This supplement is divided into five sections. In the first two sections we prove the validity of the Extended Screen-to-the-Best Procedure and Extended Rinott’s Procedure; in both cases the extensions are to allow unequal initial sample sizes, n0i. The third section establishes the validity of the Screen-Restart-and-Select Procedure. The fourth section shows how we select [nlow, nhigh] to star...

The hybridization of multi-objective evolutionary algorithms (MOEAs) with mathematical programming techniques has gained increasing popularity in the specialized literature in the last few years. However, such hybrids normally rely on the use of gradients and, therefore, normally consume a high number of extra objective function evaluations in order to estimate the gradient information required...

Artificial bee colony (ABC), an optimization algorithm is a recent addition to the family of population based search algorithm. ABC has taken its inspiration from the collective intelligent foraging behavior of honey bees. In this study we have incorporated golden section search mechanism in the structure of basic ABC to improve the global convergence and prevent to stick on a local solution. T...

The Golden Section is proposed to be the preferred ratio in many domains. Starting with Fechner, there were several empirical studies concerning the preference of the Golden Section with inconclusive results. Our main concern is that the Golden Section can neither perceived no produced exactly since it is an irrational number. Therefore, we propose to give a closer look to preferences for ratio...

Derivative-free optimization algorithms are needed to solve real-world engineering problems that have computationally expensive and noisy objective function and constraint evaluations. In particular, we are focused on problems that involve running cumbersome simulation codes with run times measured in hours. In such cases, attempts to compute derivatives can prove futile because analytical deri...

A close reading of Hotelling's famous article on exhaustible resources reveals the following passage: 'If a mine-owner produces too rapidly, he will depress the price, perhaps to zero. If he produces too slowly, his profits, though larger, may be postponed farther into the future than the rate of interest warrants. Where is hisgolden mean? And how does this most profitable rate of production va...

Observations of Information Retrieval (IR) system user experiences reveal a strong desire for collaborative search while at the same time suggesting that collaborative capabilities are rarely, and then only in a limited fashion, supported by current searching and visualization tools. Equally interesting is the fact that observations of user experiences with Group Support Systems (GSS) reveal th...

This study introduces an effective population-based optimization algorithm, namely the Golden Search Optimization Algorithm (GSO), for numerical function optimization. The new algorithm has a simple but strategy solving complex problems. GSO starts with random possible solutions called objects, which interact each other based on mathematical model to reach global optimum. To provide fine balanc...

This paper compares six commonly used QT correction models and three available parameter estimation methods using five indices for QTc evaluation based on real and simulated electrocardiograph (ECG) datasets. The results show that the golden section approach always finds the correction factor making QTc interval uncorrelated to heart rate for all six formulas. However, the correction formulas d...