On bayes approach to univariate global optimization

In this paper the Bayesian approach to global optimization of univariate continuous functions is developed, when the objective function is modelled by Ornstein-Uhlenbeck process. The parameters of model of function to be optimised are calibrated by maximal likelihood method using the learning set. The resulting optimization algorithm is rather simple and consists of reselection of values of expected step utility function, which maximizes at each step the expected increment of minimal observed value of the objective function. The convergence of method developed is studied by theoretical and experimental way. Efficiency of the Bayes optimization method created is studied by computer simulation, too.

Law of small numbers as concentration inequalities for sums of independent random setsand random set valued mappings

In the paper we study concentration of sample averages (Minkowski's sums) of independent bounded random sets and set valued mappings around their expectations. Sets and mappings are considered in a Hilbert space. Concentration is formulated in the form of exponential bounds on probabilities of normalized large deviations. In a sense, concentration phenomenon reflects the law of small numbers, describing non-asymptotic behavior of the sample averages. We sequentially consider concentration inequalities for bounded random variables, functions, vectors, sets and mappings, deriving next inequalities from preceding cases. Thus we derive concentration inequalities with explicit constants for random sets and mappings from the sharpest available (Talagrand type) inequalities for random functions and vectors. The most explicit inequalities are obtained in case of discrete distributions. The obtained results contribute to substantiation of the Monte Carlo method in infinite dimensional spaces.

Measures of information in multistage stochastic programming

Multistage stochastic programs, which involve sequences of decisions over time, are usually hard to solve in realistically sized problems. Providing bounds for their optimal solution may help in evaluating whether it is worth the additional computations for the stochastic program versus simplified approaches. In this paper we present a summary of the results in [22] where we generalize the value of information gained from deterministic, pair solution and rolling-horizon approximation in the two-stage case to the multistage stochastic formulation. Numerical results on a case study related to a simple transportation problem illustrate the described relationships.

Modelling to generate alternatives in waste management facility expansion planning via simulation-optimization

Public sector decision-making typically involves complex problems that are riddled with competing performance objectives and possess design requirements which are difficult to capture at the time that supporting decision models are constructed. Environmental policy formulation can prove additionally complicated because the various system components often contain considerable stochastic uncertainty and there are frequently numerous stakeholders holding completely incompatible perspectives. Consequently, there are invariably unmodelled performance design issues, not apparent at the time of the problem formulation, which can greatly impact the acceptability of any proposed solutions. While a mathematically optimal solution might provide the best solution to a modelled problem, normally this will not be the best solution to the underlying real problem. Therefore, in public environmental policy formulation, it is generally preferable to be able to create several quantifiably good alternatives that provide very different approaches and perspectives to the problem. This study shows how a computationally efficient simulation optimization approach that combines evolutionary optimization with simulation can be used to generate multiple policy alternatives that satisfy required system criteria and are maximally different in decision space. The efficacy of this modelling-to-generate-alternatives method is demonstrated on a municipal sol- id waste management facility expansion case.

Stochastic progamming in the mid-term operations planning of an oil refinery

Oil refining is a series of processes that aim to separate the crude oil into pre-standardized fractions. The way these processes can be combined result in a variety of schemes where each one can be used as a production plan. This work presents a methodology, based upon stochastic programming (SP), that support the decision makers in the mid-term operations planning of an oil refinery. Results generated by running a multi-period two-stage SP model are used to measure the impact on the economic efficiency when not considering the randomness of the demand and the receipt of crude oil.

On the arithmetic of infinity oriented implementation of the multi-objective P-algorithm

The single-objective P-algorithm is a global optimization algorithm based on a statistical mod- el of objective functions and the axiomatic theory of rational decisions. It has been proven quite suitable for optimization of black-box expensive functions. Recently the P-algorithm has been generalized to multi-objective optimization. In the present paper, the implementation of that algorithm is considered using the new computing paradigm of the arithmetic of infinity. A strong homogeneity of the multi-objective P-algorithm is proven, thus enabling rather a simple application of the algorithm to the problems involving infinities and infinitesimals.

An electricity market model with generation capacity expansion under uncertainty

This article presents an electricity dispatch model with endogenous electricity generation capacity expansion for Germany over the horizon 2035. The target is to quantify how fuel and carbon price risk impacts investment incentives of thermal power plants. Results point to findings which are in line with general theory: Accounting for stochasticity increases investment levels overall and the investment portfolio tends to be more diverse.

Weighting criteria of aesthetic attractiveness of layouts of business process diagrams

The business process diagrams are widely used in business process management. The aesthetic attractiveness of the drawing of a business process diagram is especially important since the aesthetic lay- outs are also most informative and practical. We focus on the drawing of lines representing sequence flows assuming the locations of flow objects fixed. This problem is a special case of routing problem where stochastic optimization methods are among the most appropriate. To state the problem as a problem of multi-objective optimization taking into account the attitude of potential users towards the criteria of aesthetics, the assessment of importance (weighting) of the criteria is needed. In the present paper, the most important criteria are assessed using the results of a psychological experiment which are processed by the weighting method used in the Analytic Hierarchy Process.

A stochastic programming approach to optimization of information retrieval

The researDupach problem of optimization of the expected relevance of retrieved documents in search sessions with feedback is considered in this paper. This problem is solved by planning the interaction with the user with endogenous reduction of uncertainty by means of stochastic programming. An approach to build the model based on topic models of documents that takes into account past history of retrieved documents and user feedback values in the current decision is proposed. The experiments with a simulated database of documents shown a significant improvement in retrieval effectiveness over the traditional approach.

Fermat-weber location problem solving by the hyperbolic smoothing approach

The solution of the Fermat-Weber Location Problem, also known as the continuous p-median problem, is considered by using the Hyperbolic Smoothing approach. For the purpose of illustrating both the reliability and the efficiency of the method, a set of computational experiments was performed, making use of traditional test problems described in the literature.