical field theories. The general approach is outlined and applied to a specific example, namely the quantum statistical fluctuations of ultra-short optical pulses in chi((2)) parametric waveguides. This example uses a non-diagonal coherent state representation, and correctly predicts the sub-shot noise level spectral fluctuations observed in homodyne detection measurements. It is expected that the methods used wilt be applicable for higher-order correlation functions and other physical problems as well. A stochastic differencing technique for reducing sampling errors is also introduced. This involves solving nonlinear stochastic parabolic PDEs in combination with a reference process, which uses the Wigner representation in the example presented here. A computer implementation on MIMD parallel architectures is discussed. (C) 1997 Academic Press.

Online robust optimization framework for QoS guarantees in distributed soft real-time systems

In distributed soft real-time systems, maximizing the aggregate quality-of-service (QoS) is a typical system-wide goal, and addressing the problem through distributed optimization is challenging. Subtasks are subject to unpredictable failures in many practical environments, and this makes the problem much harder. In this paper, we present a robust optimization framework for maximizing the aggregate QoS in the presence of random failures. We introduce the notion of K-failure to bound the effect of random failures on schedulability. Using this notion we define the concept of K-robustness that quantifies the degree of robustness on QoS guarantee in a probabilistic sense. The parameter K helps to tradeoff achievable QoS versus robustness. The proposed robust framework produces optimal solutions through distributed computations on the basis of Lagrangian duality, and we present some implementation techniques. Our simulation results show that the proposed framework can probabilistically guarantee sub-optimal QoS which remains feasible even in the presence of random failures.