CN109146188A - A kind of adaptive cuckoo algorithm and its application method in optimization of chemical process - Google Patents
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Abstract
The invention belongs to chemical technology fields, disclose a kind of adaptive cuckoo algorithm and its application method in optimization of chemical process.The present invention proposes a kind of variable-step self-adaptive cuckoo searching algorithm (VSACS), and the arbitrary width that basic cuckoo is searched in (CS) algorithm is modified to the step-length adaptively adjusted according to the number of iterations.By the test of 15 standard test functions, result verification modified hydrothermal process has a faster convergence rate and higher solving precision.Finally modified hydrothermal process is used to make comments and instructions in reactor, tubular reactor, bioreactor etc. 3 typical chemical industry optimization problems, obtains satisfied experimental result, while further showing that the validity of the algorithm.
Description
Technical Field
The invention belongs to the technical field of chemical engineering, and particularly relates to a self-adaptive cuckoo algorithm and an application method thereof in chemical engineering optimization.
Background
With the increasingly prominent environmental and energy problems, the optimization of chemical processes is receiving more and more attention. The mathematical model of the chemical process is generally in a dynamic optimization model form. Therefore, analysis of dynamic optimization of chemical processes is a research hotspot. Dynamic optimization of chemical engineering seeks to control one or more operating variables in a chemical process so that certain index of the process is optimized. At present, scholars at home and abroad research the chemical engineering dynamic optimization problem by a plurality of methods, wherein the main methods comprise: based on extreme value principle of Pontriey gold; bellman optimality principle; a linear programming method; an iterative dynamic programming method; intelligent algorithms, etc. Since the traditional algorithm needs to solve the gradient when solving the dynamic optimization problem, and the complex practical model is difficult to achieve,' the analysis of the problem by using the intelligent algorithm has become a research direction in recent years. Cuckoo search (cuckoo search) algorithm is a novel meta-heuristic group intelligence algorithm, which was proposed by the scholars xinsheang and the like in 2009, and has received wide attention from the scholars due to the characteristics of simplicity, easy implementation, few adjustable parameters and the like. Once CS is proposed, its advantages over the existing Genetic Algorithm (GA) and particle swarm algorithm (PSO) are not apparent. The algorithm has been optimized for commercial optimization in design, phase-balancing calculations, reliability optimization optimization, and compensation gains application. However, the algorithm has some disadvantages, such as low calculation accuracy, slow convergence rate, etc. Aiming at the problems, a variable-step-size self-adaptive CS algorithm is provided, test results show that the improved algorithm can improve the solving precision and the convergence speed of the CS algorithm, and finally, the provided algorithm is applied to the chemical dynamic optimization problem to obtain a satisfactory effect.
In summary, the problems of the prior art are as follows: when the group intelligent algorithm is used for solving the optimization problem, the defects of low later convergence speed, low solving precision and the like inevitably exist.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a self-adaptive cuckoo algorithm and an application method thereof in chemical engineering optimization.
The invention is realized in such a way that a self-adaptive cuckoo algorithm and an application method thereof in chemical engineering optimization comprise the following steps:
step one, improving a random step length in a basic Cuckoo Search (CS) algorithm into a step length which is adaptively adjusted according to iteration times;
step two, testing through 15 standard test functions;
and step three, finally, the improved algorithm is used for 3 typical chemical dynamic optimization problems of batch reactors, tubular reactors, bioreactors and the like.
Further, the description of the dynamic optimization problem:
the general form of the dynamic optimization problem is as follows:
the essence of inquiry and excitation is to select a control strategy u under the condition of meeting the constraint condition so as to enable the performance index J to reach the optimum.
Further, the basic cs algorithm:
in the basic CS algorithm, the following 3 ideal states are set:
(1) laying 1 egg for each time, and randomly searching for a nest for hatching;
(2) the best position of the bird nest in the randomly searched bird nests is reserved to enter the next generation;
(3) the probability that a foreign bird egg is found by the nest owner is Pα∈[0，1]。
The updating formula for finding the nest position by cuckoo is as follows:
wherein,indicating the position of the ith nest in the t-th generation,indicating point-to-point multiplication, α is the step control quantity, L (λ) is the L vy random search path, and L-u-t-λ(lambda is more than 1 and less than or equal to 3). After the position is updated, the random number r belongs to [0, 1 ]]And PαFor comparison, if r > PαThen pairAnd changing randomly, otherwise, not changing. And finally, reserving the positions of a group of nests with better adaptation values.
Further, the step size changing strategy is as follows:
the step size of the location update in the CS algorithm is randomly moved in combination with the specific Levyflight of birds and Drosophila. The smaller the step length in the moving process, the easier the local search is, but the slower the convergence speed is, the easier the local extremum is trapped; the larger the step length is, the higher the convergence rate is, the higher the global search capability is, but the more the convergence rate is, the more the optimal value is easily jumped, and the oscillation phenomenon occurs. The step size generated by Levyllight is random but lacks adaptivity.
In order to enable the algorithm to have good global optimization capability and high search precision, the CS distribution algorithm is improved by using a step length updating formula in a document for reference so as to improve the self-adaptability of the algorithm.
Wherein stepminIs the minimum value of the step length, and the value is 0.002; p is an integer greater than 1, in the range of [1, 30 ]]FIG. 2 shows that a is a as T/T when P is 1, 3, 5, 10, 20, 30, respectivelymaxT is the current iteration number, TmaxIs a specified maximum number of iterations.
It can be seen from the formula (3) that the moving step length of the nest position is gradually reduced along with the increase of the iteration times t, a larger step length is kept at the initial stage of the iteration of the algorithm to enable the algorithm to quickly converge to the optimal nest position, meanwhile, the algorithm is prevented from falling into the local optimal position prematurely, the step length is gradually reduced along with the increase of the iteration times, the algorithm evolves into local search after the vicinity of the global optimal position is found at the later stage of the operation of the algorithm, and finer search is carried out near the optimal position, so that the CS algorithm has better adaptivity, and the convergence speed and the solving precision of the CS algorithm are greatly improved.
The literature applies the variable step length strategy to a firefly group optimization algorithm, improves the fixed step length of the firefly into the variable step length mode, ensures that individuals far away from the optimal firefly have larger step length, and enables the firefly to search in a large range, so that the globally optimal neighborhood can be searched more quickly; and the individuals near the optimal neighborhood have smaller step sizes, so that the firefly can be more accurately close to the global optimum. Through result comparison of the standard test functions, the improved algorithm is verified to improve the global search capability and the solving precision of the GSO algorithm.
Further, the variable-step-size adaptive cs (vsacs) algorithm flow:
step 1: setting the number n of cuckoo nests, searching the dimension d of the space, and initializing the positions of the nests to beFinding the optimal nest position thereinAnd an optimal solution fmin。
Step 2: (circulation body) preserving the position of the last generation of the optimal bird nestt is the current iteration number, using the location update formulaThe positions of other nests are updated to obtain a new set of nest positions, which are evaluated with the positions of the nests generated in the previous generationComparing, and replacing the nest position with the better adaptive value with the nest position with the poorer adaptive value, thereby obtaining a group of better nest positions
(Sam Kao De Risk) with random numbers r ∈ [0, 1 ] subject to uniform distribution]Probability of finding a foreign bird egg as the owner of the nest and PαComparing, retaining gtThe position of the nest with the lower probability of finding is randomly changed to obtain a group of new nest positions, and the positions of the nests are evaluated, and gtAnd comparing the adaptive value of each nest position, replacing the nest position with a better adaptive value to obtain a group of new and better nest positions:
step 3: finding out the optimal position of the bird nest obtained in step2And the optimum value fmin. If the specified iteration times or the specified precision is reached, outputting a global optimal solution fminAnd corresponding global optimum positionOtherwise, returning to the step2 to continue the iteration.
The invention has the advantages and positive effects that: the invention provides a variable-step self-adaptive cuckoo search algorithm (VSACS), which improves the random step length in the basic Cuckoo Search (CS) algorithm into the step length which is self-adaptively adjusted according to the iteration times. Through the test of 15 standard test functions, the result verifies that the improved algorithm has higher convergence rate and higher solving precision. Finally, the improved algorithm is used for 3 typical chemical dynamic optimization problems of batch reactors, tubular reactors, bioreactors and the like, a satisfactory experimental result is obtained, and meanwhile, the effectiveness of the algorithm is further shown.
Drawings
Fig. 1 is a flow chart of an adaptive cuckoo algorithm and an application method thereof in chemical engineering optimization.
Fig. 2 is a graph illustrating the variation of the coefficient α provided by the practice of the present invention.
FIG. 3 is a schematic diagram of the optimization results of the bioreactor provided by the practice of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The application of the principles of the present invention will now be further described with reference to the accompanying drawings.
As shown in fig. 1, the present invention provides a self-adaptive cuckoo algorithm and its application method in chemical optimization, including the following steps:
step S101, improving the random step length in the basic Cuckoo Search (CS) algorithm into a step length which is self-adaptively adjusted according to the iteration times;
step S102, testing 15 standard test functions;
and step S103, finally, the improved algorithm is used for 3 typical chemical engineering dynamic optimization problems of batch reactors, tubular reactors, bioreactors and the like.
Description of the dynamic optimization problem provided by the present invention:
the general form of the dynamic optimization problem is as follows:
the essence of inquiry and excitation is to select a control strategy u under the condition of meeting the constraint condition so as to enable the performance index J to reach the optimum.
The basic cs algorithm provided by the invention is as follows:
in the basic CS algorithm, the following 3 ideal states are set:
(1) laying 1 egg for each time, and randomly searching for a nest for hatching;
(2) the best position of the bird nest in the randomly searched bird nests is reserved to enter the next generation;
(3) the probability that a foreign bird egg is found by the nest owner is Pα∈[0，1]。
The updating formula for finding the nest position by cuckoo is as follows:
wherein,indicating the position of the ith nest in the t-th generation,indicating point-to-point multiplication, α is the step control quantity, L (λ) is the L yy random search path, and L u is t- λ, (1 < λ ≦ 3.) after position update, the random number r is ∈ [0, 1]And PαFor comparison, if r > PαThen pairAnd changing randomly, otherwise, not changing. And finally, reserving the positions of a group of nests with better adaptation values.
The variable step strategy provided by the invention comprises the following steps:
the step size of the location update in the CS algorithm is randomly moved in combination with the specific Levyflight of birds and Drosophila. The smaller the step length in the moving process, the easier the local search is, but the slower the convergence speed is, the easier the local extremum is trapped; the larger the step length is, the higher the convergence rate is, the higher the global search capability is, but the more the convergence rate is, the more the optimal value is easily jumped, and the oscillation phenomenon occurs. The step size generated by Levyllight is random but lacks adaptivity.
In order to enable the algorithm to have good global optimization capability and high search precision, the CS distribution algorithm is improved by using a step length updating formula in a document for reference so as to improve the self-adaptability of the algorithm.
Wherein stepminIs the minimum value of the step length, and the value is 0.002; p is an integer greater than 1, in the range of [1, 30 ]]FIG. 2 shows that a is a as T/T when P is 1, 3, 5, 10, 20, 30, respectivelymaxT is the current iteration number, TmaxIs a specified maximum number of iterations.
It can be seen from the formula (3) that the moving step length of the nest position is gradually reduced along with the increase of the iteration times t, a larger step length is kept at the initial stage of the iteration of the algorithm to enable the algorithm to quickly converge to the optimal nest position, meanwhile, the algorithm is prevented from falling into the local optimal position prematurely, the step length is gradually reduced along with the increase of the iteration times, the algorithm evolves into local search after the vicinity of the global optimal position is found at the later stage of the operation of the algorithm, and finer search is carried out near the optimal position, so that the CS algorithm has better adaptivity, and the convergence speed and the solving precision of the CS algorithm are greatly improved.
The literature applies the variable step length strategy to a firefly group optimization algorithm, improves the fixed step length of the firefly into the variable step length mode, ensures that individuals far away from the optimal firefly have larger step length, and enables the firefly to search in a large range, so that the globally optimal neighborhood can be searched more quickly; and the individuals near the optimal neighborhood have smaller step sizes, so that the firefly can be more accurately close to the global optimum. Through result comparison of the standard test functions, the improved algorithm is verified to improve the global search capability and the solving precision of the GSO algorithm.
The invention provides a variable step length self-adaptive CS (VSACS) algorithm flow which comprises the following steps:
step 1: setting the number n of cuckoo nests, searching the dimension d of the space, and initializing the positions of the nests to beFinding the optimal nest position thereinAnd an optimal solution fmin。
Step 2: (circulation body) preserving the position of the last generation of the optimal bird nestt is the current iteration number, using the location update formulaThe positions of other nests are updated to obtain a new set of nest positions, which are evaluated with the positions of the nests generated in the previous generationComparing, and replacing the nest position with the better adaptive value with the nest position with the poorer adaptive value, thereby obtaining a group of better nest positions
(Sam Kao De Risk) with random numbers r ∈ [0, 1 ] subject to uniform distribution]Probability of finding a foreign bird egg as the owner of the nest and PaComparing, retaining gtThe position of the nest with the lower probability of finding is randomly changed to obtain a group of new nest positions, and the positions of the nests are evaluated, and gtAnd comparing the adaptive value of each nest position, replacing the nest position with a better adaptive value to obtain a group of new and better nest positions:
step 3: finding out the optimal position of the bird nest obtained in step2And the optimum value fmin. If the specified iteration times or the specified precision is reached, outputting a global optimal solution fminAnd corresponding global optimum positionOtherwise, returning to the step2 to continue the iteration.
1. Function testing
1.1 Standard test function
In order to verify the effectiveness of the VSACS algorithm, the following 15 standard test functions are adopted for testing, and table 1 shows the search range, the theoretical optimal value and the standard precision of the test function when the dimensionality is 10 and 30 respectively
1.2 test results
The experimental environment was the processor: AMDAthlo dominant frequency is 2.00 GHz; memory: 512 MB; operating the system: windows XP; integration into a development environment: matlab2012 a.
The parameter settings in the VSACS algorithm are as follows: population size 25, PαThe maximum number of iterations is 500, and through experiments, the variable length strategy takes p as 30 and each test function runs 20 times independently when the dimension is 10 and 30 respectively, and the convergence refers to that the algorithm is considered to be converged if the algorithm can reach the specified solving precision under the condition of the specified maximum number of iterations, and otherwise the algorithm is not converged.A table 2 and a table 3 respectively give the experimental results when the dimension is 10 and 30The figure of merit, the worst value, and the mean reflect the quality of the solution, while the standard deviation reflects the solution accuracy that can be achieved at a given number of iterations, and also reflects the robustness and stability of the algorithm solution.
As can be seen from Table 2, from the convergence count, except for f5In addition, VSACS is significantly improved over CS, where f4，f7，f10，f12Respectively improved by 14, 11, 10 and 16 times. For each test function, the average number of iterations required for VSACS convergence is smaller than that of CS, with more than 200 or more partial functions, 294 times less for f1, 335 times less for f2, 229 times less for f7, 330 times less for f8, 263 times less for f9, 364 times less for f10, 319 times less for f12, and 323 times less for f 14. Except f5 from the standard deviation, the solving precision of VSACS is improved relative to CS, wherein f is1，f2，f8，f9，f10，f12，f14The number orders of 11, 8, 7, 16, 45, 8 and 16 are improved respectively.
TABLE 1 test function and parameter set-up thereof
Table1 Standard test funetions and its parameter settings.
As can be seen from table 3, the VSACS algorithm is still valid for most test functions at dimension 30. From the convergence times, f8 is increased by 2 times, and f13 is increased by 4 times; f. of1，f2，f10Increase 5 times, f7，f11The increase is carried out for 6 times; f. of14The increase is carried out for 7 times; f. of9，f12The improvement is 16 times; from the average iteration number, there are still more than 200 times less partial functions, where f1212 times less, f2 times less, 273 times less, f8252 times less, f10A lack of 368 times, f12264 times less. There is still an improvement in the accuracy of the large part-score function from the standard deviation, where f1，f2，f9，f12Increased by 2 orders of magnitude, f5，f8Increased by 1 order of magnitude, f10An increase of 46 orders of magnitude.
2. Application of S mathematical model of variable-step-size self-adaptive cuckoo search algorithm (VSACS) in chemical dynamic optimization
3 typical chemical dynamic optimization processes with different control characteristics, namely a batch reactor, a tubular reactor and a bioreactor, are selected, and the VSACS is used for solving the objective function.
2.1 batch reactor
The mathematical model is as follows:
max J(tf)＝CB(tf)
in this reactor, the reaction A → B → C takes place, the reaction temperature T being controlled in the process so that at the end of the reaction, the concentration of the intermediate product B can be optimized. q represents the concentration of substance J and represents the concentration of substance 5.
2.2 tubular reactor
The mathematical model is as follows:
max J(zf)＝1-xA(zf)-xB(zf)
in the reactor, under the action of 2 catalystsZ is the length of the tubular reactor, u (Z) denotes the firstThe catalyst content at the tube midpoint Z is optimized for optimal distribution of the catalyst to maximize the concentration of the target product C at the end of the reaction.
2.3 Park-Ramirez bioreactor (PR-b)
max J(tf)＝z1z5
Wherein,for the protein secretion rate constant, the optimization was aimed at the yield J (t) of secreted protein at the end of the reactionf)＝z1z5To a maximum.
TABLE 2 experimental results with dimension 10
Table2 Experimental results of 10 dimensions.
TABLE 3 experimental results with dimension 30
Table3 Experimental results of 30 dimensions.
TABLE 4 optimization results of different methods for 3 chemical engineering dynamic optimization problems
Table4 Results of 3 chemical dynamic optimization problems bydifferent methods.
2.4 Experimental results and discussion
The time domains of the above 3 cases are respectively discretized by 10, 20 and 100 parts, and independently run for 20 times. Table 4 gives the best comparison of the VSACS algorithm with other literature while giving the best graph 3 of PR-b.
Because the gradient is required to be solved when the traditional method is used for solving the dynamic optimization problem, the state equation is complex for 3 cases, particularly case 3, the state equation presents strong nonlinearity and more local extreme points, so that the difficulty in solving the gradient is high, and the VSACS algorithm is used for solving 3 cases through time domain dispersion and a Runge-Kutta method. The problem of solving a ladder is avoided. It can be seen from table 4 that the VSACS algorithm can achieve fuller results. As can be seen from table 4, for cases 1 and 2, the VSACS algorithm can solve a more optimal solution; for case 3, although the optimal value cannot reach the known optimal value, the solution with the maximum number of iterations is not different from the optimal value and the worst value, which are better than those in the literature, but the optimal value and the worst value are not different, which indicates that the optimal value and the worst value of the solution by the VSACs are not different from each other, which indicates the robustness of the solution by the VSACs algorithm.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (5)
1. A self-adaptive cuckoo algorithm and an application method thereof in chemical optimization are characterized in that the self-adaptive cuckoo algorithm and the application method thereof in the chemical optimization comprise the following steps:
step one, improving a random step length in a basic Cuckoo Search (CS) algorithm into a step length which is adaptively adjusted according to iteration times;
step two, testing through 15 standard test functions;
and step three, finally, the improved algorithm is used for 3 typical chemical dynamic optimization problems of batch reactors, tubular reactors, bioreactors and the like.
2. The adaptive cuckoo algorithm and its application in chemical engineering optimization of claim 1, wherein the description of the dynamic optimization problem:
the general form of the dynamic optimization problem is as follows:
the essence of inquiry and excitation is to select a control strategy u under the condition of meeting the constraint condition so as to enable the performance index J to reach the optimum.
3. The adaptive cuckoo algorithm and its application in chemical engineering optimization of claim 1, wherein the basic cs algorithm:
in the basic CS algorithm, the following 3 ideal states are set:
(1) laying 1 egg for each time, and randomly searching for a nest for hatching;
(2) the best position of the bird nest in the randomly searched bird nests is reserved to enter the next generation;
(3) the probability that a foreign bird egg is found by the nest owner is Pa∈[0，1]；
The updating formula for finding the nest position by cuckoo is as follows:
wherein,indicating the position of the ith nest in the t-th generation,indicating point-to-point multiplication, α is the step control quantity, L (λ) is the L vy random search path, and L to u aret-λ(1 < lambda < 3), after the position is updated, using a random number r to be in the range of 0, 1]And PαFor comparison, if r > PαThen pairRandomly changing, otherwise, not changing; and finally, reserving the positions of a group of nests with better adaptation values.
4. The adaptive cuckoo algorithm and its application in chemical engineering optimization according to claim 1, wherein the variable step size strategy: the updating formula improves the CS distribution algorithm to improve the self-adaptability.
Wherein stepminIs the minimum value of the step length, and the value is 0.002; p is an integer greater than 1, in the range of [1, 30 ]]When P is 1, 3, 5, 10, 20, 30, respectively, a follows T/TmaxT is the current iteration number, TmaxIs a specified maximum number of iterations.
5. The adaptive cuckoo algorithm and the application method thereof in chemical engineering optimization according to claim 1, wherein the variable-step-size adaptive CS algorithm flow:
step one, setting the number n of cuckoo nests, searching the dimension d of a space, and initializing the positions of the nests to beFinding the optimal nest position thereinAnd an optimal solution fmin；
Step two: preserving previous generation optimal nest positiont is the current iteration number, using the location update formulaThe positions of other nests are updated to obtain a new set of nest positions, which are evaluated with the positions of the nests generated in the previous generationComparing, and replacing the nest position with the better adaptive value with the nest position with the poorer adaptive value, thereby obtaining a group of better nest positions
And replacing the nest positions with the better adaptation values with the positions with the poorer adaptation values to obtain a new group of more optimal nest positions:
step three: finding out the optimal position of the bird nest obtained in the second stepAnd the optimum value fmin(ii) a If the specified iteration times or the specified precision is reached, outputting a global optimal solution fminAnd corresponding global optimum positionOtherwise, returning to the step2 to continue the iteration.
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