Multi-objective intelligent algorithm model design for housing environment optimization

Abstract

With the improvement of the national living standard, the buyers have higher and higher requirements for the rationality and aesthetics of the spatial planning and layout of the residential area. The traditional residential space planning method is purely manual design, which is inefficient, and the design effect will be greatly affected by the designer’s work experience and personal aesthetics. Therefore, this research attempts to combine Pareto solution set and piecewise prediction idea into genetic algorithm, propose an algorithm for solving multi-objective optimization problems, and build an intelligent housing environment planning system based on this. The statistical results of simulation experiments show that the system can output more design schemes with better overall quality than the comparison system and manual planning results, and the stability of multiple operations is higher. When the number of iterations reaches 200, the average value of Pareto optimal solution number and optimal solution quality index QPS of the former is 44 and 0.41, respectively. The expert group analyzed the design results of this method and the manual method for an actual case, and found that the results designed by this method met the requirements and the calculation efficiency was much faster than manual processing. From the simulation test data and the actual case analysis, it can be seen that the intelligent housing environment planning system designed in this study is helpful to improve the efficiency of residential space design and the stability of residential space scheme style.

Keywords

Genetic algorithm Pareto solution set optimal solution housing environment planning multi-objective optimization

1. Introduction

The current mainstream housing design method at home and abroad still relies on designers’ manual design, and the disadvantage of this method is that the quality of the design scheme will be greatly affected by the designer’s own skills, knowledge, ability, and aesthetic style [1]. For companies with poor operational strength and unable to hire high-level designers, the level of their housing environment design will be significantly limited, thus being at a disadvantage in the industry competition [2]. Therefore, the head companies in the industry have the competitive advantage of high-end services, resulting in the need for the consumer side to pay an additional premium for this, which is not conducive to the long-term development of the industry and the international transformation of domestic companies [3]. The multi-objective optimization system for housing environment built based on intelligent algorithms can fix the design concept and design style of excellent, even top designers in the form of a program and process the same work in bulk at a lower cost and expense. This is of great significance to improve the overall design quality of the housing environment design industry [4].

In this study, we propose a Pareto-based solution set feature point acquisition method to replace the original solution set feature point acquisition method in the genetic algorithm, in order to address the problem that the computational complexity increases significantly and the stability of the algorithm decreases when the computational environment changes. Specifically, we first sort the individuals in the population according to the ascending $i$ order of the objective function value, then fix the sampling interval $k$ , randomly select an integer from 1 to $k$ as the number of the first unit of the algorithm, and then extract the sample units in the same way until the objective function value of the obtained sample units reaches the maximum. In order to solve the problem that the Pareto solution set does not exist in a linear way in the objective function space and it is not possible to determine the overall evolutionary direction only by a single direction, the research team proposes to use the idea of segmentation prediction in the objective space to complete the sorting and subset division of the optimal solution set according to the objective function values of individuals in the population, so as to obtain the evolutionary direction of each subpopulation at each moment and determine the overall evolutionary direction by multiple evolutionary directions. The overall evolutionary direction of the population is determined by combining multiple evolutionary directions to improve the accuracy of the output optimal solution set. Finally, in order to reduce the computational effort of prediction, a linear prediction model is used to predict new individuals of the population in the modification system. The above three points are also the innovation and novelty of this research. By building a multi-objective intelligent optimization system based on improved genetic algorithm, the automation level of housing environment planning can be realized, so as to improve the production efficiency of enterprises and reduce the human cost.

2. Related works

In order to achieve the environmental design goal of quickly and accurately meeting the needs of residents, people have carried out a lot of research before. Takebayashi and Kyogoku [5] evaluated the radiation environment by checking the reconstruction buildings in front of Osaka Central Station, and calculated the spatial distribution of solar radiation shadow using ArcGIS and building shape data, from which the heat dissipation capacity of the design scheme of civil residential environment in front of the station was optimized. Clarissa et al. [6] found that the heat dissipation capacity of residential buildings in humid and hot climate is worse than that of residential buildings of the same type but in other climate zones. Therefore, priority and thermodynamic analysis software were used to analyze the heat dissipation of residential buildings in this environment, and the building environment was optimized based on the analysis results. The simulation analysis results showed that the heat dissipation speed of residential buildings after optimization was significantly improved. Ade-Ojo [7], in order to understand the impact of construction habits of construction workers on the construction results of residential environment, chose a civil residential project under construction in Nigeria as a case, and selected several groups of construction teams with different construction habits to carry out construction in different areas of the project. The analysis of the construction results shows that the construction environment completed by the construction team with higher spatial aesthetic ability has higher aesthetic value, and the functional requirements of the environment also meet the design requirements.

The intelligent algorithm represented by the genetic algorithm has been widely applied to multi-objective optimization problem solving in various industries by domestic and foreign scholars due to its advantages of low difficulty in understanding and high quality of output solution. Alpman [8] designed a power generation for small wind turbine efficiency method. The method is implemented based on an improved multi-objective optimization algorithm, and the wind tunnel test results show that the algorithm is effective in improving the power generation efficiency of small wind turbines.

Dovgan et al. [9] has redesigned the algorithm for discovering driving strategies in order to overcome the drawback of high computational time complexity of driving strategy multi-objective optimization algorithms in the market, which does not allow real-time optimization, and obtained the real-time multi-objective optimization algorithm for discovering driving strategies (MODS-RT). The MODS-RT algorithm has been tested on data from real-world routes and compared with MODS and traditional single-objective algorithms with the goal of discovering better intelligent driving strategies. Although MODS-RT found poorer driving strategies than MODS, it found better driving strategies than the single-objective algorithm, thus demonstrating that the multi-objective approach can be effectively applied to real-time discovery of driving strategies. Xu et al. [10] designed a decomposition-based harmonic search algorithm (called MOEA/D-HSA) in order to deal with the multi-peak multi-objective optimization problem (MMOP). In MOEA/D-HSA, multiple individuals assigned to the same weight vector form a subgroup for finding multiple different Pareto optimal sets (PSs). Then, an environmental selection method based on greedy selection is designed to dynamically adjust the subpopulation size to maintain population diversity. Finally, an improved harmonic search algorithm and an elite learning strategy are used to balance population diversity and convergence. Experimental results on the CEC 2019 test suite show that MOEA/D-HSA outperforms some state-of-the-art algorithms. Li et al. [11] proposed an end-to-end framework for solving multi-objective optimization problems using deep reinforcement learning (DRL). It was found that once a trained model is available, it can be extended to newly encountered problems without retraining the model. The solution can be obtained directly by performing a simple forward computation on the neural network, and experimental results show that the method has high generalization capability and fast solution speed compared with existing multi-objective optimization methods. Wang et al. [12] proposed a derivative-free linear feasible direction model with backtracking search technique for solving nonlinear multiobjective optimization problems. The numerical experimental results showed that this algorithm can improve the quality of the output solution of nonlinear multiobjective optimization problems compared with the traditional genetic algorithm.

To sum up, many intelligent algorithms, including genetic algorithms, have been widely used to solve various multi-objective optimization problems in real life. However, there is no improvement on the shortcomings of genetic algorithms, such as the diversity and instability of genetic algorithms and the slow convergence process, which easily leads to insufficient accuracy of the results calculated by the algorithms. Moreover, the research on applying intelligent algorithms to housing environment planning and space design is also very rare. However, this application may have a significant impact on improving the overall design level and design efficiency of the industry, so it is necessary to carry out this research.

3. Design of housing environment planning method based on improved multi-objective intelligent algorithm

3.1 Multi-objective optimization algorithm design incorporating Pareto solution set and segment prediction

Most of the traditional housing environment optimization models are centered on genetic algorithms, but the optimization magnitude of such models is insufficient and the quality of optimization results needs to be improved [13]. Therefore, this study attempts to construct a multi-objective optimization algorithm based on Pareto solution set and segmented prediction methods for composing an intelligent planning system for housing environments, the latter will be presented in the next section.

The housing environment’s spatial planning needs to consider the cost, space, practicality and other objectives, which belongs to the dynamic multi-objective optimization problem. At present, static multi-objective algorithms are mostly used as the framework for solving [14]. However, the current commonly used dynamic multi-objective optimization algorithms have the disadvantages of unstable diversity of solutions and slow convergence process. As a classical optimization algorithm, the genetic algorithm is widely used in all walks of life. However, due to its own more or less of the above shortcomings, it is not suitable for directly solving the optimization problem of housing environmental planning and design in this study. Therefore, a multi-objective optimization algorithm integrating Pareto solution set and subsection prediction is proposed in this study [15]. The basic framework of the improved algorithm is the non-inferior ranking genetic framework, because this algorithm has the advantages of simple calculation logic, superior performance and fast calculation speed, and is more suitable for solving multi-objective optimization problems. In this study, prediction is used to deal with the problem of dynamic multi-objective optimization. When the algorithm detects the change of the calculation conditions, the Pareto optimal solution of the evolution output at the previous time is sorted according to the objective function value and divided into three segments, and then the moving direction of the center point of the solution set of each segment is calculated. The algorithm also systematically samples each Pareto subset to obtain feature points, and is used to predict the population of subsequent generations. Finally, according to the difficulty of the problem to be solved, the algorithm will automatically generate some individuals randomly in the surrounding space of the predicted population to improve the genetic diversity. When the algorithm detects that the calculation parameters have not changed, the guidance individual can be inserted to improve the convergence speed of the algorithm. The improved algorithm is designed in detail below.

When the computational environment changes, a large amount of historical data needs to be used in order to predict the Pareto solution set, and to reduce the complexity of the algorithm needs to extract the optimal frontier of feature points from the dataset [16]. Traditional feature point extraction methods are either too complex or not stable enough, so now a novel method for obtaining feature points of Pareto solution set is proposed, which obtains the required feature points by using systematic pump-and-place in the target space. $i$ , specifically, we first sort the individuals in the population according to the ascending order of the objective function values, then fix the sampling interval $k$ and randomly select an integer from 1 to $k$ as the number of the first unit of the algorithm. In addition, to ensure that the extracted solution set has sufficient range, the boundary points of the solution set need to be set to describe the PF frontier feature points [17]. After finishing the Pareto solution set feature point extraction, it is also necessary to calculate the moving direction of the population, and set the moment $t$ , the population center $c^{t}$ set as:

$\displaystyle c^{t}={\sum\limits_{x^{t}\in p^{t}}{x^{t}}}\mathord{\left/{% \vphantom{{\sum\limits_{x^{t}\in p^{t}}{x^{t}}}{\left|{p^{t}}\right|}}}\right.% \kern-1.2pt}{\left|{p^{t}}\right|}$ (1)

Where, $x^{t}$ is the coordinate of each sample on the $x$ axis at that moment, $p^{t}$ represents the solution set of the population calculation at that moment, $c^{t}=(c_{1}^{t},c_{2}^{t},\ldots,c_{n}^{t})$ , $n$ represents the number of dimensions of the decision variables. Also, when the population is not fully converged, there are some solutions in the population that do not belong to the Pareto solution set, which affects the centroid calculation of the whole population. Therefore, a more accurate description of the moving direction of the population solution set is needed, and the centroid calculation formula is modified to Eq. (2).

$\displaystyle c^{t}={\sum\limits_{x^{t}\in ps^{t}}{x^{t}}}\mathord{\left/{% \vphantom{{\sum\limits_{x^{t}\in ps^{t}}{x^{t}}}{\left|{p^{t}s}\right|}}}% \right.\kern-1.2pt}{\left|{p^{t}s}\right|}$ (2)

According to Eq. (2), the direction of movement of the population at $t-1$ , $d^{t}$ , see Eq. (3), at the time of:

$\displaystyle d^{t}=c^{t}-c^{t-1}$ (3)

Where $d^{t}=(d_{1}^{t},d_{2}^{t},\ldots,d_{n}^{t})$ , $ps^{t}$ are the optimal set of solutions at that moment. However, the Pareto solution set does not exist in a linear manner in the objective function space, and it is not possible to determine the overall evolutionary direction by individual directions only. Therefore, this study proposes a method to carry out segmental prediction in the objective space [18]. The method completes the ranking of the optimal solution set based on the objective function values of the individuals in the population and divides it into three uniform subsets $PS_{1}^{t}$ , $PS_{2}^{t}$ , $PS_{3}^{t}$ , the division is based on the size of the objective function, and the evolutionary direction of each subpopulation at that moment is obtained $d_{1}^{t}$ , $d_{2}^{t}$ , $d_{3}^{t}$ , and the population center of $PS_{1}^{t}$ is:

$\displaystyle c1^{t}={\sum\limits_{x^{t}\in ps_{1}^{t}}{x^{t}}}\mathord{\left/% {\vphantom{{\sum\limits_{x^{t}\in ps_{1}^{t}}{x^{t}}}{\left|{ps_{1}^{t}}\right% |}}}\right.\kern-1.2pt}{\left|{ps_{1}^{t}}\right|}$ (4)

The other two subsets of population centers were calculated by formulas similar to Eq. (4). In the improved multi-objective optimization algorithm, a linear prediction model is chosen to reduce the computational effort of prediction. If the computational environment remains unchanged, individuals that play a leading role can be added to the population to speed up the convergence of the algorithm, and the leading individuals are generated through Eq. (5) that

$\displaystyle x^{\textit{iter}+1}=x^{\textit{iter}}+d^{\textit{iter}}$ (5)

In Eq. (5), iter represents the number of iterations of the population, and $d^{\textit{iter}}$ is the direction of genetic evolution of the population in two adjacent generations. It can be found by $d^{\textit{iter}}=c^{\textit{iter}}-c^{\textit{iter}-1}$ and $c^{\textit{iter}}$ is calculated by Eq. (6).

$\displaystyle c^{\textit{iter}}={\sum\limits_{x^{\textit{iter}}\in ps^{\textit% {iter}}}{x^{\textit{iter}}}}\mathord{\left/{\vphantom{{\sum\limits_{x^{\textit% {iter}}\in ps^{\textit{iter}}}{x^{\textit{iter}}}}{\left|{ps^{\textit{iter}}}% \right|}}}\right.\kern-1.2pt}{\left|{ps^{\textit{iter}}}\right|}$ (6)

Where $ps^{\textit{iter}}$ is the set of optimal solutions computed by the population in the iter generation. If the computational environment changes, the first segment feature points are obtained from $x^{t+1}=x^{t}+d1^{t}$ and $x^{t}\in PS_{1}^{t}$ , and the other two feature points are computed in a similar way to it. After finding the feature solution sets of the three subsets, the boundary detection needs to be carried out so as to prevent the new populations generated by the prediction from appearing outside the decision space, and the boundary detection method is shown in Eq. (7).

$\displaystyle y_{i}=\left\{{\begin{array}[]{l}x_{i},(l_{i}\leqslant x_{i}% \leqslant v_{i})\\ \textit{Ran}(l_{i},0.5(x_{i}+l_{i})),x_{i}<l_{i}\\ \textit{Ran}(v_{i},0.5(x_{i}+v_{i})),x_{i}>v_{i}\\ \end{array}}\right.$ (7)

In Eq. (7), $l_{i}$ , $v_{i}$ are the lower and upper boundaries of individuals on the detection space $x$ axis, respectively, and $\textit{Ran}()$ is a function to generate random numbers in the developed data range. Since the more complex the problem to be optimized, the lower the quality of the population solution, the study devises a method to automatically maintain the population diversity, which is described as follows. The number of randomly generated individuals used to maintain the population diversity is adjusted by keeping its individual size constant in the population evolution to predict the number of solution sets generated at subsequent moments. And the randomly generated individuals are obtained by means of Gaussian variation. At this point, the design of the multi-objective optimization algorithm incorporating the Pareto solution set and segmentation prediction is completed, and its computational flow is shown in Fig. 1.

Figure 1.

Computational flow chart of multi-objective optimization algorithm incorporating Pareto solution set and segmental prediction.

The process in Fig. 1 is shown clearly and does not need to be described. The common dynamic multi-objective optimization algorithm used in this study, the non-inferiority ranking genetic algorithm (NSGA for short), is described below [19]. This algorithm is simpler and more efficient than the more traditional dynamic multi-objective algorithms, so it is widely used. It should be noted that NSGA uses Eq. (8) to calculate the crowding distance of an individual $i$ , $P[i]_{\textit{dis}\tan ce}$ .

$\displaystyle P[i]_{\textit{dis}\tan ce}=P[i]_{\textit{dis}\tan ce}+(P[i+1].m-% P[i-1]._{m})/(f_{m}^{\max}-f_{m}^{\min})$ (8)

In Eq. (8), $P[i].m$ means the value of the $m$ objective function of the numbered $i$ individual, and $f^{\min}$ , $f^{\max}$ represent the minimum and maximum values of the $m$ objective function in the solution set. The parameters $\beta_{qi}$ and the children $C_{k}^{1}$ and $C_{k}^{2}$ in NSGA are calculated in Eqs (9) and (10), respectively.

$\displaystyle\beta_{qi}=\left\{{\begin{array}[]{l}(2u_{i})^{\frac{1}{\eta_{c}+% 1}},u_{i}\leqslant 0.5\\ \left({\frac{1}{2(1-u_{i})}}\right)^{\frac{1}{\eta_{c}+1}},u_{i}>0.5\\ \end{array}}\right.$ (9)

Where $u_{i}$ is a random number in the range (0, 1) and the parameter $\eta_{c}$ is a non-negative real number known as the crossover distribution index.

$\displaystyle\left\{{\begin{array}[]{l}c_{k}^{1}=0.5[{(1-\beta_{qi})P_{k}^{1}+% (1+\beta_{qi})P_{k}^{1}}]\\ \\ c_{k}^{2}=0.5[{(1-\beta_{qi})P_{k}^{2}+(1+\beta_{qi})P_{k}^{2}}]\\ \end{array}}\right.$ (10)

Where $P_{k}^{1}$ and $P_{k}^{2}$ are the parent individuals. The variation operators of polynomial variation in NSGA $c_{k}$ and $\delta_{k}$ are calculated in Eqs (11) and (12), respectively.

$\displaystyle c_{k}=p_{k}+({p_{k}^{u}-p_{k}^{l}})\delta_{k}$ (11)

Where $p_{k}$ , $p_{k}^{l}$ , and $p_{k}^{u}$ represent the decision variables of the parent individuals in the $k$ dimension and their lower and upper bounds, respectively. $c_{k}$ is the decision variable of the child $c$ in the $k$ dimension, and $\delta_{k}$ is the coefficient calculated from the polynomial distribution.

$\displaystyle\delta_{k}=\left\{{\begin{array}[]{l}(2r_{k})^{\frac{1}{\eta_{m}+% 1}-1},r_{k}<0.5\\ 1-{2({1-r_{k}})}]^{\frac{1}{\eta_{m}+1}},r_{k}\geqslant 0.5\\ \end{array}}\right.$ (12)

In Eq. (12), $r_{k}$ is the number obtained by using uniform random sampling between (0, 1) and $\eta_{m}$ is the variance distribution index. The classical NSGA algorithm calculation process is shown in Fig. 2, which has shown the NSGA algorithm steps clearly and will not be repeated.

Figure 2.

Classical NSGA algorithm calculation flow chart.

3.2 Construction of housing environment planning system based on improved intelligent algorithm

Now we use the designed improved multi-objective optimization algorithm to build a complete house environment planning system, which consists of three parts: house environment planning scheme generation, scheme performance evaluation, and multi-objective optimization algorithm, and the process of building the system is described in detail below [20]. Firstly, we need to input house environment parameters into the system, including environment level, sunlight intensity and change law, building spacing specification, etc., and then the system generates all environment design schemes that meet each restriction. Then the performance of each scheme with each dimensional objective is evaluated by the housing environment planning evaluation system. Finally, the better solution set of each dimensional objective is output by multi-objective optimization algorithm, and the operation flow of the system is shown in Fig. 3.

Figure 3.

Intelligent house environment planning system computing process.

As shown in Fig. 3, the first step of the system needs to establish the housing environmental information model according to the input parameters, then calculate and determine the objectives of each required optimization, get the corresponding evaluation criteria, find the relationship between the variable parameters and the objective function see, and output a series of solutions through the multi-objective optimization algorithm. In the pre-environmental planning stage in the system, it is necessary to select the housing environmental planning factors that affect the output solutions according to the optimization-seeking objectives, and to reduce the system computation, only the factors with greater influence are listed as variable variables, and the factors with less influence are fixed and set to common values. Referring to the industry involved norms and practices, the results of the design variable selection are obtained as shown in Fig. 4.

Figure 4.

Planning scheme design variable selection structure diagram.

It can be seen from Fig. 4 that the variables to be considered in the optimal design of residential environment are divided into fixed variables and variable variables. The former includes the standard building area of the house, the plan form of single building, and other design variables. The latter mainly includes the height, orientation, splicing form, and layout position of the house, which together constitute the design scheme of residential environment. The type of variables in Fig. 4 can also be fine-tuned according to the needs of specific design projects. Before determining the final optimization objective function, it is necessary to classify the optimization objectives. In general, optimization objectives can be divided into rigid objectives that must be met and flexible objectives that can be selectively met, and these objectives can be further divided into sub objectives. See Table 1 for the indicator system.

Table 1

Evaluation indicators of housing environment planning quality

Core target name	Total target name	Sub target no	Sub target name
Rigid target	Safety requirements	#01	Fire safety distance
		#02	Sight safety distance
	Mandatory index requirements	#03	Height limit control
		#04	Plot ratio control
Elastic target	Client requirements	#05	Landscape performance
		#06	Reasonable function
		#07	Environmental comfort
	Environmental requirements	#08	Energy consumption saving
		#09	Material consumption saving
	Development end requirements	#10	Increase value
		#11	Cost savings
	Design end requirements	#12	Aesthetic value of appearance
		#13	Design diversity

Combined with the evaluation index system in Table 1, the classification process and results can be obtained, as shown in Fig. 5.

Figure 5.

Process and results of stage optimization target categorization.

Then, referring to the evaluation standards of domestic and foreign housing environment planning, we can determine the performance evaluation primary indicators of the planning scheme are wind environment, thermal environment, light environment, sound environment and other environments, and the corresponding secondary indicators are wind speed and wind pressure, heat island intensity, shade area and shade rate, sunshine hours and lighting coefficient, indoor and outdoor noise level, volume ratio and green area rate. The following then design the mathematical model in the system, housing environment planning is essentially a dynamic multi-objective planning problem, its design variables are $X=[BS_{n},BO_{n},CF_{n},BP_{n},\textit{SFA}_{n},\textit{SFF}_{n}]$ , $BS_{n}$ , $BO_{n}$ , $CF_{n}$ , $BP_{n}$ , $\textit{SFA}_{n}$ , $\textit{SFF}_{n}$ represent the number of floors of the $n$ house, orientation (unit: degrees, the specified sitting north to south direction is 0 degrees, east to south is negative), residential collocation form (take the value of 1, 2, 3 represent point distribution, double row, and triple row, respectively), the location of the house datum point (the southern bottom edge of the house focus as the reference point, the planning area is cut into 3 m $\times$ 3 m grid, using the grid number positioning), standard floor area (unit square meters), standard floor plan form, and all variables are unrestricted variable attributes, except $BP_{n}$ variable is fixed as variable attributes. The constraints of the above design variables are set as $10\leqslant BS_{n}\leqslant 33$ , $-30\leqslant BO_{n}\leqslant 30$ , $CF_{n}=$ 1 or 2 or 3, $0\leqslant BP_{n}\leqslant N_{g}-1$ , $600\leqslant\textit{SFA}_{n}\leqslant 1000$ , $1\leqslant\textit{SFF}_{n}\leqslant 3$ according to the domestic and international design requirements and practices. After verification, it is found that the setting results of the above parameter constraints are reasonable. According to the aforementioned evaluation indexes of the housing environment planning scheme, the optimization objectives of the mathematical model are the volume ratio objective $f_{1}(X)$ , the open space performance objective $f_{2}(X)$ , the daylighting performance objective $f_{3}(X)$ , and the thermal environment performance objective $f_{4}(X)$ . The calculation methods of the objective functions of these four objectives are shown in Eqs (13) to (16), respectively.

$\displaystyle f_{1}(X)=\min 5-\textit{FAR}(X)$ (13)

In the Eq. (13), FAR is the plot ratio, and the larger the indicator, the greater the development benefit.

$\displaystyle f_{2}(X)=\min 1-\textit{OSP}(X)$ (14)

In Eq. (14), OSP is the open space potential of the house, which is the ratio of all the area in the area that can be converted into open space to the total area.

$\displaystyle f_{3}(X)=\min 1-\textit{SSR}(X)$ (15)

In Eq. (15), SSR is the house daylight satisfaction rate.

$\displaystyle f_{4}(X)=\min(\textit{MRI}-S(X))/(\textit{MRI}-W(X))$ (16)

In Eq. (16), MRI, $S()$ , $W()$ represent the overall average radiation intensity of the house, the overall radiation intensity of the house in summer and winter, respectively. The final result of several attempts and adjustments, the planning system of the housing environment planning program generation process is fixed in the form of Fig. 6.

Figure 6.

Flow of housing environment optimization plan generation.

The progressive layout in Fig. 6 refers to the distribution of buildings in a certain order, and here the single houses are selected to be laid out in a sequential row. The specified screening is divided into two types, one is to incorporate the houses before screening the grid according to the grid attributes, and the other is to screen the layout rationality of the scheme. So far, the design of the housing environment planning system based on the improved multi-objective optimization algorithm is completed.

4. Housing environment planning system performance test

To test the practical application value and quality of recommended solutions of a housing environment planning system based on an improved multi-objective optimization algorithm. A simulation test was designed and carried out. By adjusting the parameters for many times, the adjustment range of the algorithm parameters is set according to the common application of genetic algorithm, and verified by the test method of expanding the parameter setting range, this set of parameter value range is reasonable. The finally determined algorithm parameter settings for simulation test are shown in Table 2.

Table 2
Model parameter settings

Number	Parameter name	Numerical value	Number	Parameter name	Numerical value
#01	Mutation probability	0.12	#05	Variance Distribution Index	20
#02	Crossover probability	0.88	#06	Cross Distribution Index	20
#03	Population size	50	#07	Elite ratio	50%
#04	Variance ratio	0.5	#08	Grid size	$3m\times 3m$

The system logic is implemented in Python 3.0 programming language, the computer running memory is 8GB, CPU is i7-8700T, and the system is WIN10. Finally, the house environment in the simulation experiment is a square plan plot of $200m\times 200m$ , with all other buildings and environments around the planning plot that cannot be designed and adjusted. The results of the optimization search are selected: the normalized value of the objective function, the convergence algebra, the quality of Pareto optimal solutions (referred to as QPS), and the number of Pareto optimal solutions (referred to as NPS) index evaluation, and the calculation method of QPS is shown in Eq. (17).

$\displaystyle\textit{QPS}=1-\sqrt{\sum\limits_{i=1}^{K}{(F(X)\ast)^{2}}}$ (17)

In Eq. (17), $K$ is the dimension of Pareto front solution, and $F(X)\ast$ is the normalized value of all objective functions. In addition, the simulation test replaced the optimization algorithm with NSGA algorithm, xgboost algorithm, RESNET algorithm and the designer’s manual design method to build a comparative planning system. First, the FDA series of representative fda1 test functions are used to test each method, and the test results are evaluated by convergence metric (CM) and inverse generation distance (IgD). The test results show that the $t$ -test output p value of the data difference between the IgD and the comparison planning methods is 0.536, which is greater than the significance level, and it is considered that there is no significant difference. However, the CM index of the former is significantly lower than that of other comparison methods, indicating that the training convergence speed and population diversity of the research design method are not significantly different from that of the comparison method, but the converged solution is better than that of the comparison method. After the test, the normalized values $F_{1}(X)\ast$ and $F_{2}(X)\ast$ of the objective functions $F_{1}(X)$ and $F_{2}(X)$ are obtained, and the graph is shown in Fig. 7. In addition, the measurement type data in the test shall be subject to the f-difference significance test.

Figure 7.

Spatial distribution of Pareto optimal solution output by each planning system.

Figure 8.

Comparison of convergence performance of various systems.

Different colors in Fig. 7 are used to represent different housing environment planning systems, “p_s_ga” represents the housing environment planning system based on the improved multi-objective optimization algorithm designed in this study, “NSGA” represents the housing environment planning system based on the NSGA algorithm, and “artistic” represents the scheme manually designed by the designer. The black solid line represents the ideal Pareto frontier. It can be seen from Fig. 7 that the xgboost system as a whole is closest to the ideal Pareto front, but like the “NSGA” system, the distribution is more concentrated, and premature convergence is more likely to occur. The optimal solution set of the “p_s_ga” system as a whole is closest to the ideal Pareto front, and the distribution is scattered. Moreover, the difference significance test p value of the optimal solution data is 0.007, which indicates that there is a significant difference in the data. The optimal solution sets of RESNET system and artificial design method are also distributed more dispersed, but are farther from the ideal Pareto frontier than the “p_s_ga” system. It shows that the optimal solution output by the “p_s_ga” system performs better on the core targets $F_{1}(X)$ and $F_{2}(X)$ . Then analyze the convergence performance of each system, as shown in Fig. 8.

The subgraphs (a), (b), (c) and (d) in Fig. 8 are, respectively used to show the P_ S_ The change curve of $F_{1}(X)\ast$ and $F_{2}(X)\ast$ values of the intelligent planning system for housing environment constructed by GA algorithm, NSGA algorithm, RESNET algorithm and xgboost algorithm with the increase of iteration times. The manual design method does not have the number of training rounds, so it does not participate in the comparison here. The colors of the data lines in Fig. 8 are used to distinguish different normalized objective functions. According to Fig. 8_ S_ The $F_{1}(X)\ast$ and $F_{2}(X)\ast$ numerical convergence performance of the intelligent planning system for housing environment constructed by GA algorithm, RESNET algorithm and xgboost algorithm is good. With the increase of the number of iterations, both of them show a monotonic decreasing law and eventually converge. When the two objective functions converge, P_ S_ The normalized objective function values of GA algorithm planning system are 0.21 and 0.16, respectively, which are significantly lower than the planning system constructed by the latter two algorithms, and the value is the lowest in the comparison method. With the increase of the number of iterations, the values of the systems $F_{1}(X)\ast$ and $F_{2}(X)\ast$ constructed based on NSGA algorithm also show a downward trend with the whole, but there is a phenomenon of local rebound, which indicates that the convergence performance of the system is relatively poor, and the convergence speed of the two systems is faster and the convergence function value is higher, which also proves that the ability of the system to solve the global optimal solution is worse. Then analyze the change of the number of optimal solutions of each system in the training process. See Fig. 9 for the statistical results.

Figure 9.

Comparison of the number of Pareto optimal solutions of each system.

In Fig. 9, the horizontal axis represents the iterative training times of the system, and the comparison is based on 200 times. The vertical axis represents the number of Pareto optimal solutions output by the system under the premise of each iteration number. Different data line colors still represent different system types. It can be seen from Fig. 9 that with the increase of iteration times, the number of Pareto optimal solutions output by the intelligent planning system for housing environment constructed based on NSGA algorithm fluctuates repeatedly and greatly, and does not tend to be stable. However, with the increase of the number of iterations_ S_ The number of Pareto optimal solutions output by the intelligent planning system for housing environment based on GA algorithm, RESNET algorithm and xgboost algorithm generally increases first and then tends to be stable. When the number of iterations is less than 140, the number of Pareto optimal solutions output by the system also fluctuates greatly, but when the number of iterations is more than 140, the number of Pareto optimal solutions output by the system fluctuates significantly. When the number of iterations reaches 200, The output Pareto optimal solutions of the three systems are 44, 41 and 38, respectively. Then analyze the quality of Pareto optimal solution output by each system. See Fig. 10 for the statistical results.

Figure 10.

Quality comparison of Pareto optimal solution output by each system.

The vertical axis in Fig. 10 represents the quality of the Pareto optimal solution output by the system, and the evaluation index is QPS. The colors of different data lines represent different QPS statistical dimensions, and the subgraphs (a), (b), (c) and (d), respectively represent the values based on P_S_GA algorithm, NSGA algorithm, RESNET algorithm, and xgboost algorithm to build Pareto optimal solution quality statistical results of housing environment planning system. It can be seen from Fig. 10 that as the number of training iterations of the system increases_ S_ The maximum value, average value and minimum value of Pareto optimal solution quality index QPS of the system of GA algorithm, RESNET algorithm and xgboost algorithm all show a trend of first increasing and then stabilizing. When iteration $=$ 200, P_ S_ The maximum value, average value and minimum value of QPS in GA algorithm planning system are 0.88, 0.78 and 0.64, respectively, which are higher than the corresponding values of all comparative systems. However, as the number of training iterations of the system increases, the maximum, average and minimum values of the system QPS constructed based on the NSGA algorithm do not show a significant growth trend. Finally, the performance of main indicators of each system under the worst, normal and optimal conditions of initial parameters is analyzed, as shown in Table 3.

Table 3

Statistics of main performance indicators of each system under various initial parameters

Type of situation	Comparison indicator	P_S_GA	NSGA	ResNet	XGBoost	Artificial
Worst case	Ideal Pareto front average distance of the optimal solution	0.148	0.442	0.371	0.152	0.196
	$F_{1}(X)\ast,F_{2}(X)\ast$ mean	0.372	0.455	0.396	0.507	0.491
	Number of optimal solutions	43	31	37	35	/
	Optimal solution QPS mean	0.61	0.22	0.59	0.33	0.35
Common case	Ideal Pareto front average distance of the optimal solution	0.093	0.230	0.143	0.091	0.095
	$F_{1}(X)\ast,F_{2}(X)\ast$ mean	0.185	0.224	0.199	0.208	0.187
	Number of optimal solutions	44	29	41	38	/
	Optimal solution QPS mean	0.78	0.32	0.73	0.41	0.80
Best case	Ideal Pareto front average distance of the optimal solution	0.074	0.163	0.115	0.079	0.071
	$F_{1}(X)\ast,F_{2}(X)\ast$ mean	0.140	0.182	0.183	0.174	0.142
	Number of optimal solutions	45	25	43	38	/
	Optimal solution QPS mean	0.91	0.50	0.84	0.48	0.92

Pay attention to the worst case, normal case, and optimal case of parameter initialization based on the algorithm in Table 3. The reference industry characteristics correspond to the worst 20% of the manual design cases, the middle 60% of the quality, and the best 20% of the quality schemes. Observing Table 2, it can be seen that in the normal and optimal cases, the quality of the output scheme of the planning method constructed based on the P_S_GA algorithm and the manual planning method is roughly the same, and is significantly better than other common comparison methods, such as the normal case and the optimal case., the average QPS of the optimal solution for the planning method constructed based on the P_S_GA algorithm and the manual planning method are 0.78, 0.80 and 0.91, 0.92, respectively. However, in the worst case, the quality of the output solution of the artificial design scheme is significantly lower than that of the planning method based on the P_S_GA algorithm. For example, in the worst case, the QPS averages of the two optimal solutions are 0.61 and 0.35, respectively. The proposed residential environmental planning method is not much different from the manual planning results in the quality of the output scheme, but the output solution stability in extreme cases is higher than that of the manual design scheme.

In order to further verify the application value of the housing environment optimization design method based on the improved genetic algorithm proposed in this study, a domestic project under civil housing planning and construction is selected as an example, and the housing environment is designed using this method and manual method, respectively. For reasons of confidentiality, the specific information of the selected project cannot be disclosed. The case test results show that it takes 14.7 seconds for the method designed in this study to output the optimal design scheme set, and it takes 14.3 hours for the manual method to design. Moreover, after the evaluation of experts in the industry, the design schemes obtained by the two methods meet the requirements of various environmental design evaluation indicators.

5. Discussion

At present, the main living environment requirements of domestic and foreign residents for civil residences are concentrated in the following points. First, the proportion of non-residential land should be as small as possible to ensure that residents have enough space for outdoor activities. The second point is the extent to which non-residential land can be built into public open space. If there is enough non-residential land around the house, but very little of it can be developed into public open space, these spaces will not be able to provide more suitable spaces for residents. home value. The third point is the sunshine conditions, specifically, how much external surface area of the house can be covered by sunshine, and whether the heat supply of sunshine can meet the living and living needs of residents. The four objective functions of the housing environment optimization model proposed in this study are designed based on the above-mentioned residents’ needs.

Judging from the status quo of residential environmental planning, most domestic residential environmental planning and design are formed by artificial design, which is highly dependent on the designer’s personal experience, aesthetic style and other subjective factors, resulting in the quality of residential environmental planning largely determined by Due to the designer’s personal ability, if the designer’s ability is insufficient, he has no experience in environmental planning and design of a certain type of house, or deliberately adjusts the design method, it may lead to the situation that the environmental planning quality of the house cannot satisfy most residents. Therefore, carrying out this research and designing a housing environment planning system based on intelligent multi-objective optimization algorithm that can take into account various factors has certain application potential.

The analysis results of this research show that the planned output of the planning system based on the improved genetic algorithm is the ideal Pareto frontier average distance of the optimal solution, $F_{1}(X)\ast$ the $F_{2}(X)\ast$ mean value, the number of optimal solutions, and the QPS average value of the optimal solution under normal conditions. They are 0.093, 0.185, 44, and 0.78, which are obviously better than the output scheme of the intelligent house environment planning system constructed based on other algorithms, but slightly worse than the design of the artificial designer. The analysis results in the optimal case are consistent with those in the normal environment. On the contrary, in the worst case, the average distance between the ideal Pareto frontier, $F_{1}(X)\ast$ the $F_{2}(X)\ast$ mean value, the number of optimal solutions, and the QPS of the optimal solution between the system designed in this study and the optimal solution of the manual planning method are 0.148 and 0.148, respectively. 0.372, 43, 0.61 and 0.196, 0.491, none (the number of optimal solutions under the manual planning method is related to the subjective analysis ability, so this item is not shown) and 0.35. The former data is still significantly better than the output scheme of the smart house environment planning system based on other algorithms, and it is also significantly better than the artificially designed scheme. It shows that the planning method proposed in this study not only has the planning ability that is highly close to the quality of the artificial design scheme under normal circumstances, but also the quality of the planning scheme is less affected by extreme negative parameters, and the overall stability is higher than that of the planning constructed by other intelligent algorithms. Systems and manual design approaches. This is because the Pareto optimal solution is used in the improved genetic algorithm to sort and segment the objective function values, so as to calculate the moving direction brought by the center of each segment of the solution set, so that the convergence accuracy and speed of subsequent calculations will be faster.

6. Conclusion

In order to improve the efficiency and rationality of housing environment planning, this research attempts to construct an improved multi-objective optimization algorithm by integrating the Pareto solution set and segmented prediction ideas into the genetic algorithm, and based on this, a multi-objective intelligent housing environment optimization multi-objective design is designed. Intelligent algorithm system. The simulation results show that the system designed in this study is closer to the ideal Pareto frontier as a whole than the system constructed based on the NSGA algorithm, with better convergence and no convergence rebound phenomenon. When iteration $=$ 200, the former are 0.21 and 0.16 $F_{1}(X)\ast$ , $F_{2}(X)\ast$ respectively, which are significantly higher than those of the comparative intelligent planning methods, and the corresponding numerical difference with the manual planning results are small. At this time, the number of Pareto optimal solutions of this method is 44, and the QPS average value of the optimal solution quality index is 0.78, the number and quality of QPS Pareto optimal solutions of the planning system constructed based on NSGA algorithm, ResNet algorithm and XGBoost algorithm are 44, 41, 38 and 0.32, 0.73, 0.41, respectively. The simulation experimental data proves that the intelligent housing environment planning system based on the improved multi-objective optimization algorithm proposed in this study can output more design schemes with better overall quality than the traditional housing environment planning system, and it is more stable in multiple runs. higher. However, due to the limitation of research conditions, the actual community planning project could not be selected to verify the value of the design scheme of the system, and the intelligent planning system designed in this study still has the disadvantage of slow calculation speed, which is also the place to be improved in the future improvement research.

References

Leng

Han

. Effect of environmental planning on elderly individual quality of life in severe cold regions: A case study in northeastern China. Sustainability. 2022; 14(6): 1–17.

Yang

Wang

. Design of high-isolation wideband dual-polarized compact MIMO antennas with multiobjective optimization. IEEE Trans Antennas Propag. 2018; 66(3): 1522–1527.

Zille

Ishibuchi

Mostaghim

Nojima

. A framework for large-scale multiobjective optimization based on problem transformation. IEEE Trans Evol Comput. 2018; 22(2): 260–275.

Zhang

. Thermodynamic design of public space based on outdoor thermal comfort – Take Yangpu Bridge riverside park competition scheme as an example. IOP Conf Ser: Earth Environ Sci. 2019; 310(3): 1–6.

Takebayashi

Kyogoku

. Thermal environmental design in outdoor space focusing on radiation environment influenced by ground cover material and solar shading, through the examination on the redevelopment buildings in front of central osaka station. Sustainability. 2018; 10(2): 337–347.

Clarissa

Prakoso

Dewi

. Design strategies of life outside and life inside for livable multi-family housing environment. IOP Conf Ser: Earth Environ Sci. 2021; 764(1): 012019–012026.

Ade-Ojo

. Awareness of the LEED requirements for green housing development among built-environment professionals in Nigeria. Built Environ Project Asset Manage. 2022; 12(4): 521–536.

Alpman

. Multiobjective aerodynamic optimization of a microscale ducted wind turbine using a genetic algorithm. Turk J Electr Eng Comput Sci. 2018; 26(1): 618–629.

Dovgan

Gams

Filipic

. A real-time multiobjective optimization algorithm for discovering driving strategies. Transp Sci. 2019; 53(3): 695–707.

10.

Gao

Dang

. A decomposition-based harmony search algorithm for multimodal multiobjective optimization. Discrete Dyn Nat Society. 2022; 2022(5): 1–12.

11.

Zhang

Wang

. Deep reinforcement learning for multiobjective optimization. IEEE Trans Cybern. 2020; 51(6): 3103–3114.

12.

Wang

Zhu

Song

. Derivative-free feasible backtracking search methods for nonlinear multiobjective optimization with simple boundary constraint. Asia-Pac J Oper Res. 2019; 36(3): 1950012.1–1950012.15.

13.

Chen

Yao

. Two-archive evolutionary algorithm for constrained multi-objective optimization. IEEE Trans Evol Comput. 2019; 23(2): 303–315.

14.

Cai

Liu

. Hierarchical clustering of bipartite networks based on multiobjective optimization. IEEE Trans Network Sci Eng. 2020; 7(1): 421–434.

15.

Wang

Zhou

Yan

. Optimizing train-set circulation plan in high-speed railway networks using genetic algorithm. J Adv Transp. 2019; 2019(PT.1): 8526953.

16.

Kwong

Zhang

. Learning to decompose: A paradigm for decomposition-based multiobjective optimization. IEEE Trans Evol Comput. 2018; 23(3): 376–390.

17.

Zareizadeh

Helfroush

Rahideh

Kazemi

. A robust gene clustering algorithm based on clonal selection in multiobjective optimization framework. Expert Syst Appl. 2018; 113(15): 301–314.

18.

Diaz

Behr

Acero

. Coastal housing recovery in a postdisaster environment: A supply chain perspective. Int J Prod Econ. 2022; 247(C): 108463–108469.

19.

Lei

. Promotion and renewal of the outdoor environment of the collective housing that promotes health-Based on the post-epidemic perspective. J Environ Prot. 2021; 12(12): 16–27.

20.

Guo

. Research on design method and construction key points of prefabricated building structure combined with machinery. J Physics Conf Ser. 2021; 1744(2): 022091–0220104.

Multi-objective intelligent algorithm model design for housing environment optimization

Abstract

Keywords

1. Introduction

2. Related works

3. Design of housing environment planning method based on improved multi-objective intelligent algorithm

3.1 Multi-objective optimization algorithm design incorporating Pareto solution set and segment prediction

Table 2 Model parameter settings

6. Conclusion

References

Table 2
Model parameter settings