CN109918827A - It is a kind of have Filtering system bound accept within limits hold back search simulation optimization calculation method - Google Patents
It is a kind of have Filtering system bound accept within limits hold back search simulation optimization calculation method Download PDFInfo
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- CN109918827A CN109918827A CN201910207267.0A CN201910207267A CN109918827A CN 109918827 A CN109918827 A CN 109918827A CN 201910207267 A CN201910207267 A CN 201910207267A CN 109918827 A CN109918827 A CN 109918827A
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Abstract
It accepts within limits to hold back the present invention relates to a kind of bound for having Filtering system and searches simulation optimization calculation method.To maximize the overall service satisfaction of service system as the target of optimization, establish the MIXED INTEGER type Optimized model of two heterogeneous service type service systems of tool Filtering system, then, hunting system simulation value is constantly restrained using bound through systematic manner, change the upper bound or the lower bound of search in iteration calculation each time, new gate valve value is found through dichotomy again, until converging to the latency value for meeting confidence interval.The method of the present invention can find out the near optimal solution of Optimized model under the limitation of very big, time and cost of sampling in face of solution space.
Description
Technical field
It accepts within limits to hold back the present invention relates to a kind of bound for having Filtering system and searches simulation optimization calculation method.
Background technique
The simulation optimization method of the prior art focuses on how development converges to optimum solution when sample number approaches infinitely great
Correlation theory, for simulation optimization model, in limited sample sampling number, not can guarantee can find out it is all meet with
The feasible solution of machine restraint-type.
However size generally relies on the decision of policymaker's subjectivity in practice, can only use the sample of limited quantity
This.Meanwhile the sample number needed for system emulation is bigger, then it is bigger to represent spent cost of sampling；And it is insufficient in sample number
In the case of, simulation optimization, which does not ensure that, can find feasible solution.In addition, in the optimization problem that processing has discrete variable,
It needs to estimate sub- gradient function (Subgradient), finite difference calculus is commonly used in the research work in passing document
(FiniteDifferences), it generally requires to spend great calculating simulation time cost.
Therefore, the technology of the present invention mainly utilizes the Optimization Skill of random search algorithm, through systematic manner using up and down
Boundary constantly restrains hunting system simulation value, changes the upper bound or the lower bound of search in iteration calculation each time, then penetrate two points
Method finds new gate valve value, until converging to the latency value for meeting confidence interval.
Summary of the invention
It accepts within limits to hold back the purpose of the present invention is to provide a kind of bound for having Filtering system and searches simulation optimization calculation method,
This method can find out the near optimal solution of Optimized model under the limitation of very big, time and cost of sampling in face of solution space.
To achieve the above object, the technical scheme is that a kind of bound of tool Filtering system is accepted within limits to hold back to search and be imitated
True optimized calculation method establishes tool Filtering system to maximize the overall service satisfaction of service system as the target of optimization
Two heterogeneous service type service systems MIXED INTEGER type Optimized model；Then, it is accepted within limits using bound and holds back search optimization calculation
Method calculates the optimum value of the overall service satisfaction of service system.
In an embodiment of the present invention, the MIXED INTEGER type of two heterogeneous service type service systems of the tool Filtering system
Optimized model is as follows:
Objective function: d1·R1(τ)+d2·R2(τ)
Restraint-type 1:W (τ, s1,s2)≤ε
Restraint-type 2:
Restraint-type 3:0 < τ < 1
Restraint-type 4:s1,s2∈positive integer
Wherein, d1、d2It distributes to screen customer by classification of service gate valve value to point of the service equipment of two kinds of service types
With ratio；R1(τ)、R2(τ) respectively indicates the satisfaction of the service equipment of two kinds of service types；Restraint-type 1 indicates customer's expectation etc.
To time W (τ, s1,s2) it is less than default expectation waiting time gate valve value ε；The left side of restraint-type 2 indicates the service people of service equipment
The sum of member, the deployment cost of service equipment and operation cost, the right indicate master budget B, β1、β2It respectively indicates and uses two every year
The depreciation amortized cost of the service equipment of kind service type, the service that p (τ) expression customer is assigned to second of service type are set
Standby allocation probability, ci, what i=1,2 respectively indicated two kinds of service types employs attendant's cost；Restraint-type 3 indicates service
The value range of classification gate valve value τ；Restraint-type 4 indicates s1、s2Attendant's number of the service equipment of two kinds of service types is positive whole
Number.
In an embodiment of the present invention, described accepted within limits using bound holds back search optimization algorithm, calculates the total of service system
The optimum value of body service satisfaction the specific implementation process is as follows:
Step S1, according to restraint-type 2, s is selected1、s2The set C of all possible combinations；
Step S2, the number of iterations n=0 of setting optimization solution；
Step S21, one group of solution (s is taken from set C1 (n),s2 (n)), set algorithm number of iterations k=0；
Step S22, whenWhen, it enablesAnd enter step S25, wherein Δ τ is one previously given
Sufficiently small positive value；If it is not, working asWhen, then set k ← k+1 andEnter step S23；
Step S23, according to τkSetting, execute M duplicate l-G simulation test, the waiting time W recordedj(s1 (n),
s2 (n)), j=1,2,3 ... M, and calculate its average value:
And it calculates95% confidence intervalIts
In, γ is half length of confidence interval；
If step S24, default expectation waiting time gate valve value ε meets inequalityOr it when algorithm iteration number k=K, then setsAnd more
New set C ← C { (s1 (n),s2 (n))}；Conversely, if default expectation waiting time gate valve valueWhen, settingτ=τk, and return to step S22 and continue to execute；If default expectation waiting time gate valve valueWhen, then it setsAnd it returns to step S22 and continues to execute；
Step S25, as set C=φ, bound restrains search algorithm loop termination and enters step S3；Conversely,
Number of iterations n ← n+1 of setting optimization solution, resumes step S21 are continued to execute；
Step S3: the obtained solution of search algorithm is restrained for boundUtilization feasibility proving program determines solution
Feasibility, to leave out infeasible solution；Enable C*Indicate all after feasibility proving program is selectedThe solution set of composition；
Finally export optimal expectation waiting time gate valve valueAnd service system can be calculated
Overall service satisfaction optimum value be SL (τ*)。
Compared to the prior art, the invention has the following advantages:
1. simulation optimization algorithm proposed by the invention is analyzed and is existed in stochastic system in a manner of construction prediction model
Complexity optimization problem, and under the theoretical basis of statistics, from many different systems, through the side of emulation experiment
Formula finds out the optimal system of desired performance, provides policymaker and make reference.
2. simulation optimization algorithm proposed by the present invention can analyze the challenge that general mathematic(al) mode can not be analyzed, and
It is able to come the important factor and confidence level of analyzing influence system performance through experimental design.
3. the present invention develops a set of efficient simulation optimization algorithm, an optimization problem with randomness is solved, and can
Simulation optimization algorithm proposed by the present invention is written in software program, scientific algorithm is carried out through computer and system is simulated, it is high
Efficient solve stochastic optimization problems.
Detailed description of the invention
Fig. 1 is two heterogeneous service type service systems of present invention tool Filtering system.
Specific embodiment
With reference to the accompanying drawing, technical solution of the present invention is specifically described.
It accepts within limits to hold back the present invention provides a kind of bound for having Filtering system and searches simulation optimization calculation method, to maximize
Target of the overall service satisfaction of service system as optimization, establishes two heterogeneous service type service systems of tool Filtering system
MIXED INTEGER type Optimized model；Then, it is accepted within limits using bound and holds back search optimization algorithm, calculate the overall service of service system
The optimum value of satisfaction.
Specifically, the present invention has Filtering system, it will transmit through classification of service gate valve value and determine that distinguishing past two kinds of differences services class
The service equipment of type, as shown in Fig. 1.In the case where meeting waiting time limitation, it is expected that making entirely to service through this gate valve value is adjusted
The service satisfaction of system reaches maximum.Through information system previously according to the kind class feature assignment of customer, then distributed to
The service equipment of different service types can maximize service system in the case where meeting permissible waiting time and master budget limitation
Level of security.Customer can not only maximize service system as can be suitably assigned to the service equipment of suitable service type
Service satisfaction, moreover it is possible to meet efficiency of service requirement.
In the present invention, a MIXED INTEGER type Optimized model with random restraint-type is solved, as follows:
Maximize objective function: d1·R1(τ)+d2·R2(τ)
Meet:
Restraint-type 1:W (τ, s1,s2)≤ε
Restraint-type 2:
Restraint-type 3:0 < τ < 1
Restraint-type 4:s1,s2∈positive integer
Wherein, d1、d2It distributes to screen customer by classification of service gate valve value to point of the service equipment of two kinds of service types
With ratio；R1(τ)、R2(τ) respectively indicates the satisfaction of the service equipment of two kinds of service types；Restraint-type 1 indicates customer's expectation etc.
To time W (τ, s1,s2) it is less than default expectation waiting time gate valve value ε；The left side of restraint-type 2 indicates the service people of service equipment
The sum of member, the deployment cost of service equipment and operation cost, the right indicate master budget B, β1、β2It respectively indicates and uses two every year
The depreciation amortized cost of the service equipment of kind service type, the service that p (τ) expression customer is assigned to second of service type are set
Standby allocation probability, ci, what i=1,2 respectively indicated two kinds of service types employs attendant's cost；Restraint-type 3 indicates service
The value range of classification gate valve value τ；Restraint-type 4 indicates s1、s2Attendant's number of the service equipment of two kinds of service types is positive whole
Number.
The modeling conceptual depiction of this mathematical model is as follows:
1, the objective function of Optimized model is the overall service satisfaction for maximizing service system: being waited through screening expectation
Time gate threshold values τ obtains the allocation proportion d of customer1、d2, the satisfaction R of the different service type service equipment of two kinds of weighting aggregation1
(τ)、R2(τ)。
2, first restraint-type guarantees efficiency of service requirement: expectation waiting time W (τ, the s of customer1,s2) need to be less than one
It is expected that waiting time gate valve value ε.
3, Article 2 restraint-type be master budget limitation: the attendant of service equipment, the deployment cost of service equipment and
The summation of operation cost is no more than a given master budget B.
4, the assignment range of Article 3 formula restraint-type specification expectation waiting time gate valve value τ: adjustment expectation waiting time door
Threshold values τ need to be between 0% and 100%.
5, Article 4 restraint-type indicates that attendant's number, the service equipment number of two kinds of service type service device configurations are all
Positive integer.
6, this mathematic optimal model is by the target using the overall service satisfaction that maximizes service system as optimization, decision
Variable first is that customer to be sorted is assigned to the expectation waiting time gate valve value τ of different service type service equipment, belong to company
Ideotype variable；And another decision variable is the configuration number s of the attendant of two kinds of service types, service equipment1、s2, belong to from
Dissipate type variable.
Subordinate list one and subordinate list two converge whole the technology of the present invention a kind of MIXED INTEGER type with random restraint-type to be dealt with
The related symbol of Optimized model defines.
Subordinate list one, the decision variable of Optimized model and the whole table of performance indicators remittance
The whole table of pa-rameter symbols remittance of subordinate list two, Optimized model
| Parameter | Definition |
| d1 | The efficiency of service of the service equipment of service type I is a constant between 0 and 1. |
| d2 | The efficiency of service of the service equipment of service type II is a constant between 0 and 1. |
| c1 | Service type I employs the cost of attendant. |
| c2 | Service type II employs the cost of attendant. |
| ε | The efficiency requirements value of customer's expectation waiting time. |
| B | The master budget amount of money for building service equipment He employing attendant. |
| β1 | The annual service equipment depreciation amortized cost for using service type I. |
| β2 | The annual service equipment depreciation amortized cost for using service type II. |
| p(τ) | When gate valve value of classifying is τ, customer is assigned to the allocation probability of service type II. |
| R1(τ) | When gate valve value of classifying is τ, service satisfaction of the customer in service type I. |
| R2(τ) | When gate valve value of classifying is τ, service satisfaction of the customer in service type II. |
In this MIXED INTEGER type Optimized model with random restraint-type, as mathematical function R1(τ)、R2(τ), p (τ)
With W (τ, s1,s2) when can not be expressed with analytic equation, the present invention proposes simulation optimization algorithm, looks for through the method for system emulation
Mathematical function estimated value out calculates classification of service gate valve value τ and two kinds of safety check station personnel depaly numbers and s1、s2Optimal solution.
Even if sometimes in certain particular examples, function R1(τ)、R2(τ), p (τ) and W (τ, s1,s2) can be with mathematical solution
Analysis pattern calculates functional value, but also can calculate numerical value because function excessively complexity is difficult with computer, causes Optimized model
The solution time increase significantly.And be even more that functional value can not be given expression to mathematical expression in randomness optimization problem, this can only be used
Invention proposes simulation optimization algorithm to solve.
Specifically, the present invention is accomplished by the following way:
Bound proposed by the invention, which is accepted within limits, holds back search optimization algorithm, is when constantly restraining search using bound to wait
Between simulation value, change the upper bound or lower bound in iteration each time, then find new classification of service gate valve value through dichotomy, until
Converge to the latency value for meeting confidence interval.This bound convergence search algorithm can continue to carry out main program step below
Until exporting optimal classification of service gate valve value τ*.The pa-rameter symbols of algorithm are as follows: enabling k be expressed as algorithm iteration number, K is maximum
Number of iterations,For the upper bound of classification of service gate valve value,τFor the lower bound of classification of service gate valve value, M is the repetition time of simulation test
Number, θ1、θ2The gradient parameter of solution is improved for each iteration.
Bound accepts the main program for holding back search algorithm within limits:
Step S1, according to restraint-type 2, s is selected1、s2The set C of all possible combinations；
Step S2, the number of iterations n=0 of setting optimization solution；
Step S21, one group of solution (s is taken from set C1 (n),s2 (n)), set algorithm number of iterations k=0；
Step S22, whenWhen, it enablesAnd enter step S25, wherein Δ τ is one previously given
Sufficiently small positive value；If it is not, working asWhen, then set k ← k+1 andEnter step S23；
Step S23, according to τkSetting, execute M duplicate l-G simulation test, the waiting time W recordedj(s1 (n),
s2 (n)), j=1,2,3 ... M, and calculate its average value:
And it calculates95% confidence intervalIts
In, γ is half length of confidence interval；
If step S24, default expectation waiting time gate valve value ε meets inequalityOr it when algorithm iteration number k=K, then setsAnd more
New set C ← C { (s1 (n),s2 (n))}；Conversely, if default expectation waiting time gate valve valueWhen, settingτ=τk, and return to step S22 and continue to execute；If default expectation waiting time gate valve valueWhen, then it setsAnd it returns to step S22 and continues to execute；
Step S25, as set C=φ, bound restrains search algorithm loop termination and enters step S3；Conversely,
Number of iterations n ← n+1 of setting optimization solution, resumes step S21 are continued to execute；
Step S3: the obtained solution of search algorithm is restrained for boundUtilization feasibility proving program determines solution
Feasibility, to leave out infeasible solution；Enable C*Indicate all after feasibility proving program is selectedThe solution set of composition；
Algorithm output: the available optimal expectation waiting time gate valve value of search algorithm is restrained through this boundAnd the optimum value that can calculate the overall service satisfaction of service system is SL (τ*)。
Bibliography:
[1] bibliography to sort with option program (Ranking and Selection): Andrad'ottir, S.,
Kim,S.H.(2010)Fully sequential procedures for comparing constrained systems
via simulation.Naval Research Logistics,vol.57,pp.403--421.。
The above are preferred embodiments of the present invention, all any changes made according to the technical solution of the present invention, and generated function is made
When with range without departing from technical solution of the present invention, all belong to the scope of protection of the present invention.
Claims (3)
1. a kind of bound for having Filtering system, which is accepted within limits to hold back, searches simulation optimization calculation method, which is characterized in that maximize clothes
Target of the overall service satisfaction of business system as optimization establishes two heterogeneous service type service systems of tool Filtering system
MIXED INTEGER type Optimized model；Then, it is accepted within limits using bound and holds back search optimization algorithm, the overall service for calculating service system is full
The optimum value of meaning degree.
2. a kind of bound for having Filtering system according to claim 1, which is accepted within limits to hold back, searches simulation optimization calculation method,
It is characterized in that, the MIXED INTEGER type Optimized model of two heterogeneous service type service systems of the tool Filtering system is as follows:
Objective function: d1·R1(τ)+d2·R2(τ)
Restraint-type 1:W (τ, s1,s2)≤ε
Restraint-type 2:
Restraint-type 3:0 < τ < 1
Restraint-type 4:s1,s2∈positive integer
Wherein, d1、d2To screen the distribution ratio that customer distributes the service equipment to two kinds of service types by classification of service gate valve value
Example；R1(τ)、R2(τ) respectively indicates the satisfaction of the service equipment of two kinds of service types；When restraint-type 1 indicates that customer it is expected to wait
Between W (τ, s1,s2) it is less than default expectation waiting time gate valve value ε；The left side of restraint-type 2 indicates the attendant of service equipment, clothes
The sum of the deployment cost for equipment of being engaged in and operation cost, the right indicate master budget B, β1、β2It respectively indicates annual using two kinds of services
The depreciation amortized cost of the service equipment of type, p (τ) indicate that customer is assigned to point of the service equipment of second of service type
With probability, ci, what i=1,2 respectively indicated two kinds of service types employs attendant's cost；Restraint-type 3 indicates classification of service door
The value range of threshold values τ；Restraint-type 4 indicates s1、s2Attendant's number of the service equipment of two kinds of service types is positive integer.
3. a kind of bound for having Filtering system according to claim 2, which is accepted within limits to hold back, searches simulation optimization calculation method,
It is characterized in that, described accepted within limits using bound holds back search optimization algorithm, calculates the best of the overall service satisfaction of service system
Value the specific implementation process is as follows:
Step S1, according to restraint-type 2, s is selected1、s2The set C of all possible combinations；
Step S2, the number of iterations n=0 of setting optimization solution；
Step S21, one group of solution (s is taken from set C1 (n),s2 (n)), set algorithm number of iterations k=0；
Step S22, whenWhen, it enablesAnd enter step S25, wherein Δ τ is one previously given enough
Small positive value；If it is not, working asWhen, then set k ← k+1 andEnter step S23；
Step S23, according to τkSetting, execute M duplicate l-G simulation test, the waiting time W recordedj(s1 (n),s2 (n)),
J=1,2,3 ... M, and calculate its average value:
And it calculates95% confidence intervalWherein, γ
It is half length of confidence interval；
If step S24, default expectation waiting time gate valve value ε meets inequalityOr it when algorithm iteration number k=K, then setsAnd more
New set C ← C { (s1 (n),s2 (n))}；Conversely, if default expectation waiting time gate valve valueWhen, settingτ=τk, and return to step S22 and continue to execute；If default expectation waiting time gate valve valueWhen, then it setsAnd it returns to step S22 and continues to execute；
Step S25, as set C=φ, bound restrains search algorithm loop termination and enters step S3；Conversely, setting
Optimize number of iterations n ← n+1 of solution, resumes step S21 is continued to execute；
Step S3: the obtained solution of search algorithm is restrained for boundUtilization feasibility proving program determines the feasible of solution
Property, to leave out infeasible solution；Enable C*Indicate all after feasibility proving program is selectedThe solution set of composition；Finally
Export optimal expectation waiting time gate valve valueAnd the total of service system can be calculated
The optimum value of body service satisfaction is SL (τ*)。
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