CN111598447A - Reservoir group joint optimization scheduling method based on HMAQGA - Google Patents

Reservoir group joint optimization scheduling method based on HMAQGA Download PDF

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CN111598447A
CN111598447A CN202010412939.4A CN202010412939A CN111598447A CN 111598447 A CN111598447 A CN 111598447A CN 202010412939 A CN202010412939 A CN 202010412939A CN 111598447 A CN111598447 A CN 111598447A
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individuals
reservoir
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reservoir group
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CN111598447B (en
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郭玉雪
许月萍
尤延锋
谢京凯
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Zhejiang University ZJU
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    • G06Q10/06312—Adjustment or analysis of established resource schedule, e.g. resource or task levelling, or dynamic rescheduling
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    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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Abstract

The invention discloses a reservoir group joint optimization scheduling method based on HMAQGA, which comprises the following steps: firstly, acquiring basic information of a reservoir group, and generalizing a system; secondly, analyzing the reservoir group tasks, and constructing a reservoir group multi-target combined optimization scheduling mathematical model; then, performing HMAQGA to solve the reservoir group multi-objective joint optimization scheduling model to obtain a Pareto non-inferior solution set; and finally, determining the optimal reservoir group scheduling operation scheme in the Pareto solution set by adopting a fuzzy optimization method based on combined empowerment. The invention realizes global optimization, improves the calculation efficiency and meets the requirement of autonomously selecting the optimal scheduling scheme of the reservoir group.

Description

Reservoir group joint optimization scheduling method based on HMAQGA
Technical Field
The invention belongs to the technical field of reservoirs in the field of water conservancy and hydropower, and particularly relates to a reservoir group joint optimization scheduling method based on HMAQGA.
Background
The reasonable and efficient reservoir dispatching mode can obtain more considerable social and economic benefits under the condition that hardware facilities are not changed. With the continuous enlargement of the scale of the reservoir group in the watershed, the requirements on the combined operation mode of the reservoir group are also continuously improved. Therefore, how to quickly and accurately find the optimal scheduling scheme of the large-scale reservoir group through the construction and the solution of the model and provide a theoretical basis for reservoir group joint scheduling becomes an urgent problem to be solved. In recent years, with the increasing of mathematical programming and computer level, a multi-objective evolutionary algorithm of a Pareto non-inferior solution set theory is introduced on the basis of a traditional intelligent algorithm, and the multi-objective evolutionary algorithm, such as a multi-objective genetic algorithm, a multi-objective particle swarm algorithm, a multi-objective leaping algorithm, a multi-objective ant colony algorithm and the like, is widely applied to reservoir cluster joint optimization scheduling. However, the randomness of the optimization process is high in part of intelligent optimization algorithms, the phenomenon that solution results are inconsistent frequently occurs for many times, and the algorithm is easy to fall into local search and is easy to get early. Therefore, aiming at a complex reservoir group optimization scheduling model, how to select a reasonable and efficient optimization algorithm to solve the model is worth further research.
The quantum mechanics of the last century is provided, so that the basic structure of a substance can be known from an atomic level, and the quantum algorithm is provided by applying the professor of Shor to information science at the end of the century. In 1996, Narayanan combines the thought of quantum multi-universe, introduces the thought into a genetic algorithm, provides a brand-new quantum derivation algorithm, and succeeds in application of the problem of travelers. In 2000, K.H.Han et al introduced quantum state vector coding mode into genetic algorithm, initiated quantum genetic algorithm, proposed quantum revolving gate updating mode, realized individual chromosome quantum gene heredity, improved quantum genetic algorithm feasibility.
Due to the advantages of high calculation efficiency, good optimization performance, high precision and the like, a plurality of scholars are added into the research of the multi-target quantum genetic algorithm, so that the multi-target quantum genetic algorithm becomes a powerful tool for solving the multi-target optimization problem. In the field of reservoir scheduling, the application of a quantum genetic algorithm is less, particularly in the multi-objective problem, documents in the application aspect of the quantum genetic algorithm are scarce, and the reservoir group joint optimization scheduling based on the multi-objective quantum genetic algorithm, which is proposed at the present stage, has the defects of easy local optimal solution, non-inferior solution uneven distribution and the like. Meanwhile, when a multi-objective decision method is adopted to process a non-inferior solution set, the evaluation index weight needs to be determined based on the combination of subjective and objective factors.
Disclosure of Invention
The invention aims to provide a reservoir group joint optimization scheduling method based on a Harmonic distance multi-objective adaptive quantum genetic Algorithm (HMAQGA) aiming at the defects that the traditional multi-objective quantum genetic Algorithm is easy to fall into local convergence, the distribution of non-inferior solutions of an external file set is uneven, individuals are difficult to converge to the front edge of the non-inferior solutions and the like, and an optimal reservoir group scheduling scheme is selected by adopting a fuzzy optimization method based on combination weight on the basis of the non-inferior solutions of the external files.
The technical scheme is as follows: a reservoir group combined optimization scheduling method based on HMAQGA comprises the following steps:
step 1: acquiring basic information data of a reservoir group, comprising the following steps: the basic characteristic parameters, the relation curve of water level-reservoir capacity, the relation curve of downstream water level-discharge flow and the like of each reservoir generalize a reservoir group system according to the hydraulic and hydrological relations among the reservoirs;
step 2: analyzing the reservoir group task, constructing a reservoir group multi-target combined optimization scheduling model with the maximum generating capacity, the minimum water shortage, the minimum water abandonment, the maximum minimum output and the like as objective functions, and taking water balance, reservoir discharge flow, unit flow capacity, downstream flood control flow and reservoir water level as constraints;
step 3: performing HMAQGA to solve a reservoir group multi-objective joint optimization scheduling model to obtain a Pareto (Pareto) non-inferior solution set;
step 4: and determining the optimal reservoir group dispatching operation scheme in the Pareto non-inferior solution set by adopting a fuzzy optimization method based on combined weighting.
Further, Step 3: executing an HMAQGA to solve a reservoir group multi-target joint optimization scheduling model to obtain a Pareto non-inferior solution set, specifically:
step 3-1, selected fromThe water level value of each reservoir in each time interval is used as a decision variable, the upper limit and the lower limit of the water level value of each reservoir are determined, the period time interval T of the integral dispatching of the reservoir group is divided, the group size N is determined, and the maximum iteration number N is determinedgenNumber of decision variables NdNumber of qubits NqCross probability PcCatastrophe factor gkNumber of catastrophe individuals NkExternal archive set size NpNumber of fitness grids Ngrid；
Step 3-2, initializing each individual in the population by setting the iteration number g to 0, wherein the probability amplitude of each individual is paired (α)i,l,βi,l) All initial values are
Figure BDA0002493901720000021
Generating N number of chromosome(s) constituting an initial population q (g);
step3-3, measurement of all individuals in the population Q (g)
Figure BDA0002493901720000022
Obtaining corresponding definite solution, calculating the non-dominant sorting grade [ P ] of all individualsi g]rank(i ═ 1, 2.., N), harmonic distance
Figure BDA0002493901720000023
And performing fast non-dominated sorting on the data based on the harmonic distance, and selecting N according to a corresponding principlepIndividual as initial external archive set
Figure BDA0002493901720000024
Step3-4, based on adaptive grid mechanism, archiving sets from outside
Figure BDA0002493901720000025
Selecting a target individual for each individual;
step 3-5, updating the population Q (g) based on the quantum revolving door U (theta) according to a quantum adjusting strategy, and correcting the individual probability amplitude by adopting a formula (1) through a quantum H gate to obtain a new population Q (g + 1);
step 3-5, updating the population Q (g) by adopting a quantum rotating gate U (theta) according to a quantum adjusting strategy in the table 1, and correcting the individual probability amplitude by utilizing a quantum H gate according to the following formula to obtain a new population Q (g + 1);
Figure BDA0002493901720000031
[ α 'of formula (II)'iβ′i]For the updated gene of quantum revolving door, [ αiβ″i]Is a gene after the modification of the H gate,
Figure BDA0002493901720000032
step 3-6, the updated population Q (t +1) and the external archive set
Figure BDA0002493901720000033
Combining, N + N after combinationpMeasuring individual individuals to obtain corresponding definite solution, and calculating non-dominant ranking grades of all individuals
Figure BDA0002493901720000034
Harmonic distance
Figure BDA0002493901720000035
And performing fast non-dominant sorting on the data, and selecting the top NpIndividual components form an updated external archive set
Figure BDA0002493901720000036
Step 3-7, generating a random probability value P (P ∈ [0,1 ]]) When P is less than or equal to PiCarrying out quantum crossing operation, and utilizing binomial crossing to fully exchange information among population individuals; when P > PiSkipping quantum crossing operation and carrying out the next step;
step 3-8, g for each runkPerforming quantum catastrophe operation once in each iteration, and selecting N with minimum harmonic distancekThe individual performs a regeneration operation such thatNkInitializing individuals;
step 3-9, judging whether the iteration number g reaches NgenIf yes, stopping running and outputting a result; if not, g is equal to g +1, and the process returns to Step3-4 to continue the evolution.
Further, Step3-3 specifically comprises the following steps:
step 3-3-1 constructs two parameters n for each individual iiAnd SiWherein n isiRepresenting the number of individuals, S, dominating an individual i in the current populationiRepresents the set of all individuals dominated by individual i;
step 3-3-2 search for all n i0 individuals, storing them in subset F1That is, a set of non-dominant individuals having a rank of 1, and the individuals in the set are assigned the same non-dominant rank P [ i]rankThe remaining set of individuals is P1. Then search for P1All of n ink1 individuals, they are stored in subset F2I.e. a second level set of non-dominant individuals, to which individuals within the set are assigned a same non-dominant rank P [ i ]]rank+1. And so on until all individuals in the population are ranked, each individual being assigned a non-dominant rank;
step 3-3-3 calculates the blending distance d of the individual according to the following formulaiAnd replacing the crowding distance in the original fast non-dominated sorting method by the harmonic distance to better evaluate the crowding degree of the individual:
Figure BDA0002493901720000037
in the formula (d)i,kRepresenting the Euclidean distance between the individual i and the k-th adjacent individual, wherein k represents the total individual number minus 1;
step 3-3-4 non-dominated sorting selects elite individuals to form an external archive set. By the above operation, each individual i has two parameters P [ i]rank、diI.e., non-dominant rank and harmonic distance. At this time, selecting elite individuals to form an external archive set by adopting the following principle: when the non-dominant grades are different among individuals, selectingIndividuals with lower grades are used for ensuring the convergence of the population; and when the non-dominant grades among the individuals are the same, selecting the individual with larger harmonic distance to ensure the diversity of the population.
Further, Step3-4 specifically comprises the following steps:
step 3-4-1 initializes the external archive set. Not being dominated by individuals in all external archive sets for the current individual. Thus, the individuals that dominate or weakly dominate the current individual are first selected from the external archive set to form a "target set" in which the target individuals for the current individual will be generated.
And Step 3-4-2 self-adaptive gridding is used for dividing a target solution set space. The space is divided into N according to the size of the target solution set space (individual fitness value)gridAnd each individual is distributed in the corresponding grid according to the respective fitness value. And calculating the average fitness value of each grid, and replacing the individual fitness value in the grid with the average fitness value of the grid. The average fitness value calculation formula of each grid is as follows:
Figure BDA0002493901720000041
in the formula, n represents the number of objective functions; f. ofi(x) And (3) representing the fitness value corresponding to the ith objective function of the individual x.
And Step 3-4-3, selecting the optimal target individual by roulette. The grid of the optimal individual is selected by adopting a roulette method, and the grid is more likely to be selected when the fitness value of the grid is larger. After the grid is selected, an individual is randomly selected from the grid to serve as a target individual of the current individual.
Further, Step4 determines an optimal reservoir group dispatching operation scheme in the Pareto solution set by adopting a fuzzy optimization method based on combined empowerment, and specifically comprises the following steps:
step 4-1 determines index set V ═ { V ═ V1,v2,...,vnIn which v isj(j 1, 2.. times, n) represents a fuzzy factor influencing object judgment at the j th time;
step 4-2, determining scheme j indexes according to the index setCharacteristic value x of iij(i 1, 2.. multidot.m; j 1, 2.. multidot.n), establishing a corresponding eigenvalue matrix X:
Figure BDA0002493901720000042
step 4-3, normalizing the established characteristic value matrix based on a standardization method to obtain a relative membership matrix R:
Figure BDA0002493901720000051
step 4-4, determining the combination weight W of each factor to be { W ═ W by a fuzzy combination weighting method according to the importance degree of each factor1,w2,...,wnThat is, the subjective weight w of each evaluation index is determined by adopting a hierarchical Analysis (AHP) methodj' determining objective weight w of each evaluation index by entropy weight methodjAnd then based on wj＝λwj′+(1-λ)wj"(λ ∈ (0,1)) determines the final combining weight w of each indexj。
Step 4-5 substitutes the relative membership calculation formula according to the weight W and the relative membership matrix R of each index
Figure BDA0002493901720000052
In (d), a preferable value of (U) ═ μ1,μ2,...,μm) The solution with the highest preference value is the best solution sought.
By adopting the technical scheme, the invention has the following beneficial effects:
(1) the requirement of multi-target combined optimal scheduling of the reservoir group is met;
(2) the blending distance is utilized to carry out non-dominated sorting of the non-inferior solution set, the external archive set is updated, the influence of the change of all adjacent individuals of a certain solution on the spatial density degree of the solution is fully considered, so that the density degree of the individuals in the solution space is evaluated, the uniform distribution of the non-inferior solution individuals is ensured, good diversity is realized, and the global convergence is accelerated;
(3) selecting the most appropriate target individual for each individual by adopting a self-adaptive grid mechanism to guide the evolution of the individual, guiding the population to approach to the Pareto real front edge, ensuring the distribution of the population individuals, promoting the solution set to be uniformly distributed in a solution space and avoiding the population from gathering in a local area;
(4) the probability amplitude of the quantum H gate is adopted for correction, the individuals updated by the quantum revolving gate are corrected, the situation that the population is trapped into local optimum so as to cause premature convergence of the algorithm is avoided, and the overall optimization performance of the algorithm is enhanced;
(5) quantum catastrophe operation is introduced, premature convergence of the algorithm can be effectively prevented when extreme problems are calculated, and therefore the overall optimization performance of the algorithm is enhanced;
(6) the adopted multi-target decision method combines subjective and objective weights, enhances the autonomous decision capability of the reservoir group multi-target scheduling system, and avoids excessive subjective preference brought in the decision process.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic diagram of a reservoir group system;
FIG. 3 is an HMAQGA flow diagram;
FIG. 4 is a flow diagram of a multi-objective decision making method;
FIG. 5 is a spatial distribution diagram of a combined scheduling scheme set of an upstream reservoir group of the yellow river;
Detailed Description
The present invention is further illustrated by the following examples, which are intended to be purely exemplary and are not intended to limit the scope of the invention, as various equivalent modifications of the invention will occur to those skilled in the art upon reading the present disclosure and fall within the scope of the appended claims.
The invention provides a reservoir group joint optimization scheduling method based on HMAQGA (high mobility group algorithm-assisted genetic algorithm), aiming at the defects that the traditional multi-target quantum genetic algorithm is easy to fall into local convergence, an external archive set is non-poor solution unevenly distributed, an individual is difficult to converge to a non-poor solution front edge and the like. The method includes the steps of maintaining external files in a fast non-dominated sorting mode based on harmonic distance, guiding the evolution direction of a population based on a self-adaptive network mechanism, correcting the probability amplitude of the updated population according to a quantum H gate, preventing the population from falling into local optimum by using a quantum catastrophe technology, determining an optimal reservoir group operation scheduling scheme by using a combined weighted fuzzy optimization method on the basis of non-inferior solution set, and achieving multi-objective combined optimal scheduling of the reservoir group.
As shown in fig. 1, a reservoir group joint optimization scheduling method based on HMAQGA includes the following steps:
step 1, acquiring basic information data of a reservoir group, wherein the basic information data comprises the following steps: the basic characteristic parameters, the relation curve of water level-reservoir capacity, the relation curve of downstream water level-discharge flow and the like of each reservoir are generalized according to the hydraulic and hydrological relations among the reservoirs, and a generalized diagram is shown in FIG. 2;
step 2: analyzing the tasks of the reservoir group, and constructing a reservoir group multi-target combined optimization scheduling model which takes the maximum generated energy, the minimum water shortage, the minimum water abandonment and the maximum minimum output as objective functions and takes water balance, reservoir discharge flow, unit flow capacity, downstream flood control flow and reservoir water level as constraints:
minF(x)＝{f1(x),f2(x),…,fn(x)} (1)
Figure BDA0002493901720000071
wherein, F (x) a set of objective functions; f. ofn(x) Expressed as an objective function with maximum power generation, minimum water shortage, minimum water abandonment, maximum minimum output and the like; n represents the target number of the optimized scheduling of the water resource system; i represents a reservoir serial number, i 1, 2.., N; j represents a time period number, j 1, 2.., T; t is tjRepresents the number of hours (h) of period j; pi,jRepresenting the output magnitude (W) of the reservoir i in the time period j; vi,jIndicating the amount of water (m) stored in the reservoir i in the time period j3)；
Figure BDA0002493901720000072
and
Figure BDA0002493901720000073
Respectively representing the discharge, power generation, life, industry, agriculture, ecology and water abandon flow (m) of the reservoir i in the time period j3/s)；
Figure BDA0002493901720000074
Represents the interval flow (m) of the reservoir i in the time period j3S); and respectively representing a lower limit value and an upper limit value, Kw, of the variable; i isi+1,jRepresents the warehousing flow (m) of the downstream reservoir i +1 in the time period j3/s)；
Step 3: performing HMAQGA to solve the reservoir group multi-objective joint optimization scheduling model to obtain a Pareto non-inferior solution set, wherein a flow chart is shown in FIG. 3;
step 4: and determining the optimal reservoir group dispatching operation scheme in the Pareto non-inferior solution set by adopting a fuzzy optimization method based on combined weighting, wherein a flow chart is shown in FIG. 4.
Step 3: the method comprises the following steps of executing an HMAQGA to solve a reservoir group multi-target joint optimization scheduling model, and obtaining a Pareto solution set:
step 3-1, selecting the water level value of each reservoir in each time interval as a decision variable, determining the upper limit and the lower limit of the water level value of each reservoir, dividing the period T of the integral dispatching of the reservoir group, determining the population size N and the maximum iteration number NgenNumber of decision variables NdNumber of qubits NqCross probability PcCatastrophe factor gkNumber of catastrophe individuals NkExternal archive set size NpNumber of fitness grids Ngrid；
Step 3-2, initializing each individual in the population by setting the iteration number g to 0, wherein the probability amplitude of each individual is paired (α)i,l,βi,l) All initial values are
Figure BDA0002493901720000075
Generating N number of chromosome(s) constituting an initial population q (g);
step3-3, measurement of all individuals in the population Q (g)
Figure BDA0002493901720000076
To obtainCalculating the non-dominant ranking [ P ] of all individuals according to the determined solutioni g]rank(i ═ 1, 2.., N), harmonic distance
Figure BDA0002493901720000077
And performing fast non-dominated sorting on the data based on the harmonic distance, and selecting N according to a corresponding principlepIndividual as initial external archive set
Figure BDA0002493901720000081
The method specifically comprises the following steps:
step 3-3-1 constructs two parameters n for each individual iiAnd SiWherein n isiRepresenting the number of individuals, S, dominating an individual i in the current populationiRepresents the set of all individuals dominated by individual i;
step 3-3-2 search for all n i0 individuals, storing them in subset F1That is, a set of non-dominant individuals having a rank of 1, and the individuals in the set are assigned the same non-dominant rank P [ i]rankThe remaining set of individuals is P1. Then search for P1All of n ink1 individuals, they are stored in subset F2I.e. a second level set of non-dominant individuals, to which individuals within the set are assigned a same non-dominant rank P [ i ]]rank+1. And so on until all individuals in the population are ranked, each individual being assigned a non-dominant rank;
step 3-3-3 calculates the blending distance d of the individual according to the following formulaiAnd replacing the crowding distance in the original fast non-dominated sorting method by the harmonic distance to better evaluate the crowding degree of the individual:
Figure BDA0002493901720000082
in the formula (d)i,kRepresenting the Euclidean distance between the individual i and the k-th adjacent individual, wherein k represents the total individual number minus 1;
step 3-3-4 non-dominated sorting selection of elite individuals to form external archiveAnd (4) collecting. By the above operation, each individual i has two parameters P [ i]rank、diI.e., non-dominant rank and harmonic distance. At this time, selecting elite individuals to form an external archive set by adopting the following principle: when the non-dominant grades are different among individuals, selecting the individuals with lower grades to ensure the convergence of the population; and when the non-dominant grades among the individuals are the same, selecting the individual with larger harmonic distance to ensure the diversity of the population.
Step3-4, based on adaptive grid mechanism, archiving sets from outside
Figure BDA0002493901720000083
The method specifically comprises the following steps of:
step 3-4-1 initializes the external archive set. Not being dominated by individuals in all external archive sets for the current individual. Thus, the individuals that dominate or weakly dominate the current individual are first selected from the external archive set to form a "target set" in which the target individuals for the current individual will be generated.
And Step 3-4-2 self-adaptive gridding is used for dividing a target solution set space. The space is divided into N according to the size of the target solution set space (individual fitness value)gridAnd each individual is distributed in the corresponding grid according to the respective fitness value. And calculating the average fitness value of each grid, and replacing the individual fitness value in the grid with the average fitness value of the grid. The average fitness value calculation formula of each grid is as follows:
Figure BDA0002493901720000084
in the formula, n represents the number of objective functions; f. ofi(x) And (3) representing the fitness value corresponding to the ith objective function of the individual x.
And Step 3-4-3, selecting the optimal target individual by roulette. The grid of the optimal individual is selected by adopting a roulette method, and the grid is more likely to be selected when the fitness value of the grid is larger. After the grid is selected, an individual is randomly selected from the grid to serve as a target individual of the current individual.
Step 3-5, updating the population Q (g) by adopting a quantum rotating gate U (theta) according to a quantum adjusting strategy in the table 1, and correcting the individual probability amplitude by utilizing a quantum H gate according to the following formula to obtain a new population Q (g + 1);
Figure BDA0002493901720000091
[ α 'of formula (II)'iβ′i]For the updated gene of quantum revolving door, [ αiβ″i]Is a gene after the modification of the H gate,
Figure BDA0002493901720000092
TABLE 1 adjustment strategy for quantum turn gates
Figure BDA0002493901720000093
Step 3-6, the updated population Q (t +1) and the external archive set
Figure BDA0002493901720000094
Combining, N + N after combinationpMeasuring individual individuals to obtain corresponding definite solution, and calculating non-dominant sequencing grades [ P ] of all individualsi t+1]rank(i＝1,2,...,N+Np) Harmonic distance
Figure BDA0002493901720000095
And performing fast non-dominant sorting on the data, and selecting the top NpIndividual components form an updated external archive set
Figure BDA0002493901720000096
Step 3-7, generating a random probability value P (P ∈ [0,1 ]]) When P is less than or equal to PcCarrying out quantum crossing operation, and utilizing binomial crossing to fully exchange information among population individuals; when P > PcSkipping quantum crossing operation and carrying out the next step;
step 3-8, g for each runkPerforming quantum catastrophe operation once in each iteration, and selecting N with minimum harmonic distancekThe individual performs a regeneration operation to make NkInitializing individuals;
step 3-9, judging whether the iteration number g reaches NgenIf yes, stopping running and outputting a result; if not, g is equal to g +1, and the process returns to Step3-4 to continue the evolution.
Step 4: the method for determining the optimal reservoir group dispatching operation scheme in the Pareto non-inferior solution set by adopting the fuzzy optimization method based on combined empowerment comprises the following steps:
step 4-1 determines index set V ═ { V ═ V1,v2,...,vnIn which v isj(j 1, 2.. times, n) represents a fuzzy factor influencing object judgment at the j th time;
step 4-2, determining characteristic value x of index i of scheme j according to index setij(i 1, 2.. multidot.m; j 1, 2.. multidot.n), establishing a corresponding eigenvalue matrix X:
Figure BDA0002493901720000101
step 4-3, normalizing the established characteristic value matrix based on a standardization method to obtain a relative membership matrix R:
Figure BDA0002493901720000102
step 4-4, determining the combination weight W of each factor to be { W ═ W by a fuzzy combination weighting method according to the importance degree of each factor1,w2,...,wnThat is, the subjective weight w of each evaluation index is determined by adopting a hierarchical Analysis (AHP) methodj' determining objective weight w of each evaluation index by entropy weight methodjAnd then based on wj＝λwj′+(1-λ)wj"(λ ∈ (0,1)) determines the final combining weight w of each indexj。
The method comprises the following specific steps:
step 4-4-1, determining subjective weight of each evaluation index by adopting an AHP method, analyzing logical relation among all factors in the system, and establishing a hierarchical structure of the system;
and Step 4-4-2, measuring the relative importance degree of each factor by using a nine-level scale method, and solving a judgment matrix. The importance scale values may be selected from table 2. If the set of n factors in layer A is B ═ B1,B2,B3,...Bn}，n≥2，bijIs the relative degree of importance between factors i and j;
TABLE 2 selection of importance Scale values
Figure BDA0002493901720000103
Figure BDA0002493901720000111
And Step 4-4-3, calculating the weight of each layer element, and checking the consistency of the weights. In order to avoid subjectivity and one-sidedness of the result obtained by the researched problem, the consistency of the matrix needs to be checked and judged;
step 4-4-4, calculating the combined weight of each element, synthesizing the weight of each single-layer element, determining the weight coefficient of the lower-layer element relative to the upper-layer element, and obtaining the subjective weight w of the evaluation indexj′；
Step 4-4-5 adopts an entropy weight method to determine objective weight of each evaluation index, and firstly, a decision matrix R is established (R ═ Rij)m×n，(i＝1,2,3...,m；j＝1,2,3...,n)。
Step 4-4-6 normalizes all indexes in the matrix R according to a non-proportional transformation method to obtain a normalized matrix X (X ═ X)ij)m×n，(i＝1,2,3...,m；j＝1,2,3...,n)。
Step 4-4-7, calculating according to the formula 4-19 to obtain entropy values H of all evaluation indexesj：
Figure BDA0002493901720000112
Wherein:
Figure BDA0002493901720000113
1,2,3, m, j 1,2,3. To ensure lnfijHas practical significance, and the following formula is adopted for fijCorrection of (1):
Figure BDA0002493901720000114
step 4-4-8 calculates the entropy weight of each evaluation index by using the following formula:
Figure BDA0002493901720000115
step 4-4-9 uses the AHP method and the entropy weight method to respectively calculate subjective weight w of each evaluation indexj' and objective weight wj"thereafter, the combined weight value w of each index is determined by the formula (4-22)j：
wj＝λwj′+(1-λ)wj″，j＝1,2,3...,n (11)
In the formula, λ represents a preference coefficient, λ ∈ (0, 1).
Step 4-5 substitutes the relative membership calculation formula according to the weight W and the relative membership matrix R of each index
Figure BDA0002493901720000121
In (d), a preferable value of (U) ═ μ1,μ2,...,μm) The solution with the highest preference value is the best solution sought.
The reasonability and the effectiveness of the method are explained by taking the upstream dragon-sheep gorge-Liu family gorge reservoir group combined optimization scheduling of the yellow river basin as an example. The Longyang fyday reservoir is positioned at the position of a 'cock' of the yellow river main stream, the dead water level of the reservoir is 2530m, the normal water storage level is 247 hundred million m with the storage capacity below 2600m3Flood limited water level 2594m, xingli reservoir capacity 193.5 hundred million m3Regulating reservoir for many years. The Liu family gorge reservoir is an annual regulation reservoir and bears multiple tasks in the upstream area of the yellow river, including power generation, water supply, ice prevention and the like. The Liu family gorge reservoir dead water level is 1717m, the normal water storage level is 1735m, the flood limit water level is 1727m, and the installed capacity of the power station reaches 135 ten thousandkW。
The method takes the discharge flow of each time interval of each reservoir as a decision variable, adopts HMAQGA to carry out optimization scheduling, realizes the maximum total generated energy and the maximum minimum generated output of the reservoir group, and takes water balance, water level limitation, generator set flow capacity, ecological flow, ice prevention flow and the like as constraint conditions. The specific parameters for determining HMAQGA were set as: the population size N is 100, and the global iteration number Ngen5000 quantum catastrophe factor gkExternal archive set size N30 p100, cross probability Pc0.9, the number of adaptive grids NgridThe scheduling scheme set spatial distribution is shown in fig. 5, 20. As can be seen from the graph 5, the dispatching scheme set is in a non-convex curve in spatial distribution, the dispatching scheme is widely and uniformly distributed, the two targets of the total generating capacity of the reservoir group and the total minimum output of the reservoir group are mutually restricted and mutually conflicted, and an obvious inverse proportion relation exists, so that the reservoir group optimized dispatching scheme set solved by the improved quantum genetic algorithm is reasonable and effective.
Based on the Pareto non-inferior solution set, the optimal scheduling scheme of the reservoir group is determined by adopting a fuzzy optimization method of combined weighting, and the relative importance degree of each index, the weight result of each index and the relative goodness value of each scheme are shown in tables 3, 4 and 5. On the basis, 20 schemes are selected as candidate schemes in the solution space uniformly, through scheme optimization, the total generated energy of the reservoir group corresponding to the scheduling scheme 3 is 124.84 hundred million kW.h, the total minimum output value of the reservoir group is 98.40 thousand kW, and the total water abandon amount of the reservoir group is 0.26 hundred million m3See table 5 for details.
TABLE 3 calculation table of relative importance and subjective weighting of each index
Figure BDA0002493901720000122
Figure BDA0002493901720000131
TABLE 4 index weight results table
Figure BDA0002493901720000132
TABLE 5 reservoir group Multi-objective Joint optimization scheduling solution summary table
Figure BDA0002493901720000133

Claims (5)

1. A reservoir group combined optimization scheduling method based on HMAQGA is characterized by comprising the following steps:
step 1: acquiring basic information data of a reservoir group, comprising the following steps: the basic characteristic parameters, the water level-reservoir capacity relation curve and the downstream water level-discharge flow relation curve of each reservoir generalize a reservoir group system according to the hydraulic and hydrological relations among the reservoirs;
step 2: analyzing the reservoir group task, constructing a reservoir group multi-target combined optimization scheduling mathematical model with the maximum generating capacity, the minimum water shortage, the minimum water abandonment and the maximum minimum output and with the water balance, the reservoir discharge flow, the unit flow capacity, the downstream flood control flow and the reservoir water level as constraints;
step 3: performing HMAQGA to solve a reservoir group multi-target joint optimization scheduling model to obtain a Pareto non-inferior solution set;
step 4: and determining the optimal reservoir group dispatching operation scheme in the Pareto non-inferior solution set by adopting a fuzzy optimization method based on combined weighting.
2. The HMAQGA-based reservoir group joint optimization scheduling method of claim 1, wherein Step3 comprises the steps of:
step 3-1, selecting the water level value of each reservoir in each time interval as a decision variable, determining the upper limit and the lower limit of the water level value of each reservoir, dividing the period T of the integral dispatching of the reservoir group, determining the population size N and the maximum iteration number NgenNumber of decision variables NdNumber of qubits NqCross probability PcCatastrophe factor gkNumber of catastrophe individuals NkExternal archive set size NpFitness grid Ngrid；
Step 3-2, initializing each individual in the population by setting the iteration number g to 0, wherein the probability amplitude of each individual is paired (α)i,l,βi,l) All initial values are
Figure FDA0002493901710000017
Generating N number of chromosome(s) constituting an initial population q (g);
step3-3, measurement of all individuals in the population Q (g)
Figure FDA0002493901710000012
Computing the non-dominated ranking of all individuals
Figure FDA0002493901710000013
Harmonic distance
Figure FDA0002493901710000014
And performing fast non-dominated sorting on the data based on the harmonic distance, and selecting N according to a corresponding principlepIndividual as initial external archive set
Figure FDA0002493901710000015
Step3-4, based on adaptive grid mechanism, archiving sets from outside
Figure FDA0002493901710000016
Selecting a target individual for each individual;
step 3-5, updating the population Q (g) based on the quantum revolving door U (theta) according to a quantum adjusting strategy, and correcting the individual probability amplitude by adopting a formula (1) through a quantum H gate to obtain a new population Q (g + 1);
Figure FDA0002493901710000021
in the formula (2)α′iβ′i]For the updated gene of quantum revolving door, [ αiβ″i]Is a gene after the modification of the H gate,
Figure FDA0002493901710000027
step 3-6, the updated population Q (g +1) and the external archive set
Figure FDA0002493901710000022
Combining, N + N after combinationpIndividual subjects perform the measurements and the non-dominated ranking of all subjects is calculated
Figure FDA0002493901710000023
Harmonic distance
Figure FDA0002493901710000024
And performing fast non-dominant sorting on the data, and selecting the top NpIndividual components form an updated external archive set
Figure FDA0002493901710000025
Step 3-7, generating a random probability value P (P ∈ [0,1 ]]) When P is less than or equal to PcCarrying out quantum crossing operation, and utilizing binomial crossing to fully exchange information among population individuals; when P > PcSkipping quantum crossing operation and carrying out the next step;
step 3-8, g for each runkPerforming quantum catastrophe operation once in each iteration, and selecting N with minimum harmonic distancekThe individual performs a regeneration operation to make NkInitializing individuals;
step 3-9, judging whether the iteration number g reaches NgenIf yes, stopping running and outputting a result; if not, g is equal to g +1, and the process returns to Step3-4 to continue the evolution.
3. The HMAQGA-based reservoir group joint optimization scheduling method of claim 2, wherein Step3-3 comprises the steps of:
step 3-3-1 constructs two parameters n for each individual iiAnd SiWherein n isiRepresenting the number of individuals, S, dominating an individual i in the current populationiRepresents the set of all individuals dominated by individual i;
step 3-3-2 search for all ni0 individuals, storing them in subset F1That is, a set of non-dominant individuals having a rank of 1, and the individuals in the set are assigned the same non-dominant rank P [ i]rankThe remaining set of individuals is P1(ii) a Then search for P1All of n inkStore them in subset F for 1 individual2I.e. a second level set of non-dominant individuals, to which individuals within the set are assigned a same non-dominant rank P [ i ]]rank+1(ii) a And so on until all individuals in the population are ranked, each individual being assigned a non-dominant rank;
step 3-3-3 calculates the blending distance d of the individual according to the following formulaiAnd replacing the crowding distance in the original fast non-dominated sorting method by the harmonic distance to better evaluate the crowding degree of the individual:
Figure FDA0002493901710000026
in the formula (d)i,kRepresenting the Euclidean distance between the individual i and the k-th adjacent individual, wherein k represents the total individual number minus 1;
step 3-3-4 non-dominated sorting selects elite individuals to form an external archive set: by the above operation, each individual i has two parameters P [ i]rank、diNamely the non-dominant grade and the harmonic distance, at this time, the elite individuals are selected to form an external archive set by adopting the following principle: when the non-dominant grades are different among individuals, selecting the individuals with lower grades to ensure the convergence of the population; and when the non-dominant grades among the individuals are the same, selecting the individual with larger harmonic distance to ensure the diversity of the population.
4. The HMAQGA-based reservoir group joint optimization scheduling method of claim 2, wherein Step3-4 comprises the steps of:
step 3-4-1 initializing external archive sets
For the current individual, the current individual is not dominated by the individuals in all the external archive sets, so that the individual which dominates or weakly dominates the current individual is selected from the external archive sets to form a target set, and the target individual of the current individual is generated in the set;
step 3-4-2 self-adaptive gridding division target solution set space
The space is divided into N according to the size of the target solution set space (i.e. the fitness value of the individual)gridEach individual is distributed in the corresponding grid according to the respective fitness value, the average fitness value of each grid is calculated, and the average fitness value of each grid is used for replacing the individual fitness value in each grid; the average fitness value calculation formula of each grid is as follows:
Figure FDA0002493901710000031
in the formula, n represents the number of objective functions; f. ofi(x) Representing the fitness value corresponding to the ith objective function of the individual x;
step 3-4-3 adopts roulette to select optimal target individual
And selecting a grid of the optimal individual by adopting a roulette method, wherein the grid is more likely to be selected when the fitness value of the grid is larger, and after the grid is selected, randomly selecting an individual from the grid as a target individual of the current individual.
5. The HMAQGA-based reservoir group joint optimization scheduling method of claim 1, wherein Step4 comprises the steps of:
step 4-1 determines index set V ═ { V ═ V1,v2,...,vnIn which v isj(j ═ 1, 2.., n) represents the fuzzy factor of the ith influence object judgment;
step 4-2, determining characteristic value x of index j of scheme i according to index setij(i＝1,2,...,m；j ═ 1, 2.. times, n), a corresponding eigenvalue matrix X is established:
Figure FDA0002493901710000032
step 4-3, normalizing the established characteristic value matrix based on a standardization method to obtain a relative membership matrix R:
Figure FDA0002493901710000041
step 4-4, determining the combination weight W of each factor to be { W ═ W by a fuzzy combination weighting method according to the importance degree of each factor1,w2,...,wnThat is, the subjective weight w of each evaluation index is determined by adopting a hierarchical Analysis (AHP) methodj' determining objective weight w of each evaluation index by entropy weight methodjAnd then based on wj＝λwj′+(1-λ)wj"(λ ∈ (0,1)) determines the final combining weight w of each indexj。
Step 4-5 substitutes the relative membership calculation formula according to the weight W and the relative membership matrix R of each index
Figure FDA0002493901710000042
In (d), a preferable value of (U) ═ μ1,μ2,...,μm) The solution with the highest preference value is the best solution sought.
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