یک مدل چند بهینه سازی عینی برای ایجاد تصمیم های سرمایه گذاری بهره وری انرژی

A multiple objective optimisation model is formulated to help decision makers to make an optimal decision when investing in energy-efficient building retrofitting. The objectives are to maximise the energy savings and minimise the payback period for a given fixed initial investment. The model is formulated as a multi-objective optimisation problem with the net present value (NPV), initial investment, energy target and payback period as constraints and it is solved using genetic algorithms (GAs). The optimal decision is reached by choosing the most optimal actions during energy retrofit in buildings. The model is applied to a case study of a building with 25 facilities that can be retrofitted that illustrates the potential of high energy savings and short payback periods. The sensitivity analysis is also performed by analysing the influence of the auditing error of the facilities, wrongly specified energy savings, the initial investment, changes in interest rate and the changes of electricity prices on the payback period, the maximum energy saved and NPV of the investment. The outcome of this analysis proves that the model is robust.

The current energy shortage around the world is the reason that energy efficiency is a subject of interest today. The most viable option to counteract this problem is by reducing the current energy consumption. With buildings consuming around 40% of the world's total energy [1], it would be beneficial to invest in building energy efficiency retrofit projects. In order to improve the energy efficiency of buildings, inefficient facilities are often replaced by highly advanced energy efficient ones. A whole range of facilities can be retrofitted if there is unlimited funding, although usually this is not the case. Nevertheless the following are some of the retrofit actions that can be taken [2], [3] and [4]: • Building improvements – insulating the roof, replacing the single glazing windows with double glazing windows and installing solar shading. • HVAC system improvements – installing energy efficient systems with advanced controls. • Energy efficient lighting – replacing incandescent lighting by compact fluorescent lighting (CFL) or LED lighting. • Replacing inefficient equipment – replacing cathode ray tube (CRT) computer monitors with liquid crystal displays (LCD). • Electromechanical improvements – installing power factor correcting capacitors to improve the power factor. The main problem is that most investors are reluctant to invest in energy saving projects such as retrofit projects. This is because such projects are often not able to compete with other investments within the institutions or companies due to unclear benefits. But this is not the case if an investment in energy-efficiency projects is made with the help of decision making tools that can identify large monetary savings. Furthermore, this makes energy efficiency projects competitive with other projects. A decision can be made using the following two approaches [5], [6], [7], [8] and [9]: • In the first approach, an energy expert carries out an energy analysis of the building and several alternative scenarios will be developed and evaluated. • In the second approach decision-making tools such as multi-objective or multi-criteria combined with simulations are applied to assist the decision maker to reach a final decision among a given set of alternative actions. The multi-criteria technique in the second approach has been used to assist the designers to select the most feasible actions during the initial stages of a renovation project, for energy efficiency improvement of a building [9]. The major setback of this technique is that it is based on predefined sets of actions and scenarios that should be pre-evaluated. In such a case there is no guarantee that the solution reached is the optimal one [7]. Due to the complexity of decision-making problems especially ones with multiple objectives, the multi-objective optimisation technique is a suitable candidate to model these problems, because it can explore potentially an unlimited number of alternatives. This technique is used by many researchers mainly with the objective to reduce the cost of the materials and to maximise energy savings. The possibility to use the multi-objective optimisation model to solve the decision problems that consider as many options as possible is widely accepted. [8] Simultaneously minimises the following three objectives: the energy consumption of the building; the initial investment cost; and the annual carbon dioxide emission. [9] Studies a similar problem to balance the energy, environment, financing and social factors. The hybrid decision system is suggested by [10] for sustainable renovation of office buildings and improvements in energy performance, where the decision-maker is facing the challenge of making trade-offs between renovation costs, environmental impacts and improved building quality. The weakness of these studies is that they do not consider the payback period of the investment as one of the objectives. They consider a case of unlimited funding which is not always possible because most of the time there are budget constraints. Another shortfall of these researches is that they do not perform the sensitivity analysis or the robustness test on the model. According to [11] every model has a high probability of having uncertainty with regard to some of its parameters. This issue can be addressed by performing the sensitivity analysis or the robustness test. In the study [12] a sensitivity analysis is used before the decision making to validate the robustness of the design decision related to the energy consumption and comfort. The study in [13] makes use of sensitivity analysis to predict the night cooling performance of internal convective heat transfer modelling and the result reveals that some choices of the convectional algorithm may affect the energy and predictions related to the thermal comfort. The study in [14] inspects the robustness of the methodology used to estimate the hourly energy consumption of a given building that considers discrepancies of the parameters within a building. The results show that the methodology can eliminate the errors caused by discrepancies. The research in this paper addresses these shortcomings of the previous researches by constructing a model that will maximise the energy savings and minimise the payback period of the investment, and there will be trade-off between the two if necessary. The contribution of this paper is the addition of the payback period of the investment as an objective, something that has never been considered by previous studies. A sensitivity analysis is performed to illustrate the robustness of the model. The model is constrained by budget, targeted energy savings and acceptable payback periods. This model also considers the time value of money by making use of the net present value (NPV). The research conducted by [8] and [9] present a model that is applicable to the design phase of the building, while the research under this study will present a model that can be used during the operation stage of the building. The model in this paper is applicable to many similar energy retrofit and renovation projects. Because of the complexity of the multi-objective optimisation models, an easy way to solve them is to use the genetic algorithms (GA). GA can be viewed as a family of computational models that are inspired by evolution. To illustrate the effectiveness of the model obtained in this paper, GA is used to solve the multi-objective optimisation model. Note that other types of popular algorithms, such as particle swarm optimisation, simulated annealing, ant colony, and so forth, may also be applied to solve the obtained model. The paper is organised as follows: in Section 2, an optimisation model for investment decision making in buildings energy-efficiency projects is formulated. In Section 3 the optimisation model is applied to a case study. The results and simulations of the case study are presented in Section 4. The conclusion is given in the last section.

The optimisation model is formulated as multi-objective optimisation with constraints. The decisions given by the model are optimal which result in maximum energy savings and low payback periods. The optimisation model is sensitive to the changes in constraints. Any such a change in constraints prominently affects the choice of optimal actions. The model is applied to six different cases and has proved to be efficient. The results show that it is impossible to achieve certain objectives, for instance it is impossible to save 10% of the baseline energy with the initial investment of only $62,500. The initial investment directly affects the energy saved and the payback period of the investment. During sensitivity analysis it is realised that the changes in some parameters affects both the energy savings and payback period. The optimisation model is found to be robust as it satisfies the constraints even under the influence of outside parameters. The proposed optimisation model is not restricted to buildings alone, it may also be applied in industries where extra constraints like maintenance costs might be added to make the problem even more complex.