CN104715124B - A kind of truss size optimal design method based on cloud model Differential Evolution Algorithm - Google Patents

Abstract

The invention discloses a kind of truss size optimal design method based on cloud model Differential Evolution Algorithm, it is during the mutation operation of Differential Evolution Algorithm, the characteristics of having using cloud model in uncertainty with being changed among certainty, stabilization again, the guiding sampling mechanism generation new individual that randomness is blended with steady tendency is used in search space to keep the diversity of population, instruct to develop using the information of the optimal solution obtained in search procedure simultaneously and operate, and many male parents' intersection Local Search operations are merged, accelerate convergence of algorithm speed；In addition, adaptively dynamically adjusting the value of probability of crossover according to current Evolution States information, strengthen the robustness of algorithm with this；Above-mentioned steps are repeated until meeting end condition, the result of the dimensionally-optimised design of the optimum individual obtained in calculating process, as truss；Compared with congenic method, the present invention can reduce the probability for being absorbed in local optimum, accelerate convergence rate, improve the performance of Optimal Design of Trusses.

Description

A kind of truss size optimal design method based on cloud model Differential Evolution Algorithm

Technical field

The present invention relates to Optimal Design of Trusses field, more particularly, to a kind of truss based on cloud model Differential Evolution Algorithm Size optimal design method.

Background technology

The size evolutionary optimization design to truss is needed in Optimal Design of Trusses, when many.Generally, truss size is excellent Change refers under conditions of given truss structure, material, layout topological sum shape, optimizes the area of section of each group rod member so that The overall weight of truss structure is minimized, it is desirable to is met area of section in the range of specified upper lower limit value, and is met each group The stress constraint of rod member and displacement constraint.Generally, the design variable in the dimensionally-optimised design process of truss takes rod member Cross-sectional area.In the Optimal Design of Trusses application of actual numerous and complicated, many Optimal Design of Trusses problems are often higher-dimension, no Continuously, it can not lead, and be the characteristic of strong constraint.These problems are often difficult to effectively using the method for tradition towards mathematical characteristic Solve.For this present situation, intelligent optimization algorithm is applied in Optimal Design of Trusses by people, thus using computer intelligence, The rapidly structure of optimization truss.For example, Li Feng etc. proposed a kind of truss based on particle swarm optimization algorithm in 2009 Optimization Design；Li Feng etc. proposed what is designed based on Immune Clonal Selection Algorithm evolution truss structural optimization in 2010 again Method；Tang and life etc. proposed a kind of dimensionally-optimised method of the truss based on Differential Evolution Algorithm in 2011；Week book is respected Propose within 2012 a kind of using the method that truss structural optimization design is carried out based on comentropy modified particle swarm optiziation.

Differential Evolution Algorithm is a kind of modern intelligence optimization algorithm proposed in recent years, and its structure is very simple, it is easy to compile Cheng Shixian, superior performance.Differential Evolution Algorithm has been successfully applied to the every field such as electronics, electric power, metallurgy and building.By In the superior performance of Differential Evolution Algorithm, people solve Structural Engineering optimization problem using Differential Evolution Algorithm, but Conventional differential evolution algorithmic often exists in the dimensionally-optimised design problem of solution truss and is easily absorbed in local optimum, convergence rate Slowly, optimization design shortcoming of low quality.

The content of the invention

The present invention mainly solves the technical problem present in prior art, and purlin is applied to for conventional differential evolution algorithmic Existed during the dimensionally-optimised design of frame and be easily absorbed in local optimum, convergence rate is slow, the not high shortcoming of optimization design precision proposes one The truss size optimal design method based on cloud model Differential Evolution Algorithm is planted, the present invention, which can be reduced, is absorbed in the general of local optimum Rate, accelerates convergence rate, improves the performance of Optimal Design of Trusses.

Technical scheme：A kind of truss size optimal design method based on cloud model Differential Evolution Algorithm, bag Include following steps：

Step 1, the truss structure of optimization design as needed sets up the mathematical modulo of the minimum optimization aim of following form Type：

Solve the area of section A=[A of each group rod member₁,A₂,....,A_D] so that the gross weight of truss structureMinimize, it is desirable to meet area of section in the range of specified upper lower limit value, and meet each group bar The stress constraint of part and displacement constraint, wherein D represent that how many group of truss structure wants the rod member of optimization design, A_jFor jth group bar The area of section of part, ρ_jFor the density of jth group rod member, L_jFor the length of jth group rod member；

Step 2, user's initiation parameter, the initiation parameter includes truss structure, and how many organizes the bar for wanting optimization design Number of packages D, Population Size Popsize, maximum evaluate number of times MAX_FEs；

Step 3, current evolution algebraically t=0, and the Initial hybridization rate Cr of each individual is set_i ^t=0.9, wherein subscript i= 1 ..., Popsize, Evaluation: Current number of times FEs=0；

Step 4, initial population is randomly generatedWherein:Subscript i=1 ..., Popsize, andFor population P_tIn i-th of individual, its random initializtion formula is：

Wherein subscript j=1 ..., D, and D represents that how many group of truss structure wants the rod member of optimization design；To plant Group P_tIn i-th of individual, store the area of section of D group rod members, rand (0,1) is to obey to be uniformly distributed between [0,1] Random real number produce function, Lo_jAnd Up_jThe respectively lower bound of the span of the area of section of jth group rod member and the upper bound；

Step 5, population P is calculated as follows_tIn each individual adaptive value：

Wherein adaptive value is smaller, shows more outstanding, the ρ of individual_jFor jth group The density of rod member, L_jFor the length of jth group rod member, M is pre-defined one big number, and λ is penalty coefficient, if optimization design The areas of section of D group rod members λ=0 when meeting stress constraint and displacement constraint, otherwise λ=1；

Step 6, Evaluation: Current number of times FEs=FEs+Popsize, and preserve population P_tThe minimum individual of middle adaptive value is most Excellent individual Best^t；

Step 7, counter i=1 is made；

Step 8, if counter i is more than Population Size Popsize, step 15 is gone to, step 9 is otherwise gone to；

Step 9, individual is calculatedCurrent hybrid rate NCr_i ^t, computing formula is as follows:

Wherein r1 is the real number randomly generated between [0,1]；

Step 10, with NCr_i ^tFor individualCurrent hybrid rate, using normal cloud model produce individualExperiment individualAnd calculate experiment individualAdaptive valueComprise the following steps that:

Step 10.1, counter j=1 is made；

Step 10.2, a positive integer jRand is randomly generated between [1, D]；

Step 10.3, if counter j is more than D, step 10.9 is gone to, step 10.4 is otherwise gone to；

Step 10.4, a random real number r2 is produced between [0,1], if r2 is less than individualCurrent hybrid rateOr jRand is equal to counter j, then goes to step 10.5, otherwise go to step 10.7；

Step 10.5, expectEntropySuper entropy He=En/10.0；

Step 10.6, using Ex as expectation, En is entropy, and He is super entropy, and a water dust Val is produced using normal state cloud generator, If water dust Val value is beyond [Lo_j,Up_j] between scope, then water dust Val is regenerated using same method, until Water dust Val value is without departing from [Lo_j,Up_j] between scope, thenGo to step 10.8；

Step 10.7,

Step 10.8, counter j=j+1 is made, step 10.3 is gone to；

Step 10.9, experiment individual is calculatedAdaptive valueGo to step 11；

Step 11, as follows in individualWith experiment individualBetween select individual and enter population of future generation：

Step 12, more new individual as followsHybrid rate

Step 13, counter i=i+1 is made；

Step 14, step 8 is gone to；

Step 15, Evaluation: Current number of times FEs=FEs+Popsize, preserves population P_tThe minimum individual of middle adaptive value is most Excellent individual Best^t；

Step 16, a positive integer RI1 is randomly generated between [1, Popsize], then to individualPerform many male parents Intersect Local Search and obtain individualAnd calculate individualAdaptive valueComprise the following steps that:

Step 16.1, three real numbers r3, r4, r5 are randomly generated between [0,1]；

Step 16.2, coefficient r6=1.0-r3-r4-r5；

Step 16.3, two positive integers that are unequal and being also all not equal to RI1 are randomly generated between [1, Popsize] RI2,RI3；

Step 16.4, counter j=1 is made；

Step 16.5, if counter j is more than D, step 16.8 is gone to, step 16.6 is otherwise gone to；

Step 16.6,

Step 16.7, counter j=j+1 is made, step 16.5 is gone to；

Step 16.8, individual is calculatedAdaptive valueEvaluation: Current number of times FEs=FEs+1, goes to step Rapid 17；

Step 17, if individualAdaptive value be less than individualAdaptive value, then make individual Otherwise individual is keptIt is constant；

Step 18, population P is preserved_tThe minimum individual of middle adaptive value is optimum individual Best^t, current evolution algebraically t=t+1；

Step 19, repeat step 7 is to step 18 until Evaluation: Current number of times FEs reaches end, implementation procedure after MAX_FEs In obtained optimum individual Best^tThe as result of the dimensionally-optimised design of truss.

The invention has the advantages that：Have present invention utilizes cloud model and carried in uncertainty certainty, stablize it In again the characteristics of change, the guiding sampling mechanism generation blended in search space using randomness and steady tendency is new Individual, can keep the diversity of population, so as to reduce the probability for being absorbed in local optimum, while using being obtained in search procedure The information of optimal solution operates to instruct to develop, and merges many male parents' intersection Local Search operations, can accelerate convergence of algorithm speed Degree；In addition, adaptively dynamically adjusting the value of probability of crossover according to current Evolution States information, the robust of algorithm can be strengthened Property；Compared with congenic method, the present invention can reduce the probability for being absorbed in local optimum, accelerate convergence rate, improve truss optimization The performance of design.

Brief description of the drawings

Fig. 1 is the truss structure figure of design to be optimized in embodiment.

Fig. 2 is flow chart of the invention.

Embodiment

Below by embodiment, and with reference to accompanying drawing, the present invention is described in further detail.

The present embodiment is based on document (X.S.Yang, and A.Hossein Gandomi.Bat algorithm:a novel approach for global engineering optimization.Engineering Computations,29(5), Exemplified by Optimal Design of Trusses problem in 464-483,2012.).

The specific implementation step of the present invention is as follows：

Step 1, the truss structure of design to be optimized is as shown in figure 1, wherein H=100cm, La=100cm, Lb=100cm, And A₁,A₂,A₃The area of section of three groups of rod members of optimization design is respectively needed, and is required to meet A₁=A₃, therefore can be by The dimensionally-optimised design engineering technology problem of the truss sets up the Mathematical Modeling for minimizing optimization aim：

Meet constraint：

Wherein min is expressed as minimizing；

Step 2, user's initiation parameter, the initiation parameter includes truss structure, and how many organizes the bar for wanting optimization design Number of packages D=2, Population Size Popsize=100, maximum evaluate number of times MAX_FEs=200000；

Step 3, current evolution algebraically t=0, and the Initial hybridization rate of each individual is setWherein subscript i =1 ..., Popsize, Evaluation: Current number of times FEs=0；

Step 4, initial population is randomly generatedWherein:Subscript i=1 ..., Popsize, andFor population P_tIn i-th of individual, its random initializtion formula is：

Wherein subscript j=1 ..., D, and D represents that how many group of truss structure wants the rod member of optimization design；To plant Group P_tIn i-th of individual, store the area of section of D group rod members, rand (0,1) is to obey to be uniformly distributed between [0,1] Random real number produce function, Lo_j=0 and Up_j=1 is respectively the lower bound of span of the area of section of jth group rod member and upper Boundary；

Step 5, population P is calculated as follows_tIn each individual adaptive value：

Wherein adaptive value is smaller, shows more outstanding, the M=of individual 10³⁵, λ is penalty coefficient, if λ when the area of section of the D group rod members of optimization design meets stress constraint and displacement constraint =0, otherwise λ=1；

Step 6, Evaluation: Current number of times FEs=FEs+Popsize, and preserve population P_tThe minimum individual of middle adaptive value is most Excellent individual Best^t；

Step 7, counter i=1 is made；

Step 8, if counter i is more than Population Size Popsize, step 15 is gone to, step 9 is otherwise gone to；

Step 9, individual is calculatedCurrent hybrid rateComputing formula is as follows:

Wherein r1 is the real number randomly generated between [0,1]；

Step 10, withFor individualCurrent hybrid rate, using normal cloud model produce individualExperiment individualAnd calculate experiment individualAdaptive valueComprise the following steps that:

Step 10.1, counter j=1 is made；

Step 10.2, a positive integer jRand is randomly generated between [1, D]；

Step 10.3, if counter j is more than D, step 10.9 is gone to, step 10.4 is otherwise gone to；

Step 10.4, a random real number r2 is produced between [0,1], if r2 is less than individualCurrent hybrid rateOr jRand is equal to counter j, then goes to step 10.5, otherwise go to step 10.7；

Step 10.5, expectEntropySuper entropy He=En/10.0；

Step 10.6, using Ex as expectation, En is entropy, and He is super entropy, and a water dust Val is produced using normal state cloud generator, If water dust Val value is beyond [Lo_j,Up_j] between scope, then water dust Val is regenerated using same method, until Water dust Val value is without departing from [Lo_j,Up_j] between scope, thenGo to step 10.8；

Step 10.7,

Step 10.8, counter j=j+1 is made, step 10.3 is gone to；

Step 10.9, experiment individual is calculatedAdaptive valueGo to step 11；

Step 11, as follows in individualWith experiment individualBetween select individual and enter population of future generation：

Step 12, more new individual as followsHybrid rate Cr_i ^t：

Step 13, counter i=i+1 is made；

Step 14, step 8 is gone to；

Step 15, Evaluation: Current number of times FEs=FEs+Popsize, preserves population P_tThe minimum individual of middle adaptive value is most Excellent individual Best^t；

Step 16, a positive integer RI1 is randomly generated between [1, Popsize], then to individualPerform many male parents Intersect Local Search and obtain individualAnd calculate individualAdaptive valueComprise the following steps that:

Step 16.1, three real numbers r3, r4, r5 are randomly generated between [0,1]；

Step 16.2, coefficient r6=1.0-r3-r4-r5；

Step 16.3, two positive integers that are unequal and being also all not equal to RI1 are randomly generated between [1, Popsize] RI2,RI3；

Step 16.4, counter j=1 is made；

Step 16.5, if counter j is more than D, step 16.8 is gone to, step 16.6 is otherwise gone to；

Step 16.6,

Step 16.7, counter j=j+1 is made, step 16.5 is gone to；

Step 16.8, individual is calculatedAdaptive valueEvaluation: Current number of times FEs=FEs+1, goes to step Rapid 17；

Step 17, if individualAdaptive value be less than individualAdaptive value, then make individual Otherwise individual is keptIt is constant；

Step 18, population P is preserved_tThe minimum individual of middle adaptive value is optimum individual Best^t, current evolution algebraically t=t+1；

Step 19, repeat step 7 is to step 18 until Evaluation: Current number of times FEs reaches end, implementation procedure after MAX_FEs In obtained optimum individual Best^tThe as result of the dimensionally-optimised design of truss.

Described specific embodiment is only to spirit explanation for example of the invention, the skill of the technical field of the invention Art personnel can be made various modifications or supplement to described specific embodiment or be substituted using similar mode, but simultaneously Do not deviate by the spirit of the present invention or surmount scope defined in appended claims.

Claims (1)

1. a kind of truss size optimal design method based on cloud model Differential Evolution Algorithm, it is characterized in that：Comprise the following steps：

Step 1, the truss structure of optimization design as needed sets up the Mathematical Modeling of the minimum optimization aim of following form：

Solve the area of section A=[A of each group rod member₁,A₂,....,A_D] so that the gross weight of truss structureMinimize, it is desirable to meet area of section in the range of specified upper lower limit value, and meet each group bar The stress constraint of part and displacement constraint, wherein D represent that how many group of truss structure wants the rod member of optimization design, A_jFor jth group bar The area of section of part, ρ_jFor the density of jth group rod member, L_jFor the length of jth group rod member；

Step 2, user's initiation parameter, the initiation parameter includes truss structure, and how many organizes the rod member number for wanting optimization design D, Population Size Popsize, maximum evaluate number of times MAX_FEs；

Step 3, current evolution algebraically t=0, and the Initial hybridization rate Cr of each individual is set_i ^t=0.9, wherein subscript i= 1 ..., Popsize, Evaluation: Current number of times FEs=0；

Step 4, initial population is randomly generatedWherein:Subscript i=1 ..., Popsize, andFor population P_tIn i-th of individual, its random initializtion formula is：

$B_{i,j}^t={\mathrm{Lo}}_j+rand(0,1)\·({\mathrm{Up}}_j-{\mathrm{Lo}}_j)$

Wherein subscript j=1 ..., D, and D represents that how many group of truss structure wants the rod member of optimization design；For in population P_t In i-th of individual, store the area of section of D group rod members, rand (0,1) be obeyed between [0,1] it is equally distributed with Machine real number produces function, Lo_jAnd Up_jThe respectively lower bound of the span of the area of section of jth group rod member and the upper bound；

Step 5, population P is calculated as follows_tIn each individual adaptive value：

Wherein adaptive value is smaller, shows more outstanding, the ρ of individual_jFor jth group rod member Density, L_jFor the length of jth group rod member, M is pre-defined one big number, and λ is penalty coefficient, if the D of optimization design The area of section of group rod member λ=0 when meeting stress constraint and displacement constraint, otherwise λ=1；

Step 6, Evaluation: Current number of times FEs=FEs+Popsize, and preserve population P_tThe minimum individual of middle adaptive value is optimal Body Best^t；

Step 7, counter i=1 is made；

Step 8, if counter i is more than Population Size Popsize, step 15 is gone to, step 9 is otherwise gone to；

Step 9, individual is calculatedCurrent hybrid rate NCr_i ^t, computing formula is as follows:

Wherein r1 is the real number randomly generated between [0,1]；

Step 10, with NCr_i ^tFor individualCurrent hybrid rate, using normal cloud model produce individualExperiment individual And calculate experiment individualAdaptive valueComprise the following steps that:

Step 10.1, counter j=1 is made；

Step 10.2, a positive integer jRand is randomly generated between [1, D]；

Step 10.3, if counter j is more than D, step 10.9 is gone to, step 10.4 is otherwise gone to；

Step 10.4, a random real number r2 is produced between [0,1], if r2 is less than individualCurrent hybrid rate NCr_i ^tOr Person jRand is equal to counter j, then goes to step 10.5, otherwise go to step 10.7；

Step 10.5, expectEntropySuper entropy He=En/10.0；

Step 10.6, using Ex as expectation, En is entropy, and He is super entropy, and a water dust Val is produced using normal state cloud generator, if Water dust Val value is beyond [Lo_j,Up_j] between scope, then water dust Val is regenerated using same method, until water dust Val value is without departing from [Lo_j,Up_j] between scope, thenGo to step 10.8；

Step 10.7,

Step 10.8, counter j=j+1 is made, step 10.3 is gone to；

Step 10.9, experiment individual is calculatedAdaptive valueGo to step 11；

Step 11, as follows in individualWith experiment individualBetween select individual and enter population of future generation：

Step 12, more new individual as followsHybrid rate Cr_i ^t：

Step 13, counter i=i+1 is made；

Step 14, step 8 is gone to；

Step 15, Evaluation: Current number of times FEs=FEs+Popsize, preserves population P_tThe minimum individual of middle adaptive value is optimum individual Best^t；

Step 16, a positive integer RI1 is randomly generated between [1, Popsize], then to individualMany male parents are performed to intersect Local Search obtains individualAnd calculate individualAdaptive valueComprise the following steps that:

Step 16.1, three real numbers r3, r4, r5 are randomly generated between [0,1]；

Step 16.2, coefficient r6=1.0-r3-r4-r5；

Step 16.3, two positive integer RI2 that are unequal and being also all not equal to RI1 are randomly generated between [1, Popsize], RI3；

Step 16.4, counter j=1 is made；

Step 16.5, if counter j is more than D, step 16.8 is gone to, step 16.6 is otherwise gone to；

Step 16.6,

Step 16.7, counter j=j+1 is made, step 16.5 is gone to；

Step 16.8, individual is calculatedAdaptive valueEvaluation: Current number of times FEs=FEs+1, goes to step 17；

Step 17, if individualAdaptive value be less than individualAdaptive value, then make individualOtherwise protect Hold individualIt is constant；

Step 18, population P is preserved_tThe minimum individual of middle adaptive value is optimum individual Best^t, current evolution algebraically t=t+1；

Step 19, repeat step 7 to step 18 terminate after MAX_FEs up to Evaluation: Current number of times FEs reaches, in implementation procedure The optimum individual Best arrived^tThe as result of the dimensionally-optimised design of truss.