CN113722972B - Indoor illumination optimization method based on positive and negative spiral whale searching algorithm - Google Patents
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Abstract
The application relates to an indoor illumination optimization method based on a positive and negative spiral whale searching algorithm. Firstly, providing a positive and negative spiral whale searching algorithm, wherein the positive and negative spiral searching algorithm comprises two improved mechanisms of inner sine and cosine spiral surrounding and outer sine and cosine spiral exploration; and then, based on a positive and negative spiral searching whale algorithm, taking the illuminance value and the installation position of a lamp in the indoor space as an optimization target, taking the building illumination design standard or the requirement of a user as the lower limit of an objective function value, multiplying the objective function value by an upper limit weight parameter to be taken as the upper limit of the objective function, and taking the sum of absolute errors of illuminance exceeding the upper limit and the lower limit after regional simulation as an adaptive function, thereby realizing indoor illuminance optimization. The method can realize the optimization of indoor illuminance.
Description
Technical Field
The application relates to the field of artificial intelligence, in particular to an indoor illumination optimization method based on a positive and negative spiral whale searching algorithm, which is applied to solving the problem of the lack of an optimal design function of international indoor illumination software DIALux evo.
Background
The whale algorithm is a novel bionic algorithm in the field of artificial intelligence and is mainly used for solving the problem of engineering optimization of complex variables or multiple targets. In the development process of the algorithm, three-layer technology needs to be paid attention to. Global exploration-finding the optimal solution meeting the target in the solution space, and the algorithm itself must have the capability of widely exploring the solution space; local search-when the algorithm is focused on the area identified as having the optimal solution, performing an accurate search to find an optimal result that meets the goal; the trip mechanism-typically having a plurality of sub-optimal solutions in the solution space, the algorithm needs a specific random or other pattern mechanism to trip in order to avoid falling into the sub-optimal solution.
(1) The standard whale algorithm was a crowd-sourcing algorithm proposed by mirjallii and Lewis in 2016, and was an optimization algorithm implemented by mimicking the predatory behavior mechanism of whale. In the whale algorithm, assuming that the number of whale populations is N and the dimension of the search space is Dim, the position of the ith whale in the Dim dimension is expressed as: x is X i ＝(X 1,i ,X 2,i ,...,X Dim,i ) I=1, 2,3., N, three specific predation modes for whales are described below:
a) Surrounding prey
In the whale algorithm, the position of the prey is determined first, through the surrounding, so that prey is performed, but the whale cannot anticipate the position of the prey in advance, so that the current optimal solution is assumed to be the position of the prey first, and other individuals in the population approach the target prey, and the behavior is expressed as follows:
X(t+1)＝X s (t)-A·D (1)
D(t)＝|C·X s (t)-X(t)| (2)
A(t)＝2a(t)·rand-a(t) (3)
C＝2·rand (4)
a(t)＝(2-2t/T max ) (5)
in the above formula, t represents the current iteration number; a is a surrounding step parameter; c is a random range parameter; x is X s The optimal solution position for the sub-population; x is the individual position of whale; a is a convergence factor of 2 decreasing linearly from 0; rand is a random number from 0 to 1; t (T) max Is the maximum number of iterations.
b) Spiral bubble net attack
The whale individual first calculates the distance from the prey, then swims upwards in a spiral form while spitting out bubbles of unequal sizes to prey on the fish and shrimp, and the mathematical model is as follows:
D′(t)＝|X s (t)-X(t)| (6)
X′(t+1)＝D′(t)·e bl ·cos(2πl)+X s (t) (7)
where D' represents the distance from the ith whale to the prey, l is a random value and b is a constant.
c) Random search for prey
When the whale is in a predation mode of non-spiral bubble net attack and surrounding prey, the whale can update the position of the whale along with the position change of a companion, and the link carries out random large-scale search on the prey so as to determine the next position which needs to be updated. Therefore, when the whale searches in a larger range and A is more than or equal to 1, the behavior of searching the hunting globally is performed by using the formula (5), so that the problem of falling into a local optimal solution is avoided, and the expression of the behavior is as follows:
in the middle ofRepresents the distance, X, of an ith whale at random rand The position of one whale is random in the current population. The standard whale algorithm can realize rapid convergence in a group-based optimal mode, but has a defect in global searching, so that the problem of algorithm precocity is easy to occur in searching a function optimal solution with a multi-peak characteristic, and a suboptimal solution is not easy to jump out.
(2) Indoor illuminance calculation
DIALux evo is a type of design software capable of illuminance planning, and can be realized from illuminance simulation of a typical general house, office, multi-floor, outdoor, street or other space. In addition, the system also has the relevant calculation functions of lighting professional design, illumination simulation 3D, power supply evaluation and the like. In the illuminance calculation part, the light distribution curve data of various lamps with different brands are usually imported, the space illuminance condition is calculated according to the lamp positions set by a user in the simulation area, or the lamps with specified brands are imported in the simulation space, and the software performs uniform configuration design under the condition of space average illuminance.
The prior art has the following defects:
(1) Part of a biological algorithm
For the spiral bubble attack formula in the standard whale algorithm, the updating track of individuals (black circles) at different positions is inspected under the calculation of the spiral bubble attack formula (7) based on the optimal solution (black boxes) of the current group and different random values l, and the updating track of the individuals is shown in figure 1.
From fig. 1, it can be observed that the update track of an individual is only in a single vector relationship with the position of the current optimal solution. In addition, if the algorithm converges rapidly in the early stage, the "random search for prey" equation (9) loses the ability to globally explore or trip sub-optimal solutions.
(2) Indoor illuminance calculation
After the user determines the brand and model of the lamp, the DIALux evo software is assigned a position in a simulation space or is configured uniformly by the software by taking the space average illuminance as a target, and illuminance calculation is performed. Therefore, the software currently lacks the following two functions, 1) how many illumination lamps are needed by the simulation space to meet building illumination regulations; 2) Lamps of the same illuminance have to be positioned where they are suitable.
Disclosure of Invention
The application aims to provide an indoor illumination optimization method based on a positive and negative spiral whale searching algorithm, which can realize optimization of indoor illumination.
In order to achieve the above purpose, the technical scheme of the application is as follows: an indoor illumination optimization method based on a positive and negative spiral whale searching algorithm firstly provides a positive and negative spiral whale searching algorithm, and comprises two improved mechanisms of inner sine and cosine spiral surrounding and outer sine and cosine spiral exploration; and then, based on a positive and negative spiral searching whale algorithm, taking the illuminance value and the installation position of a lamp in the indoor space as an optimization target, taking the building illumination design standard or the requirement of a user as the lower limit of an objective function value, multiplying the objective function value by an upper limit weight parameter to be taken as the upper limit of the objective function, and taking the sum of absolute errors of illuminance exceeding the upper limit and the lower limit after regional simulation as an adaptive function, thereby realizing indoor illuminance optimization.
In an embodiment of the present application, the inner sine and cosine spiral surrounding is implemented as follows:
because the index term in the standard whale algorithm can not be switched in time according to the requirement, disturbance factors are introduced to replace natural logarithmic terms, such as formula (1), in order to simultaneously consider the requirements of global exploration and local search
δ(t)＝exp(-30(t/T max ) b ) (1)
Wherein T is max B is used for determining a parameter decrementing time period for the total calculation times; when the algorithm is in an initial stage, the disturbance factor is maintained at 1, an individual can conduct global searching in a maximum distance mode, and when the specified time period is reached, the disturbance factor is suddenly reduced to be close to 0 so as to meet the accuracy of local searching; the ideal spiral movement track theory gradually approaches from the initial position of the individual to the optimal solution position, and according to the problem, the mathematical model of spiral bubble net attack in the standard whale algorithm is modified as follows
Wherein X is s For the sub-population optimal solution position, X i,s The i-th variable value for the current optimal solution,is the update position surrounded by the j-th whale individual by the sine and cosine spiral, and is +.>The ith variable value of the jth individual, < +.>Is X i,s And->Straight line distance of>Then is X i,s And->The included angle between the two is t, i is the current iteration number, i is a random value from 0 to 1, and n is the largest dimension of the variable.
In an embodiment of the present application, the external sine and cosine spiral exploration is implemented as follows:
if the individual can search the spiral moving track by taking the position of the optimal solution as the center, the concept of reverse elite learning is derived, and an external sine and cosine spiral exploration is provided to replace a random searching prey formula in a standard whale algorithm, wherein the specific formula is as follows:
wherein X is r X is the location of random individuals in the population i,r For the ith variable value of the random individual,is the update position surrounded by the j-th whale individual by the external sine and cosine spiral, and the +.>The ith variable value of the jth individual, < +.>Is X i,r And->Straight line distance of>Then is X i,r And->The included angle between the two.
In an embodiment of the present application, based on the forward and backward spiral whale searching algorithm, the indoor illuminance optimization process is implemented according to IO rd 、I rd And O rd To select the spiral formulas in the internal sine and cosine spiral surrounding and external sine and cosine spiral exploring, wherein IO rd If the number is larger than 0.5, selecting an inner sine and cosine spiral for surrounding, otherwise, selecting an outer sine and cosine spiral for exploring; if I rd If the number is larger than 0.5, selecting an inner sine spiral for surrounding, otherwise selecting an inner cosine spiral for surrounding; if O rd And (3) selecting an outer sine spiral exploration if the number of the outer sine spirals is larger than 0.5, otherwise selecting an outer cosine spiral exploration.
Compared with the prior art, the application has the following beneficial effects:
1) The intelligent illuminance design is performed by adopting a group intelligent algorithm in the artificial intelligence field according to building illuminance regulations, space environment or demands of life, work and the like of users as optimization conditions.
2) The design method has the advantages that the illumination value and the installation position of the lamp are used as adjustment variables in the intelligent optimization scheme, compared with the DIALux evo prior art, the design efficiency can be greatly improved, the design result meets the illumination regulation requirement, and the lamp is found to meet the regulation minimum illumination value, so that the cost of lamp cost or the space electricity requirement can be reduced.
3) Besides taking the lamp illumination value and the installation position as intelligent illumination optimization schemes, other conditions such as the number of lamps, the installation mode of the lamps, the height or the electricity demand can be extended to realize other intelligent illumination designs.
Drawings
Fig. 1 shows possible updated trajectories of spiral bubble attack formulas for different individuals.
FIG. 2 is a flow chart of the forward and reverse spiral whale searching algorithm of the application.
Fig. 3 is an indoor building design.
Fig. 4 is a construction diagram of an indoor building.
FIG. 5 is a general luminance requirement weight chart.
Fig. 6 is a diagram of the illuminance demand weight for the elderly.
Fig. 7 is a sine-cosine spiral surrounding trace plot (t-th iteration).
Fig. 8 is a sine-cosine spiral surrounding trajectory graph (increasing number of iterations).
Fig. 9 is a sine-cosine spiral surrounding trace plot (t-th iteration).
Fig. 10 is a simulation diagram of the illuminance of a preset lamp.
Fig. 11 is an illuminance value optimum simulation diagram.
Fig. 12 is a mounting position optimum simulation diagram.
Detailed Description
The technical scheme of the application is specifically described below with reference to the accompanying drawings.
The application provides an indoor illumination optimization method based on a positive and negative spiral whale searching algorithm, which comprises the steps of firstly, providing a positive and negative spiral whale searching algorithm, wherein the positive and negative spiral whale searching algorithm comprises two improved mechanisms of internal sine and cosine spiral surrounding and external sine and cosine spiral exploration; and then, based on a positive and negative spiral searching whale algorithm, taking the illuminance value and the installation position of a lamp in the indoor space as an optimization target, taking the building illumination design standard or the requirement of a user as the lower limit of an objective function value, multiplying the objective function value by an upper limit weight parameter to be taken as the upper limit of the objective function, and taking the sum of absolute errors of illuminance exceeding the upper limit and the lower limit after regional simulation as an adaptive function, thereby realizing indoor illuminance optimization.
The following is a specific implementation procedure of the present application.
1) Positive and negative spiral whale searching algorithm
Aiming at the characteristic that the standard whale algorithm aims at group optimization to realize rapid convergence, the method is poor in global exploration, and the algorithm is easy to early mature and is not easy to jump out of suboptimal solutions. Thus, the following point concept is proposed
(1) Inner sine and cosine spiral enclosure
The index term in standard whale algorithm can not be switched in time according to the requirement, in order to consider the requirements of global exploration and local search simultaneously, a disturbance factor is introduced to replace natural logarithmic term, as shown in formula (1)
δ(t)＝exp(-30(t/T max ) b ) (1)
Wherein T is max For the total number of calculations b may be used to determine the parameter decrementing period. At the beginning of the algorithm, the perturbation factor is maintained at 1, the individual performs global search at the maximum distance, and after reaching a specified time period, the perturbation factor is reduced to approach 0 to meet the accuracy of local search. The ideal spiral movement trajectory is gradually approaching from the initial position of the individual to the position of the optimal solution. According to the problem, the following correction is carried out on the mathematical model formula of the spiral bubble net attack in the standard whale algorithm
Wherein X is s For the sub-population optimal solution position, X i,s The i-th variable value for the current optimal solution,is the update position surrounded by the j-th whale individual by the sine and cosine spiral, and is +.>The ith variable value of the jth individual, < +.>Is X i,s And->Straight line distance of>Then is X i,s And->The included angle between the two is t, i is the current iteration number, i is a random value from 0 to 1, and n is the largest dimension of the variable.
(2) External sine and cosine spiral exploration
The concept of reverse elite learning is introduced, and the main idea is to solve a problem in a feasible way, calculate the reverse solution of the problem, evaluate the original solution and the reverse solution, and select a solution with better quality from the solution as an individual of the next generation. The "external sine and cosine spiral search" is a concept of searching outwards by using the distance between the individual center and the random individual position as radius to search outwards and combining the number of attempts to derive reverse elite learning, instead of searching hunting formulas in the original literature, its formulas are as (5) and (6)
Wherein X is r X is the location of random individuals in the population i,r For the ith variable value of the random individual,is the update position surrounded by the j-th whale individual by the external sine and cosine spiral, and the +.>The ith variable value of the jth individual, < +.>Is X i,r And->Straight line distance of>Then is X i,r And->The included angle between the two.
(3) Random number of trial times and mode switching
The mode switching random numbers are all random numbers from 0 to 1, wherein IO rd For the selection of internal spiral surrounding or external spiral exploration, I rd And O rd Is the choice of sine and cosine in the spiral formula. In addition, the concept of the number of attempts is introduced, and a plurality of times of calculation is performed in the same iteration process to improve the probability of searching the optimal solution.
2) Data verification results
In order to highlight the superiority of the positive and negative spiral whale searching algorithm, 17 evaluation functions are provided for carrying out independent test results of 30 times and 1000 times of algorithm iteration times, and the expression, the test dimension, the search range and the optimal solution of the evaluation functions are shown in table 1.
Table 1 expression, test dimension, search range and optimal solution
And other novel bionic algorithms, such as standard whale algorithm (WOA) 1, wolf optimization algorithm (GWO) 2, firefly Algorithm (FA) 3 and classical particle swarm optimization algorithm (PSO) 4, are used for comparing the searching performance of 50 groups, and the related parameters of each algorithm are shown in Table 2.
Table 2 algorithm parameter settings
The optimal solutions, average optimal solutions and standard deviations of the performance indexes of the 17 evaluation functions corresponding to different algorithms are shown in table 3. It can be seen from table 3 that the improved whale algorithm (IWOA) according to the present application has superior performance in terms of both preferential ability and stability of the algorithm.
TABLE 3 simulation data results
3) Indoor illuminance space target value concept
DIALux evo software can only be uniformly configured with the average illuminance as a target according to the spatial situation. Building lighting design standard GB 50034-2013_5000 was introduced as a standard for the overall space illuminance, for example residential building lighting, as shown in table 4.
Table 4 Standard illumination values for residential buildings
And (3) formulating an objective function lower limit of the space illuminance through the table information, avoiding eye injury caused by overhigh illuminance, and taking the objective function multiplied by an upper limit weight parameter as an objective function upper limit. Such as: the standard value of a general living room active area is 100 (lx), the upper limit of the illuminance of a region is 130 (lx) when a weight value is set to 0.3, and the sum of absolute errors of the illuminance exceeding the upper and lower limits after region simulation is taken as an adaptive function.
Taking simulation fig. 3-6 as an example, fig. 3 is an indoor building design drawing for simulation, fig. 4 is a structural diagram for removing only reserved structure and simulation space of furniture, and fig. 5 and 6 are respectively illuminance weight diagrams set according to the above table.
4) Indoor illumination optimization method based on positive and negative spiral whale searching algorithm
The illumination value, the position, the installation height or the electric power of the lamp in the simulation space are used as optimization targets, the building illumination design standard GB 50034-2013_5000 or the user requirement is manufactured into a weighted space similar to the one in FIG. 5 or FIG. 6 as the lower limit of the objective function value, the weighted space is multiplied by the upper limit weight parameter to be used as the upper limit of the objective function, and the sum of absolute errors of the illumination exceeding the upper limit and the lower limit after the regional simulation is used as the adaptive function, so that the indoor illumination optimization design is realized.
The method has the specific advantages that:
(1) In the positive and negative spiral searching whale algorithm, the position of the individual and the optimal solution in fig. 1 is taken as an example, and the possible updating position of the individual at the same iteration time point is shown in fig. 7, so that the updated position can be observed to search in a circular or elliptical mode by taking the optimal solution as the center, and the problem of convergence of early algorithm calculation is avoided. When the iteration times are gradually increased, the individual update positions are gradually gathered towards the optimal solution positions, and the characteristic of local search is reflected, as shown in fig. 8.
(2) Also taking the positions of the individuals and the optimal solutions in fig. 1 as examples, the update formulas of the two individuals are modified into the "external sine cosine spiral exploration" in the positive and negative spiral searching whale algorithm, and the positions of the optimal solutions in the group are regarded as random individuals, and the simulation results are shown as the track diagrams of the coordinates (-1, 7) and (5, -3) in fig. 9. The method can observe that the updating track is searched outwards by taking the individual as the center and taking the distance between the individual and the optimal solution position as the radius, so that the global searching capability in the initial calculation stage can be effectively improved.
(3) Simple example of indoor design
In order to highlight the performance of the indoor optimization design, fig. 4 is taken as an example of a simulation space, and meanwhile, when the lamps of the living room, the dining table, the vestibule and the washroom are simultaneously turned on, how to select the illuminance and the installation position of the lamps can meet the basic requirements of table 1.
First, one ceiling lamp of 1800lx is arranged in a dining table and a living room, and one ceiling lamp of 1200lx is arranged in a vestibule and a toilet, so that light source shielding is considered, and other illumination loss conditions are not considered. With table 1 as an optimization target, the upper limit weight parameter was set to 0.3, and the sum of absolute errors was found to be 5.68e+5 with 0.1 meter as a calculation unit in order to reduce the calculation amount. The space illuminance simulation is shown in fig. 10. Then, the following steps are carried out: 1) The simulation space can meet building illuminance regulations only by the lamps with the illuminance required by the simulation space; 2) The lamps with the same illumination have to be arranged where to be suitable, and two problems are taken as the optimal design problems:
1) The simulation space can meet building illuminance regulations only by the lamps with the illuminance required by the simulation space;
the illumination of the lamp is regarded as an optimization variable based on the configuration position of fig. 10, and the search range is set to be 0 to 3000 (lx). It can be found that the minimum illuminance required to meet the set illuminance requirement is dining table 501.9 (lx), living room 1908 (lx), vestibule 497 (lx) and washroom 499.4 (lx), and the total absolute error is 3.8023e+5, and the simulation result is shown in fig. 11. It can be observed that the illumination of the ceiling lamp of the living room is not greatly changed, and the illumination of the rest lamps can be reduced to about 500 (lx), so that the electricity consumption condition and the lamp cost can be greatly reduced.
2) Lamps of the same illuminance have to be positioned where they are suitable.
The total absolute error of 3.53e+5 was obtained by optimizing the lamp position in the designated area (living room/dining table/entrance/washroom) with the minimum illuminance as shown in fig. 11, and the simulation result is shown in fig. 12. From the optimization result of fig. 12, the ceiling lamp of the bathroom can be changed to a wall lamp with the same illumination to achieve the optimal illumination optimization design.
Reference is made to:
[1]Mirjalili S,Lewis A.The whale optimization algorithm.Advances in Engineering Software,2016,95:51-67.
[2]Mirjalili S,Mirjalili S M,Lewis A.grey wolf optimizer.Advances in Engineering Software,2014,69(3):46-61.
[3]Yang X.S.,Firefly algorithm for multimodal optimization.LNCS 5792:Proceeding ofthe 5th International Conference on Stochastic Algorithm:Foundation andApplications,Sapporo,Japan,2009,Berlin,Heidelberg:Springer,2009,169-178.
[4]Kennedy,J.,Eberhart,R.Particle swarm optimization.Proc.of the IEEE International Conference on Neural Networks,pp.1942-1948,(1995).。
the above is a preferred embodiment of the present application, and all changes made according to the technical solution of the present application belong to the protection scope of the present application when the generated functional effects do not exceed the scope of the technical solution of the present application.
Claims (3)
1. The indoor illumination optimization method based on the positive and negative spiral whale searching algorithm is characterized in that firstly, the positive and negative spiral whale searching algorithm is provided, and the method comprises two improved mechanisms of internal sine and cosine spiral surrounding and external sine and cosine spiral exploration; then, searching whale based on positive and negative spiralsThe algorithm takes the illuminance value and the installation position of the lamp in the indoor space as an optimization target, takes the building illumination design standard or the requirement of a user as the lower limit of an objective function value, takes the upper limit weight parameter as the upper limit of the objective function, and takes the sum of absolute errors of illuminance exceeding the upper limit and the lower limit after area simulation as an adaptation function, so that the indoor illuminance optimization is realized; based on positive and negative spiral whale searching algorithm, IO is needed for realizing indoor illumination optimization process rd 、I rd And O rd To select the spiral formulas in the internal sine and cosine spiral surrounding and external sine and cosine spiral exploring, wherein IO rd If the number is larger than 0.5, selecting an inner sine and cosine spiral for surrounding, otherwise, selecting an outer sine and cosine spiral for exploring; if I rd If the number is larger than 0.5, selecting an inner sine spiral for surrounding, otherwise selecting an inner cosine spiral for surrounding; if O rd If the number is more than 0.5, selecting an outer sine spiral search, otherwise, selecting an outer cosine spiral search; wherein IO (input/output) rd For the selection of internal spiral surrounding or external spiral exploration, I rd And O rd The sine and cosine in the spiral formula are selected respectively.
2. The indoor illumination optimization method based on the positive and negative spiral whale searching algorithm according to claim 1, wherein the internal sine and cosine spiral surrounding is realized as follows:
because the index term in the standard whale algorithm can not be switched in time according to the requirement, disturbance factors are introduced to replace natural logarithmic terms, such as formula (1), in order to simultaneously consider the requirements of global exploration and local search
δ(t)＝exp(-30(t/T max ) b ) (1)
Wherein T is max B is used for determining a parameter decrementing time period for the total calculation times; when the algorithm is in an initial stage, the disturbance factor is maintained at 1, an individual can conduct global searching in a maximum distance mode, and when the specified time period is reached, the disturbance factor is suddenly reduced to be close to 0 so as to meet the accuracy of local searching; the ideal spiral movement track theory gradually approaches from the initial position of the individual to the position of the optimal solutionAccording to this problem, the mathematical model of the spiral bubble network attack in the standard whale algorithm is modified as follows
Wherein X is s For the optimal solution position of the current sub-population, X i,s The i-th variable value for the current optimal solution,is the update position surrounded by the j-th whale individual by the sine and cosine spiral, and is +.>The ith variable value of the jth individual, < +.>Is X i,s And->Straight line distance of>Then is X i,s And->The included angle between the two is t, i is the current iteration number, i is a random value from 0 to 1, and n is the largest dimension of the variable.
3. The indoor illumination optimization method based on the positive and negative spiral whale searching algorithm according to claim 1, wherein the external sine and cosine spiral exploration is realized as follows:
if the individual can search the spiral moving track by taking the position of the optimal solution as the center, the concept of reverse elite learning is derived, and an external sine and cosine spiral exploration is provided to replace a random searching prey formula in a standard whale algorithm, wherein the specific formula is as follows:
wherein X is r X is the location of random individuals in the population i,r For the ith variable value of the random individual,is the update position surrounded by the j-th whale individual by the external sine and cosine spiral, and the +.>The ith variable value of the jth individual, < +.>Is X i,r And->Straight line distance of>Then is X i,r And->The included angle between the two is t, i is the current iteration number, i is a random value from 0 to 1, and n is the largest dimension of the variable.
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