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Compares two methods (Alienor and Twone) for solving numerically global optimization problems involving continuous functions defined on bounded and connected subsets of ². The Alienor method is about 12 years old, whereas Twone’s is only 12 months old. Considers that Twone is the generalization of the Alienor method. These methods are deterministic and use a reducing transformation allowing expression of two variables as a function of one variable.

Follows on from previous papers by the authors, where TWONE, a method for solving global optimization problems in two dimensions was presented. Presents an improved version. If Ω is a compact connect subset of R² looks for the minimum of a function f defined on Ω with values in R.² TWONE method considers the restriction of f to an α‐dense curve in R². That implies the resolution of a one dimensional problem. Gives some α‐dense curves in R² with α as small as we want. Has biomedical and biocybernetic implications.

The reducing transformation and global optimization technique called Alienor has been developed in the 1980s by Cherruault and Guillez. These methods are based on the approximating properties of α ‐dense curves. The aim of this work is to give a very large class of functions generating α ‐dense curves in a hyper‐rectangle of Rⁿ.

Shows how a hi‐dimensional optimisation problem with linear inequalities constraints is converted into a global optimisation problem of one bounded variable function f*. Then, we reduce the feasible region f* before seeking its global optimum.

Introduces new reducing transformation which allows expression of n variables in function of a single one. This allows densification of the space Rⁿ and the quality of the densification can be estimated. Applications to global optimization problems lead to the optimization of one variable function and the time of calculation for obtaining a global optimum can be estimated.

To use α‐dense curves to allow the transform of a multiple function into a single variable function in order to solve global optimization problems.

Use is made of the established Alienor method which has already been applied to biological and industrial processes. The problems tackled have a number of variables and the chosen optimization method is a variant of the Alienor method.

A new method for solving global optimization problem, called the Alienor method is now the subject of many variants. In this paper, it was found that a new reducing transformation α‐dense in Rⁿ was successful in solving this type of problem when associated to a functional depending on a large number of variables. The reducing transformation is very efficient and accurate.

This is a variant of the proven Alienor Method which has improved the resolution of global optimization problems. It showed that the reducing transformation has the advantage that a small calculation time is obtained even when the relevant series are slowly increasing. Further development of the method is anticipated.

Proved very effective for obtaining the global optimum with good precision and very short calculation time for large numbers of variables. Can be performed on micro‐calculators.

New variant of proven method. Of interest in solution of concrete problems in biology and industry.

A multi‐dimensional global optimization method has been developed. This method uses the curves of IRⁿ called α‐dense. A characterization of α‐dense curves is given in terms of γ‐stochastically independent functions as well as a constructive method to generate them by means of only one function φ called γ‐uniformly distributed has been developed. A very large class of functions which generate α‐dense curves is discussed. This class contains the γ‐uniformly distributed functions, the periodic functions and even functions which are not periodic, but which fulfil some properties.

The theoretic calculation time associated to every α‐dense curve into a fixed H of Rⁿ is inversely proportional to the discretization step depending on the length of the curve and, more directly, of the derivatives of its coordinate functions. For a given degree of density α, it is interesting to seek curves into H which may minimize the theoretic calculation time and then to solve the practical problem of computing approximations for global optimization of a given continuous function defined in H, by means of its restriction over a family of curves with the same degree of density into the cube H.

The purpose of this article is to identify and critically analyze healthcare establishment (HCE) quality parameters described in the literature. It aims to propose an integrated quality model that includes technical quality and associated supportive quality parameters to achieve optimum patient satisfaction.

The authors use an extensive in‐depth healthcare quality literature review, discerning gaps via a critical analysis in relation to their overall impact on patient management, while identifying an integrated quality model acceptable to hospital staff.

The article provides insights into contemporary HCE quality parameters by critically analyzing relevant literature. It also evolves and proposes an integrated HCE‐quality model.

Owing to HCE confidentiality, especially regarding patient data, information cannot be accessed.

The integrated quality model parameters have practical utility for healthcare service managers. However, further studies may be required to refine and integrate newer parameters to ensure continuous quality improvement.

This article adds a new perspective to understanding quality parameters and suggests an integrated quality model that has practical value for maintaining HCE service quality to benefit many stakeholders.