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Table 6. Solutions and energy consumption reduction for different values of the project lifespan. Table 7. Solutions and energy consumption reduction for different discount rates.

Table 6 Solutions and energy consumption reduction for different values of the project lifespan. Table 7. Solutions and energy consumption reduction for different discount rates.

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It has been highlighted that the MEPSO algorithm uses the surrogate model rather than the BPS to evaluate solutions, resulting in significant time saving. Subsequently, to ensure the results’ reliability, the newly generated sampling points, derived from the best solution attained through MEPSO, crossover, and mutation, are subjected to simulation utilizing the BPS methodology. Figure 1 shows the architecture of the MEVO algorithm. Figure 1. The architecture of the MEVO algorithm.
It has been highlighted that the MEPSO algorithm uses the surrogate model rather than the BPS to evaluate solutions, resulting in significant time saving. Subsequently, to ensure the results’ reliability, the newly generated sampling points, derived from the best solution attained through MEPSO, crossover, and mutation, are subjected to simulation utilizing the BPS methodology. Figure 1 shows the architecture of the MEVO algorithm. Figure 1. The architecture of the MEVO algorithm.
Table 1. Parameters used in the calculation of the objective function. 2.3. Case Study Building
Table 1. Parameters used in the calculation of the objective function. 2.3. Case Study Building
The case study is a one-story commercial building in Markham, Ontario, Canada [32] (see Figure 4). It comprises office and workshop space, covering approximately 330 m* and 720 m2, respectively, with a 7 m height. The building accommodates 15 people and operates from 10:00 to 18:00 on weekdays. Natural gas is used for space heating and hot water, while electricity is utilized for cooling, lighting, and equipment. Constructed in 1985, before the first building energy code was implemented in 1997 [33], the building’s envelope exhibits poor thermal performance. In this respect, the external walls of the office area are, from the inside to the outside, made of gypsum board, fiberglass insulation, concrete wall, and brick veneer. The workshop area has a similar wall composition but lacks an insulation layer, with an overall thickness of 30 cm. Consequently, the U-value of the office area’s external walls ranges from 1.2 W/ m?K to 1.4 W/m°K, while the workshop area’s external walls have a U-value of 2.8 W/m2K, as measured by QEA Tech Company. This poor thermal performance of the exterior walls and windows presents significant potential for energy savings through an energy-efficient retrofit of the building’s enclosure. Additionally, as a typical single-story office building in North America, the retrofit solutions can be applied to similar structures. The gross areas of the windows, doors, and exterior walls are 48 m2, 23 m2, and 1100 m7”, respectively.
The case study is a one-story commercial building in Markham, Ontario, Canada [32] (see Figure 4). It comprises office and workshop space, covering approximately 330 m* and 720 m2, respectively, with a 7 m height. The building accommodates 15 people and operates from 10:00 to 18:00 on weekdays. Natural gas is used for space heating and hot water, while electricity is utilized for cooling, lighting, and equipment. Constructed in 1985, before the first building energy code was implemented in 1997 [33], the building’s envelope exhibits poor thermal performance. In this respect, the external walls of the office area are, from the inside to the outside, made of gypsum board, fiberglass insulation, concrete wall, and brick veneer. The workshop area has a similar wall composition but lacks an insulation layer, with an overall thickness of 30 cm. Consequently, the U-value of the office area’s external walls ranges from 1.2 W/ m?K to 1.4 W/m°K, while the workshop area’s external walls have a U-value of 2.8 W/m2K, as measured by QEA Tech Company. This poor thermal performance of the exterior walls and windows presents significant potential for energy savings through an energy-efficient retrofit of the building’s enclosure. Additionally, as a typical single-story office building in North America, the retrofit solutions can be applied to similar structures. The gross areas of the windows, doors, and exterior walls are 48 m2, 23 m2, and 1100 m7”, respectively.
Figure 5. The modeled building in SketchUp. for the office and warehouse areas, respectively, while the cooling setback in both areas was set to 26 °C. The hourly annual simulation of the building model took approximately 12s ona laptop computer equipped with an 11th Gen Intel Core i7-1185G7 CPU of 3 GHz, running Microsoft Windows 10 Enterprise.
Figure 5. The modeled building in SketchUp. for the office and warehouse areas, respectively, while the cooling setback in both areas was set to 26 °C. The hourly annual simulation of the building model took approximately 12s ona laptop computer equipped with an 11th Gen Intel Core i7-1185G7 CPU of 3 GHz, running Microsoft Windows 10 Enterprise.
Table 3. Parameter settings of algorithms MEVO, MEPSO, GA, and PSO.
Table 3. Parameter settings of algorithms MEVO, MEPSO, GA, and PSO.
Figure 6. Performance of different neural networks.
Figure 6. Performance of different neural networks.
1 The values of alpha and beta were obtained by optimizing the Biggs EXP4 function [38] with 80 samples generated with LHS. * The velocity equation described by the authors of [39] was implemented using the described parameters for PSO in Table 3, which were recommended by the authors of [35]. Table 3. Cont.
1 The values of alpha and beta were obtained by optimizing the Biggs EXP4 function [38] with 80 samples generated with LHS. * The velocity equation described by the authors of [39] was implemented using the described parameters for PSO in Table 3, which were recommended by the authors of [35]. Table 3. Cont.
Table 4. Comparison of the performances of MEVO-I and MEVO-II with the metaheuristic optimiza- tion algorithms. On the other hand, the MEVO algorithms were four to six times faster than the other algorithms. It should be emphasized that the additional 9.078 min (see 1 was only applied to the first run, which involves the generation of the initial 50 s used for constructing the initial neur fewer simulations, the MEVO algorit hms are likely to achieve lower cost values t [able 4 ample: al network. These findings indicate that even with han the metaheuristic algorithms, all while requiring significantly less computation time. The = lower computational time of MEVO algorithms can be attributed to their inherent nature compared to the metaheuristic algorit hms. Indeed, MEVO saves significant compu time by avoiding extra simulations by utilizing a surrogate model and its unique i learning mechanisms. In contrast, MEPSO I, II, GA, and PSO only explore the solutior space through the execution of the building performance simulation on each solution. ationa. erative
Table 4. Comparison of the performances of MEVO-I and MEVO-II with the metaheuristic optimiza- tion algorithms. On the other hand, the MEVO algorithms were four to six times faster than the other algorithms. It should be emphasized that the additional 9.078 min (see 1 was only applied to the first run, which involves the generation of the initial 50 s used for constructing the initial neur fewer simulations, the MEVO algorit hms are likely to achieve lower cost values t [able 4 ample: al network. These findings indicate that even with han the metaheuristic algorithms, all while requiring significantly less computation time. The = lower computational time of MEVO algorithms can be attributed to their inherent nature compared to the metaheuristic algorit hms. Indeed, MEVO saves significant compu time by avoiding extra simulations by utilizing a surrogate model and its unique i learning mechanisms. In contrast, MEPSO I, II, GA, and PSO only explore the solutior space through the execution of the building performance simulation on each solution. ationa. erative
Figure 7. Box plot comparing MEVO-I and MEVO-II with the metaheuristic optimization algorithms. The x and o show the mean best cost and outliers, respectively.
Figure 7. Box plot comparing MEVO-I and MEVO-II with the metaheuristic optimization algorithms. The x and o show the mean best cost and outliers, respectively.
Figure 8. Box plot comparing MEVO-I and MEVO-II with the Bayesian optimization algorithms. The x and o show the mean best cost and outliers, respectively. Table 5. Performance of MEVO and Bayesian optimization.
Figure 8. Box plot comparing MEVO-I and MEVO-II with the Bayesian optimization algorithms. The x and o show the mean best cost and outliers, respectively. Table 5. Performance of MEVO and Bayesian optimization.
Figure 9. Cumulative percentage curves of pone values. Figure 9 illustrates the cumulative percentage frequencies concerning the number of iterations. It is clear that for MEVO-I, 90% of the runs reach convergence before the 35th iteration. In contrast, with Bayesian optimization, only 58% of the runs achieve convergence before the 35th iteration. Moreover, when Bayesian optimization achieved convergence in 77% of the runs, MEVO achieved convergence in 97% of the runs. While decreasing the number of iterations in MEVO has a relatively minor impact on the average solution quality, it reduces the time required for the optimization process.
Figure 9. Cumulative percentage curves of pone values. Figure 9 illustrates the cumulative percentage frequencies concerning the number of iterations. It is clear that for MEVO-I, 90% of the runs reach convergence before the 35th iteration. In contrast, with Bayesian optimization, only 58% of the runs achieve convergence before the 35th iteration. Moreover, when Bayesian optimization achieved convergence in 77% of the runs, MEVO achieved convergence in 97% of the runs. While decreasing the number of iterations in MEVO has a relatively minor impact on the average solution quality, it reduces the time required for the optimization process.
Figure 10. Comparison of electricity consumption. The solution yielding the best lifecycle cost of 752.6740 CAD/m? was achieved using MEVO-I, as indicated in Tables 4 and 5. This solution involves incorporating an insulation ayer with a thickness of 0.0493 m, installing windows with a U-value of 1.3 W/ m’K, and a solar heat gain coefficient (GHGC) of 0.1. The monthly electricity and natural gas consumption before and after the retrofit are compared in Figures 10 and 11. Notably, the ‘etrofit resulted in significant natural gas savings during the coldest months, specifically ‘rom. December to February. The observed outcome can be attributed to the effective orevention of heat losses, achieved through additional insulation and the installation of uigh-performance windows. Moreover, the most substantial electricity savings occurred ‘rom June to August due to the reduced demand for space cooling resulting from the lower SHGC and U-value of the windows.
Figure 10. Comparison of electricity consumption. The solution yielding the best lifecycle cost of 752.6740 CAD/m? was achieved using MEVO-I, as indicated in Tables 4 and 5. This solution involves incorporating an insulation ayer with a thickness of 0.0493 m, installing windows with a U-value of 1.3 W/ m’K, and a solar heat gain coefficient (GHGC) of 0.1. The monthly electricity and natural gas consumption before and after the retrofit are compared in Figures 10 and 11. Notably, the ‘etrofit resulted in significant natural gas savings during the coldest months, specifically ‘rom. December to February. The observed outcome can be attributed to the effective orevention of heat losses, achieved through additional insulation and the installation of uigh-performance windows. Moreover, the most substantial electricity savings occurred ‘rom June to August due to the reduced demand for space cooling resulting from the lower SHGC and U-value of the windows.
These findings indicate that the change in discount rate has a more pronounced impact on energy consumption than the change in lifespan. Specifically, when the discount rate was lowered to 3%, the resulting solution exhibited higher insulation and more efficient windows than the best solution determined through the lifespan assessment.
These findings indicate that the change in discount rate has a more pronounced impact on energy consumption than the change in lifespan. Specifically, when the discount rate was lowered to 3%, the resulting solution exhibited higher insulation and more efficient windows than the best solution determined through the lifespan assessment.
Figure 11. Comparison of natural gas consumption.
Figure 11. Comparison of natural gas consumption.
Figure 12. The relationship between the total energy consumption and the insulation investment cost
Figure 12. The relationship between the total energy consumption and the insulation investment cost
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MathematicsComputer ScienceArtificial IntelligenceMachine LearningEngineering OptimizationEvolutionary AlgorithmMathematical OptimizationBayesian OptimizationMETA optimization
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