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In real-world cases, it is common to encounter mixed discrete-continuous problems where some or all of the variables may take only discrete values. To solve these non-linear optimization problems, the use of finite element methods is very time-consuming. The purpose of this study is to investigate the efficiency of the proposed hybrid algorithms for the mixed discrete-continuous optimization and compare it with the performance of genetic algorithms (GAs).

In this paper, the enhanced multipoint approximation method (MAM) is used to reduce the original nonlinear optimization problem to a sequence of approximations. Then, the sequential quadratic programing technique is applied to find the continuous solution. Following that, the implementation of discrete capability into the MAM is developed to solve the mixed discrete-continuous optimization problems.

The efficiency and rate of convergence of the developed hybrid algorithms outperforming GA are examined by six detailed case studies in the ten-bar planar truss problem, and the superiority of the Hooke–Jeeves assisted MAM algorithm over the other two hybrid algorithms and GAs is concluded.

The authors propose three efficient hybrid algorithms, the rounding-off, the coordinate search and the Hooke–Jeeves search-assisted MAMs, to solve nonlinear mixed discrete-continuous optimization problems. Implementations include the development of new procedures for sampling discrete points, the modification of the trust region adaptation strategy and strategies for solving mix optimization problems. To improve the efficiency and effectiveness of metamodel construction, regressors f defined in this paper can have the form in common with the empirical formulation of the problems in many engineering subjects.

This paper improves the evaluation index system of green building operation effect and establishes the evaluation model of green building operation effect. It is expected to promote energy saving and emission reduction and provide a more scientific evaluation method for green building operation effect evaluation.

First, 20 key evaluation indexes are selected to establish the operation effective evaluation index system. Then, the combined weight method is proposed to determine the weight of each evaluation index. Next, the gray clustering-fuzzy comprehensive evaluation method is used to construct the green building operation effective evaluation model. Finally, the feasibility and validity of the selected model were verified by taking Shenzhen Bay One green building in Shenzhen as an example.

This paper establishes the evaluation system of green building operational effect, and evaluates green building from the angle of operational effect. Taking Shenzhen Bay One project as an example, the rationality and applicability of the model are verified.

In this paper, for the first time, relevant indexes of user experience are included in the evaluation system of green building operational effect, which makes the evaluation system more perfect. In addition, a more scientific fuzzy gray clustering method is used to evaluate the operational effect of green building, and a new evaluation model is established.

The purpose of this paper is to evaluate green buildings from the angle of greenness and improve the evaluation system. And the matter-element extension method is used to evaluate the greenness of green buildings, in order to provide useful references for the evaluation system of green buildings.

First, this paper studies the aspects of safety and durability, health and comfort, living convenience, resource-saving, environmental liability and ecological quality, etc. For the first time, carbon emission is included in the evaluation system, 18 key evaluation indexes are determined by using the Delphi method, and the green building evaluation index system is established. Then, the combined weight method is proposed to determine the weight of each evaluation index, and the greenness evaluation model of green building is established with the matter-element extension method. Finally, taking Beijing Daxing International Airport as an example, the evaluation model of green building greenness was established to evaluate the building.

In this paper, the greenness evaluation model of green building established by the matter-element extension method solves the problem of incompatibility between qualitative and quantitative material elements in multi-factor evaluation. It makes the evaluation indexes more accurate and objective relative to the affiliation calculation of the evaluation set and improves the scientific, accuracy and reliability of the evaluation model.

In this paper, for the first time, carbon emission-related indicators are included in the green building evaluation system, which makes the evaluation system more perfect. In addition, a more scientific extension matter-element method is used to evaluate the greenness of green buildings, breaking the previous rough star evaluation method.