CN111325306A - ABC-PSO hybrid algorithm-based water supply pump set scheduling method - Google Patents
ABC-PSO hybrid algorithm-based water supply pump set scheduling method Download PDFInfo
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Abstract
The invention discloses an optimized scheduling method of a water supply pump group based on an ABC-PSO hybrid algorithm of an artificial bee colony algorithm and a particle swarm algorithm, which combines the exploration capability of ABC and the solving capability of the PSO algorithm, adds an information exchange mechanism in the evolution process, namely, meets certain conditions to transmit search information in two groups, and can still achieve the required solution set precision while ensuring the solving efficiency. According to the individual performance and the actual running state in the pump set, reasonable water supply tasks are distributed for the water pumps, the pressure in the pipe network is balanced, the water use comfort degree is met, the water supply flow is reduced, and the leakage in the pipe network is reduced.
Description
Technical Field
The invention relates to a water supply pump set optimization scheduling method based on an ABC-PSO hybrid algorithm of an Artificial bee colony Algorithm (ABC) and a Particle Swarm Optimization (PSO), and belongs to the technical field of automatic control and communication information.
Background
The urban scale is getting bigger and bigger, the population is gathered in the city, the domestic water accounts for the urban water and is increased gradually, the total amount of the domestic water of the residents is large, the consumption of all people is high, and the water-saving potential is large nowadays, under the condition, how to realize the water-saving goal of the garden under the existing water supply facility condition is particularly important. The method takes the real-time water supply optimization scheduling of the urban park as a research object and water conservation as a target, and because close contact exists among all levels of pump stations in the water supply system, a single pump station and a plurality of machine sets work together, and the working condition is complex, the parallel pump set should be used as an important optimization object in the water supply scheduling system.
The existing water utilization scheduling generally aims at reducing the water supply cost, omits the application of water conservation and lacks research on the aspect of water conservation; on the other hand, the water supply scheduling is only based on historical scheduling rules, and water supply waste is caused to a certain extent due to conservation.
At present, the intelligent algorithm is widely applied to the field of engineering practice, for example, a novel swarm intelligent algorithm such as an artificial bee swarm Algorithm (ABC) has the defects of few parameters, easy realization, strong searching capability, reduced searching precision and the like. The Particle Swarm Optimization (PSO) has strong local searching capability, but falls into local optimum due to the reduction of population diversity.
Disclosure of Invention
The whole water supply dispatching system is in a multi-dimensional and nonlinear state, so that the ABC-PSO hybrid algorithm is obtained by adopting a double population evolution strategy in the solving algorithm, the exploring capacity of ABC and the solving capacity of PSO algorithm are combined to solve, the effectiveness of the ABC-PSO hybrid algorithm provided by the invention is simulated and verified by using campus water data of Hebei engineering university, and the required solution set precision can be achieved while the solving efficiency is ensured.
The invention adopts the following technical scheme:
and establishing a scheduling model under the condition of giving water supply flow and water supply lift by using water use data, water supply network operation information and pump set working condition characteristics. According to the individual performance and the actual running state in the pump set, reasonable water supply tasks are distributed for the water pumps, the pressure in the pipe network is balanced, the water use comfort degree is met, the water supply flow is reduced, and the leakage in the pipe network is reduced.
Drawings
FIG. 1 is a flow chart of an ABC-PSO hybrid algorithm; and
FIG. 2 is a graph of water supply after optimal scheduling.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
Firstly, establishing a mathematical model of a water supply pump set optimization scheduling model:
(1) an objective function:
some pump station is connected in parallel by n constant speed pumps and m speed governing pumps, and the minimum water supply is used as a target function:
F＝∑ωdQNd+∑SbQNb
in the formula QNd-rated water supply flow rate of the constant speed pump d;
QNb-rated water supply flow rate of variable speed pump b;
ωdthe control decision variable of the constant speed pump d has two states, 1 represents opening, and 0 represents closing;
Sbthe ratio of the rotational speed of the variable speed pump b is [0.7,1 ]]Is continuously variable.
Wherein, the control decision variable omega of the constant speed pumpdAnd the rotation speed ratio S of the variable speed pumpbRespectively, represented by one coordinate value of the solution vector.
(2) Constraint function:
① water supply restriction, the sum of the water supply flow of each water pump is not less than the sum of the water flow and the leakage flow of each device in the period:
in the formula Qe，t-the water supply flow rate of the water pump e during the time period t;
qαβ,t-pipe network leakage flow between nodes α, β during time period t.
②, the flow is restricted, the water supply flow of each water pump is within the allowable range of the water supply capacity:
Qmin,e≤Qe≤Qmax,e
in the formula Qmin,e-minimum supply flow of water pump e;
Qmax,e-maximum water supply flow of the water pump e;
Qe-water supply flow of the water pump e.
③ node pressure is within the allowable range:
Hmin,α≤Hα≤Hmax,α
in the formula HαPressure at node α;
Hmin,αminimum pressure at node α;
Hmax,αmaximum pressure at node α.
Solving of two and ABC-PSO hybrid algorithm
1 Artificial bee colony algorithm
ABC comprises three parts: the bee collecting and observing device is used for collecting bees, observing bees and detecting bees, the bee collecting and observing bees are used for collecting bees, and the detecting bees are used for exploring. If the dimension of the solution problem is D, then each solution xiIs a D-dimensional vector: x is the number ofi＝(xi1，xi2，…，xiD). Firstly, randomly generating initial solutions with the same number as the number of the honey bees, wherein the initial solutions are also called honey sources, the honey bees search near the honey sources to generate new solutions, and the searching process comprises the following steps:
x'ij＝xij+φ(xij-xkj)
in the formula xijIs to solve xiOf j-th dimension, x'ijIs the searched new solution x'iIs randomly selected, and k is not equal to j, phi is randomly taken to be [ -1,1 []Controlling the initial solution xiThe location of the nearby new solution.
When the search solution is better than the optimal solution, replacing the optimal solution; otherwise, the original optimal solution is kept. After the searching process is finished, the observation bees select a new honey source position according to the probability, the nectar amount of the new position is checked, if the nectar amount of the new position is better than that of the original position, the new honey source is used for replacing the original position, and otherwise, the original honey source is reserved. Probability of selecting a honey source:
in the formulaiIs solving for xiThe fitness function is the reciprocal of the objective function, and the larger the honey source adaptation value corresponding to the minimum objective function value is, the larger the probability of being selected is.
If the positions are not improved after lim it-time cyclic search, the positions are abandoned, the honey bees are converted into detection bees, and new honey sources are randomly searched, wherein the formula is as follows:
xij＝xmin,ij+rand(0,1)(xmax,ij-xmin,ij)
in the formula xijIs a new honey source solution xiThe j-th coordinate, xmax,ij、xmin,ijThe upper and lower bounds of the coordinates.
2 particle swarm algorithm
PSO treats a solution in space as a constantly moving particle, all particles having a position (vector x in D dimension)i＝(xi1，xi2，…，xiD) A solution representing the problem sought) and velocity (v)i＝(vi1，vi2，…，viD) Representing a solution change trend), the particle adjusts its own speed and position according to the difference between the optimal objective function extremum (individual objective function extremum) pbest of the current particle searched so far and the optimal objective function extremum (population objective function extremum) gbest of all particle histories, and then trends to the optimal solution. The velocity and position of the particles are updated according to the following formula:
vij(g+1)＝wvij(g)+c1r1d(g)(pbest(g)-xij(g))+c2r2d(g)(gbest(g)-xij(g))
xij(g+1)＝xij(g)+vij(g+1)
in the formula: x is the position of the particle; v is the velocity of the particle; w is an inertial weight factor, the magnitude of whichDetermining how much the particle keeps for the current speed; c. C1、c2The learning factor can adjust the step length of the particles towards pbest and gbest; r is1dAnd r2dIs a random number resulting from (0, 1); i and j represent the j-th dimensional coordinate of the ith particle solution; g is the number of iteration steps.
3ABC-PSO hybrid algorithm
In the water supply scheduling model, a feasible solution x of a parallel pump set operation scheme generated randomlyiRegarding the population as an initial population, the ABC-PSO randomly divides the population into two groups, wherein one group is evolved according to the PSO; the other group evolves according to ABC, in order to solve the problems that individuals in PSO are locally optimal due to error information and the ABC convergence speed is slow, an information exchange mechanism is added in the evolution process, namely, a certain condition is met to enable search information to be transmitted in two groups, and the specific mechanism is as follows: ABC randomly selects from a population evolved from the PSO algorithm in the process of exploring new solutions.
As shown in FIG. 1, the ABC-PSO hybrid algorithm comprises the following steps:
step 1, initializing a population, setting the population scale M, the maximum iteration Step number Max, limiting the single-cycle honeybee collection search times limit and learning factor c1And c2An inertial weight factor w;
step 2: dividing the population into two populations according to the population number in ABC and the particle number of PSO, wherein individuals in the population 1 evolve according to ABC, and individuals in the population 2 evolve according to PSO;
step 3: setting the iteration step number g to be 0;
step 4: performing information exchange every time the iteration step number is increased by 50 times, and randomly selecting a new solution in the ABC population from new particles in the PSO population at the moment;
step 5: calculating the adaptive value of the new solution in the population 1 and calculating the probability PiAccording to PiSelecting honey source, if the adaptive value of the new solution is better than the optimal solution, replacing the optimal solution with the new solution, otherwise, keeping the adaptive value unchanged, and recording as xb；
Step 6: updating pbest and gbest in the population 2, adjusting the speed and position of the particles, calculating the adaptive value of the new particles, and if the population 2 is optimal, optimizingAt xbThen replace x with itbOtherwise, the result is not changed;
step 7: recording the best individual x in the entire populationbUpdating the iteration step number g to be g +1, and outputting a final solution if the output condition is met; otherwise, go back to Step 4.
The parameter setting in the hybrid algorithm of the application is as follows: the population scale is 200; the number of honey sources in the ABC part is 50, the number of populations is 100, the solution dimension D is 5, and the single-cycle honeybee searching times lim it is 50; the number of particles in the PSO part is 100, the inertia weight factor w is linearly attenuated by 0.9 to 0.4, and the learning factor c1And c2Is 2. Output conditions are as follows: and the iteration step number reaches 500, or the solutions are continuously output for 50 times and are not updated, and the operation of the output solution set is finished when any condition is met.
The water supply scale was 4000m according to the following pump group configuration3D, meeting the maximum daily water consumption of 1437m3The highest average flow rate was 29.45L/s. The optimal operation scheme and the water supply amount in different time periods are solved by adopting an ABC-PSO hybrid algorithm as shown in the table I, the operation mode of a pump set is adjusted according to the required water consumption by taking one day as a period, and two speed regulating pumps are always started; the first constant speed pump is in an open state when the required flow is higher than 17m 3/h; the second constant speed pump is started when the required flow is higher than 50m 3/h; the flow rate required by the third constant speed pump is higher than 60m 3/h. Under different flow conditions, the water-saving effect of 27 percent can be achieved at most.
TABLE-OPTIMIZATION OPERATION SCHEME
Compared with the pump set before optimization, the optimized parallel pump set has less starting and stopping of the water pump operation, and the addition of the speed regulating pump can avoid energy loss and pipe network pressure fluctuation caused by the fact that the rotating speed of the constant speed pump is lower than the rated rotating speed during operation. Considering the time continuity of water supply, the optimum scheduled water supply amount during the water supply period of one day is shown in fig. 2. It should be noted that, as the water flow rate increases, the water saving effect decreases, when the flow rate exceeds 90m3/h, the scheduling result is equal to the original water consumption, no change occurs, which indicates that the flow rate reduction algorithm has no further space for saving water, but the time of high water consumption only accounts for 1%, the influence on the total result is very small, and the final water supply amount can be saved to 88.5% of the original water consumption.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. A water supply pump set optimization scheduling method based on an ABC-PSO hybrid algorithm of an Artificial bee colony Algorithm (ABC) and a Particle Swarm Optimization (PSO) is characterized in that a feasible solution x of an operation scheme of a parallel pump set is usediRegarding the population as an initial population, randomly dividing the population into two groups, wherein one group is evolved according to PSO, and the other group is evolved according to ABC; an information exchange mechanism is added in the evolution process, namely, information exchange is carried out in the two populations when the information exchange condition is met.
2. The method according to claim 1, wherein the information communication is specifically: ABC in exploring new solutions, the new solutions are randomly selected from new particles in a population evolved from the PSO algorithm.
3. The method of claim 2, the ABC-PSO hybrid algorithm steps being:
step 1, initializing a population;
step 2, dividing the population into two populations according to the population number in ABC and the particle number of PSO, wherein individuals in the population 1 evolve according to ABC, and individuals in the population 2 evolve according to PSO;
step 3, setting the iteration step number g to be 0;
step4, judging whether the information exchange condition is met, if so, carrying out information exchange; otherwise, performing step 5;
step 5, outputting the optimal solution of the population 1;
step 6, outputting the optimal solution of the population 2;
step 7, recording the optimal solution x in the whole populationbUpdating the iteration step number g to be g +1, and outputting a final solution if the output condition is met; otherwise, go back to Step 4.
4. The method of claim 3, wherein the individuals in population 1 specifically follow ABC evolution as follows:
ABC comprises three parts: the bee collecting, observing and detecting are responsible for the mining and detecting; firstly, randomly generating initial solutions with the same number as the number of the honey bees, wherein the initial solutions are also called honey sources, the honey bees search near the honey sources to generate new solutions, and the searching process comprises the following steps:
x'ij＝xij+φ(xij-xkj)
in the formula xijIs to solve xiOf j-th dimension, x'ijIs the searched new solution x'iIs randomly selected, and k is not equal to j, phi is randomly taken to be [ -1,1 []Controlling the initial solution xiThe location of the nearby new solution;
when the search solution is better than the optimal solution, replacing the optimal solution; otherwise, keeping the original optimal solution; after the searching process is finished, the observation bees select a new honey source position according to the probability, the nectar amount of the new position is checked, if the nectar amount of the new position is better than that of the original position, the new honey source is used for replacing the original position, otherwise, the original honey source is reserved; probability of selecting a honey source:
in the formulaiIs solving for xiThe fitness function is the reciprocal of the objective function;
if the positions are not improved after limit times of circular search, the positions are abandoned, the honey bees are converted into detection bees, and new honey sources are randomly searched, wherein the formula is as follows:
xij＝xmin,ij+rand(0,1)(xmax,ij-xmin,ij)
in the formula xijIs a new honey source solution xiThe j-th coordinate, xmax,ij、xmin,ijThe upper and lower bounds of the coordinates.
5. The method of claim 4, wherein the individuals in population 2 evolve according to PSO specifically as:
PSO treats the solution in space as a constantly moving particle, all particles having a position xi＝(xi1，xi2，…，xiD) And velocity vi＝(vi1，vi2，…，viD) The particle adjusts the speed and position of the particle according to the difference between the particle and pbest and gbest, and then the particle tends to the optimal solution; the velocity and position of the particles are updated according to the following formula:
vij(g+1)＝wvij(g)+c1r1d(g)(pbest(g)-xij(g))+c2r2d(g)(gbest(g)-xij(g))
xij(g+1)＝xij(g)+vij(g+1)
in the formula: w is an inertial weight factor, c1、c2Is a learning factor, r1dAnd r2dIs a random number resulting from (0, 1); i and j represent the j-th dimensional coordinate of the ith particle solution; g is the number of iteration steps.
6. The method of claim 5, wherein initializing the population comprises setting a population size M, a maximum iteration step number Max, a limit on the number of single-cycle honeybee search times limit, and a learning factor c1And c2An inertial weight factor w.
7. The method according to claim 6, wherein the communication condition is set such that the communication is performed every 50 times the number of iteration steps.
8. The method of claim 7, wherein the individual objective function extremum pbest is an objective function extremum that is optimal for the current particle searched thus far, and the population objective function extremum gbest is an objective function extremum that is historically optimal for all particles searched thus far.
9. The method of claim 8, wherein the output condition is set such that the number of iteration steps reaches 500, or 50 solutions are continuously output and are not updated.
10. The method according to claim 9, wherein the minimum water supply is used as the objective function by n pumping stations with constant speed pumps connected in parallel with m speed pumps.
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Application publication date: 20200623 |