WO2019080354A1 - 一种基于昂贵多目标优化问题的优化方法及系统 - Google Patents

一种基于昂贵多目标优化问题的优化方法及系统

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WO2019080354A1
WO2019080354A1 PCT/CN2017/119312 CN2017119312W WO2019080354A1 WO 2019080354 A1 WO2019080354 A1 WO 2019080354A1 CN 2017119312 W CN2017119312 W CN 2017119312W WO 2019080354 A1 WO2019080354 A1 WO 2019080354A1
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objective
task
optimization
mapping
target
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French (fr)
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骆剑平
薛虎
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深圳大学
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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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    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"

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  • the invention relates to the technical field of interval multi-objective optimization, in particular to an optimization method and system based on an expensive multi-objective optimization problem.
  • the interval multi-objective optimization problem is widespread.
  • the target In daily life, it is often required that more than one index is optimal, and often multiple indicators are required to be optimal at the same time, and a large number of problems can be attributed to A class of multi-objective optimization problems that achieve multiple objectives at the same time under certain constraints; for example, in machining, in the feed cutting, in order to select the appropriate cutting speed and feed rate, the target is: 1 The lowest machining cost, 2. High productivity, 3. The longest tool life, and the constraint that the feed amount is less than the machining allowance and tool strength.
  • One parameter is equivalent to one target (one target corresponds to one objective function). For example, when the vehicle is looking for a route, the target is: 1. the best road condition, 2. the shortest time, 3. the lowest cost, etc.; for the optimization problem of the above multiple targets, if each target is separately established independently
  • the proxy model when the amount of data is small, leads to the model being not accurate enough and expensive.
  • the proxy model optimization of Gaussian Process (GP) modeling is its main optimization method.
  • the main idea is to establish a Gaussian proxy model for each expensive optimization objective function, and then use some evolutionary algorithms to build a proxy model based on it.
  • Prediction and optimization the main disadvantage of this method is to establish an independent proxy model for each target.
  • Another improved idea is to adopt a multi-task Gaussian process (Multiple).
  • Task GP, MTGP jointly model multiple targets to increase the amount of data being modeled.
  • joint modeling tends to make the established model more inaccurate, thus affecting the evolutionary algorithms that follow. Predictive accuracy and optimization efficiency.
  • the technical problem to be solved by the present invention is to provide an optimization method and system based on the expensive multi-objective optimization problem for the above-mentioned defects of the prior art, aiming at using the established multi-task Gaussian process model for each task in the optimization process.
  • Perform prediction then map the task prediction value to the target prediction value through inverse mapping, to avoid the purpose of calculating the expensive objective function, and finally output the optimization result; by mapping multiple unrelated objective functions to a set of existing correlation or similarity
  • MTGP is used to jointly model these task series to generate MTGP model, which effectively utilizes the similarity between task series to improve the accuracy of the model, and can effectively increase the training data sample when the amount of data is small.
  • the cost of multiple unrelated target optimizations in the same task is used to jointly model these task series to generate MTGP model, which effectively utilizes the similarity between task series to improve the accuracy of the model, and can effectively increase the training data sample when the amount of data is small.
  • An optimization method based on an expensive multi-objective optimization problem wherein the optimization method based on an expensive multi-objective optimization problem comprises:
  • the target functions corresponding to the multiple unrelated targets are converted by mapping
  • the task series with similarity or correlation is jointly modeled, and the multi-task Gaussian process model is generated to predict the target and output the optimization result.
  • the optimization method based on the expensive multi-objective optimization problem wherein the task series with similarity or correlation is jointly modeled, and the multi-task Gaussian process model is generated to predict the target, and the output optimization result further includes:
  • the multi-task Gaussian process model obtains prediction values of all objective functions by inverse mapping, and predicts all objective functions.
  • the optimization method based on the expensive multi-objective optimization problem wherein when a plurality of targets in a task simultaneously reach a preset requirement, converting the target functions corresponding to the plurality of unrelated targets by mapping includes the following steps:
  • the optimization method based on the expensive multi-objective optimization problem, wherein the associating the objective function into a set of related or similar task series by mapping the target function to the plurality of unrelated objective functions includes the following steps:
  • mapping and transforming a plurality of unrelated objective functions After mapping and transforming a plurality of unrelated objective functions, a plurality of unrelated objective functions are concentrated into a set of tasks having correlation or similarity;
  • the optimization method based on the expensive multi-objective optimization problem wherein the task series with similarity or correlation is jointly modeled, the multi-task Gaussian process model is generated to predict the target, and the output optimization result includes the following steps. :
  • Gaussian joint modeling based on a series of related or similar tasks obtained by conversion
  • the two objective functions are denoted as f 1 and f 2 respectively , then define:
  • h 1 and h 2 are defined intermediate variables, a 1 , a 2 , b 1 , and b 2 are real numbers, and
  • establishing a Gaussian process model for f 1 and f 2 is equivalent to establishing a Gaussian process model for h 1 and h 2 , and obtaining the distribution of h 1 and h 2 by the distribution of f 1 and f 2 , or by h 1 And the distribution of h 2 , then obtain the distribution of f 1 and f 2 .
  • f 1 and f 2 and the Gaussian process model estimates h 1 and h 2 Gaussian process models for conversion; relevance or similarity by acquiring h of f 1 and f 2 mapping between 1 and h 2 h 1 and h 2, by correlation or similarity between h 1 and h 2 2 multitasking process jointly Gaussian modeled h 1 and H; after completion of joint model, by obtaining reverse mapping f 1 and f 2 of Predictive value.
  • the optimization method based on the expensive multi-objective optimization problem, wherein, when predicting the objective function, obtaining a predicted value by using the established multi-task Gaussian process model for any input vector x* with Correct with Perform reverse mapping to get with among them, Represents the ith target value for input j.
  • An optimization system based on an expensive multi-objective optimization problem wherein the system includes:
  • mapping module configured to convert a target function corresponding to multiple unrelated targets by mapping when multiple targets in a task reach the preset requirement at the same time
  • An association module configured to convert an objective function to a plurality of unrelated objective functions in a task series having relevance or similarity by mapping
  • a modeling module for jointly modeling a series of tasks with similarity or correlation, generating a multi-task Gaussian process model to predict the target, and outputting the optimization result;
  • a prediction module configured to acquire prediction values of all the objective functions by using the inverse mapping to the multi-task Gaussian process model, and predict all the objective functions.
  • the present invention provides an optimization method and system based on an expensive multi-objective optimization problem, the method comprising: mapping a plurality of unrelated targets corresponding to an objective function when a plurality of targets in a task simultaneously reach a preset requirement Transforming; transforming the objective function into a set of related or similar task series through mapping to associate multiple unrelated objective functions; jointly modeling the series of similarities or correlations to generate more
  • the task Gaussian process model predicts the target and outputs the optimization result.
  • each task is predicted by using the established multi-task Gaussian process model, and then the task prediction value is mapped to the target prediction value through inverse mapping to avoid calculation.
  • the present invention generates a MTGP model by mapping a plurality of unrelated objective functions into a set of tasks with correlation or similarity, and then using MTGP to jointly model the task series. Effectively use the similarity between task series to improve the accuracy of the model Degrees, while in the small amount of data that can effectively increase the sample training data, reducing multiple unrelated target cost optimization of the same task.
  • FIG. 1 is a flow chart of a preferred embodiment of an optimization method based on an expensive multi-objective optimization problem of the present invention.
  • FIG. 2 is a schematic diagram of MTGP modeling and prediction based on mapping and inverse mapping in a preferred embodiment of the optimization method based on the expensive multi-objective optimization problem of the present invention.
  • FIG. 3 is a functional block diagram of a preferred embodiment of an optimization system based on an expensive multi-objective optimization problem of the present invention.
  • FIG. 1 is a flow chart of a preferred embodiment of an optimization method based on the expensive multi-objective optimization problem of the present invention.
  • an optimization method based on an expensive multi-objective optimization problem includes the following steps:
  • Step S100 When multiple targets in a task reach the preset requirement at the same time, the target functions corresponding to the plurality of unrelated targets are converted by mapping.
  • step S100 specifically includes the following steps:
  • h 1 and h 2 are defined intermediate variables, a 1 , a 2 , b 1 , and b 2 are real numbers, and
  • step S200 the target function is converted into a set of task series with correlation or similarity by mapping to associate a plurality of unrelated objective functions.
  • step S200 specifically includes the following steps:
  • establishing a Gaussian process model for f 1 and f 2 is equivalent to establishing a Gaussian process model for h 1 and h 2 , and obtaining a distribution of h 1 and h 2 by the distribution of f 1 and f 2 , Or by the distribution of h 1 and h 2 , the distribution of f 1 and f 2 is obtained.
  • step S300 the task series with similarity or correlation is jointly modeled, and a multi-task Gaussian process model is generated to predict the target, and the optimization result is output.
  • step S300 specifically includes the following steps:
  • the Gaussian process model of f 1 and f 2 is transformed with the estimates of the Gaussian process models of h 1 and h 2 .
  • the pre-set requirement is to propose the goal: 1.
  • the road condition is best, 2.
  • the time is the shortest, 3.
  • the cost is the lowest; then these three are irrelevant goals, one
  • the target corresponds to an objective function, which can be represented by f1 (representing road conditions), f2 (representing time), and f3 (representing cost), respectively, and converting three standard functions f1, f2, and f3 by mapping to obtain h1, h2, and H3, then h1, h2, and h3 are a set of tasks with correlation or similarity, and the task series with similarity or correlation is jointly modeled to generate multi-task Gaussian process models for multiple targets. Optimize to meet preset requirements and plan a best route for users to meet multiple target requirements.
  • step S300 further includes: obtaining, by using the reverse mapping, the predicted values of all the objective functions on the multi-task Gaussian process model, and predicting all the objective functions.
  • the target for the optimization problem of double after passing through the correlation or similarity of h 1 and h 2 multitasking joint Gaussian process model between h 1 and h 2 further comprising: reverse
  • the map obtains the predicted values of f 1 and f 2 .
  • FIG. 2 is a schematic diagram of MTGP modeling and prediction based on mapping and inverse mapping in a preferred embodiment of the optimization method based on the expensive multi-objective optimization problem of the present invention; when predicting the objective function, For any input vector x* (or solution), the predicted value is obtained from the established multitasking Gaussian process model with Correct with Perform reverse mapping to get with among them, Represents the ith target value for input j.
  • the generated model can be easily embedded into some expensive multi-objective optimization frameworks, such as MOEA/D-EGO (MOEA/D-EGO is an algorithm framework for expensive multi-objective optimization, and the algorithm is built separately for each objective function.
  • MOEA/D-EGO is an algorithm framework for expensive multi-objective optimization, and the algorithm is built separately for each objective function.
  • the GP model which predicts each target value using the established independent model in the prediction process, constitutes an expensive multi-objective optimization system.
  • the specific embedding method is to replace the MOEA/D-EGO with the above-mentioned multi-objective MTGP model. A method of establishing a normal GP model for each target.
  • the main key point of the present invention is that in the expensive multi-objective optimization problem, a mapping technique is adopted for each unrelated target function, and the target is mapped to a set of tasks with similarity or correlation, and then the pair is similar.
  • sexual or related task series for GP joint modeling (MTGP) to improve the accuracy of the model; in addition, in the prediction process, reverse mapping is used to restore the predicted value from the task series to the target series; joint modeling utilizes the training task
  • MTGP GP joint modeling
  • the program may be stored in a computer readable storage medium, and the program may include the flow of the method embodiments as described above when executed.
  • the storage medium described therein may be a memory, a magnetic disk, an optical disk, or the like.
  • An embodiment of the present invention further provides an optimization system based on an expensive multi-objective optimization problem. As shown in FIG. 3, the system includes:
  • the mapping module 10 is configured to convert the target functions corresponding to the plurality of unrelated targets by mapping when multiple targets in a task reach the preset requirement at the same time;
  • the association module 20 is configured to convert the target function to a plurality of unrelated target functions in a task series with correlation or similarity by mapping;
  • the modeling module 30 is configured to jointly model the task series with similarity or correlation, generate a multi-task Gaussian process model to predict the target, and output the optimization result;
  • the prediction module 40 is configured to obtain prediction values of all the objective functions by using the inverse mapping to the multi-task Gaussian process model, and predict all the objective functions; as described above.
  • the present invention discloses an optimization method and system based on an expensive multi-objective optimization problem, the method comprising: when a plurality of targets in a task simultaneously reach a preset requirement, corresponding to a plurality of unrelated targets
  • the objective function is transformed by mapping; the objective function is transformed into a set of related or similar task series through the mapping to link multiple unrelated objective functions; the task series with similarity or correlation is combined Modeling, generating a multi-task Gaussian process model to predict the target and output the optimization result; in the optimization process, using the established multi-task Gaussian process model to predict each task, and then mapping the task prediction value to the target prediction through inverse mapping Values, to avoid the purpose of calculating expensive objective functions, and finally to output optimization results; the present invention maps task series by mapping multiple unrelated objective functions into a set of tasks with correlation or similarity, and then using MTGP Modeling produces MTGP models, effectively using the similarities between task series to Accuracy of the model, while in the small amount of data can effectively increase the sample training data,
  • mapping of the present invention uses a linear mapping to map an objective function to a task sequence, thereby establishing similarity between tasks.
  • multi-objective optimization other methods are used to establish task similarity, thereby performing joint modeling. It can be seen that it is the same as the present embodiment; the application of the present invention is not limited to the above examples, and those skilled in the art can modify or change according to the above description, all of which are subject to the appended claims. The scope of protection.

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Abstract

一种基于昂贵多目标优化问题的优化方法及系统，当一个任务中多个目标同时达到预设要求时，将多个不相关的目标对应的目标函数通过映射进行转换(S100 )；将目标函数通过映射转换到一组具有相关性或者相似性的任务系列中对多个不相关的目标函数进行关联(S200)；将具有相似性或相关性的任务系列进行联合建模，生成多任务高斯过程模型；本方法在优化环节，利用建立的多任务高斯过程模型对每个任务进行预测，然后通过逆映射将任务预测值映射到目标预测值，达到避免计算昂贵目标函数的目的，最后输出优化结果；降低了多个不相关目标优化的成本。

Description

一种基于昂贵多目标优化问题的优化方法及系统 技术领域
本发明涉及区间多目标优化技术领域，具体涉及一种基于昂贵多目标优化问题的优化方法及系统。
背景技术
现有技术中，在实际应用中,区间多目标优化问题普遍存在，在日常生活中，经常要求不止一项指标达到最优，往往要求多项指标同时达到最优，大量的问题都可以归结为一类在某种约束条件下使多个目标同时达到最优的多目标优化问题；例如，在机械加工时，在进给切削中，为选择合适的切削速度和进给量，提出目标：1.机械加工成本最低，2.生产率高，3.刀具寿命最长，同时还要满足进给量小于加工余量、刀具强度等约束条件，一个参数就相当于一个目标(一个目标对应一个目标函数)；再例如，在车辆寻找路线时，提出目标：1.路况最好，2.时间最短，3.成本最低等；针对上述的多个目标的优化问题，如果每一个目标进行分别建立独立的代理模型，在数据量较小的时候会导致模型建立不够准确，且成本昂贵。
所以，现有技术中，对于昂贵多目标(此处的昂贵多目标中的昂贵是指单独对每个目标函数进行建模优化时成本较高的意思)优化问题(Expensive multiobjective optimization problems)，基于高斯过程(Gaussian Process，GP)建模的代理模型优化是其主要优化方法，其主要的思路是对每一个昂贵优化目标函数分别建立高斯代理模型，然后再采用一些进化算法进行基于建立的代理模型的预测和优化；该方法主要的缺点是对每个目标分别建立独立的代理模型，在数据量较小的时候会导致模型建立不够准确；另一种改进的思路是采用多任务高斯过程(Multiple Task GP，MTGP)对多个目标联合建模来增加建模的数据数量，但是，由于目标之间缺少相关性，联合建模往往会使建立的模型更加不准确，从而影响到后面进化算法的预测准确度及优化效率。
因此，现有技术还有待于改进和发展。
发明内容
本发明要解决的技术问题在于，针对现有技术的上述缺陷，提供一种基于昂贵多目标优化问题的优化方法及系统，旨在在优化环节，利用建立的多任务高斯 过程模型对每个任务进行预测，然后通过逆映射将任务预测值映射到目标预测值，达到避免计算昂贵目标函数的目的，最后输出优化结果；通过将多个不相关的目标函数映射到一组存在相关性或相似性的任务系列中，然后利用MTGP将这些任务系列进行联合建模产生MTGP模型，有效利用任务系列之间的相似性来提高模型的准确度，同时在数据量较小时能有效增加训练的数据样本降低了同一任务中多个不相关目标优化的成本。
本发明解决技术问题所采用的技术方案如下：
一种基于昂贵多目标优化问题的优化方法，其中，所述基于昂贵多目标优化问题的优化方法包括：
当一个任务中多个目标同时达到预设要求时，将多个不相关的目标对应的目标函数通过映射进行转换；
将目标函数通过映射转换到一组具有相关性或者相似性的任务系列中对多个不相关的目标函数进行关联；
将具有相似性或相关性的任务系列进行联合建模，生成多任务高斯过程模型对目标进行预测，并输出优化结果。
所述的基于昂贵多目标优化问题的优化方法，其中，所述将具有相似性或相关性的任务系列进行联合建模，生成多任务高斯过程模型对目标进行预测，并输出优化结果还包括：
对所述多任务高斯过程模型通过逆向映射获取所有目标函数的预测值，对所有目标函数进行预测。
所述的基于昂贵多目标优化问题的优化方法，其中，所述当一个任务中多个目标同时达到预设要求时，将多个不相关的目标对应的目标函数通过映射进行转换包括以下步骤：
预先设置所述一个任务中多个目标同时要达到的预设要求；
获取所述一个任务中多个不相关的目标，建立每一个目标对应的目标函数；
将多个不相关的目标函数进行映射转换。
所述的基于昂贵多目标优化问题的优化方法，其中，所述将目标函数通过映射转换到一组具有相关性或者相似性的任务系列中对多个不相关的目标函数进行关联包括以下步骤：
当将多个不相关的目标函数进行映射转换后，多个不相关的目标函数集中到一组具有相关性或者相似性的任务系列中；
当转换得到所述任务系列后，多个不相关的目标函数完成关联操作。
所述的基于昂贵多目标优化问题的优化方法，其中，所述将具有相似性或相关性的任务系列进行联合建模，生成多任务高斯过程模型对目标进行预测，并输出优化结果包括以下步骤：
根据转换得到的具有相关性或者相似性的任务系列，进行高斯联合建模；
当完成所述高斯联合建模后，生成多任务高斯过程模型多个目标进行预测，根据所述预设要求对多个目标进行优化。
所述的基于昂贵多目标优化问题的优化方法，其中，
当所述目标函数为两个不相关的目标函数时，两个目标函数分别表示为f 1和f 2，则定义：
Figure PCTCN2017119312-appb-000001
其中，h 1和h 2为定义的中间变量，a 1,a 2,b 1,和b 2为实数，且
Figure PCTCN2017119312-appb-000002
所述的基于昂贵多目标优化问题的优化方法，其中，当
Figure PCTCN2017119312-appb-000003
则
Figure PCTCN2017119312-appb-000004
,即
Figure PCTCN2017119312-appb-000005
其中，对f 1和f 2建立高斯过程模型等价于对h 1和h 2建立高斯过程模型，通过f 1和f 2的分布，则获取得到h 1和h 2的分布，或者通过h 1和h 2的分布，则获取得到f 1和f 2的分布。
所述的基于昂贵多目标优化问题的优化方法，其中，当已知h 1和h 2的分布，对于f 1和f 2的均值和方差，则：
Figure PCTCN2017119312-appb-000006
Figure PCTCN2017119312-appb-000007
则得到：
Figure PCTCN2017119312-appb-000008
Figure PCTCN2017119312-appb-000009
f 1和f 2的高斯过程模型与h 1和h 2的高斯过程模型的估计值进行转换；h 1和h 2之间具有相关性或相似性，通过对f 1和f 2映射获取h 1和h 2，通过h 1和h 2之间的相关性或相似性对h 1和h 2采用多任务高斯过程进行联合建模；联合建模完成后，通过逆向映射获取f 1和f 2的预测值。
所述的基于昂贵多目标优化问题的优化方法，其中，在对所述目标函数进行预测时，对于任一输入矢量x*，通过建立的多任务高斯过程模型获得预测值
Figure PCTCN2017119312-appb-000010
和
Figure PCTCN2017119312-appb-000011
对
Figure PCTCN2017119312-appb-000012
和
Figure PCTCN2017119312-appb-000013
进行逆向映射则获得
Figure PCTCN2017119312-appb-000014
和
Figure PCTCN2017119312-appb-000015
其中，
Figure PCTCN2017119312-appb-000016
表示对于输入j的第i个目标值。
一种基于昂贵多目标优化问题的优化系统，其中，所系统包括：
映射模块，用于当一个任务中多个目标同时达到预设要求时，将多个不相关的目标对应的目标函数通过映射进行转换；
关联模块，用于将目标函数通过映射转换到一组具有相关性或者相似性的任务系列中对多个不相关的目标函数进行关联；
建模模块，用于将具有相似性或相关性的任务系列进行联合建模，生成多任务高斯过程模型对目标进行预测，并输出优化结果；
预测模块，用于对所述多任务高斯过程模型通过逆向映射获取所有目标函数的预测值，对所有目标函数进行预测。
本发明提供了一种基于昂贵多目标优化问题的优化方法及系统，所述方法包括：当一个任务中多个目标同时达到预设要求时，将多个不相关的目标对应的目标函数通过映射进行转换；将目标函数通过映射转换到一组具有相关性或者相似性的任务系列中对多个不相关的目标函数进行关联；将具有相似性或相关性的任 务系列进行联合建模，生成多任务高斯过程模型对目标进行预测，并输出优化结果；在优化环节，利用建立的多任务高斯过程模型对每个任务进行预测，然后通过逆映射将任务预测值映射到目标预测值，达到避免计算昂贵目标函数的目的，最后输出优化结果；本发明通过将多个不相关的目标函数映射到一组存在相关性或相似性的任务系列中，然后利用MTGP将任务系列进行联合建模产生MTGP模型，有效利用任务系列之间的相似性来提高模型的准确度，同时在数据量较小时能有效增加训练的数据样本，降低了同一任务中多个不相关目标优化的成本。
附图说明
图1是本发明基于昂贵多目标优化问题的优化方法的较佳实施例的流程图。
图2是本发明基于昂贵多目标优化问题的优化方法的较佳实施例中基于映射和逆映射的MTGP建模及预测的示意图。
图3是本发明基于昂贵多目标优化问题的优化系统的较佳实施例功能原理框图。
具体实施方式
为使本发明的目的、技术方案及优点更加清楚、明确，以下参照附图并举实施例对本发明进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。
实施例一
请参见图1，图1是本发明基于昂贵多目标优化问题的优化方法的较佳实施例的流程图。如图1所示，一种基于昂贵多目标优化问题的优化方法，其中，包括以下步骤：
步骤S100，当一个任务中多个目标同时达到预设要求时，将多个不相关的目标对应的目标函数通过映射进行转换。
具体地，步骤S100具体包括如下步骤：
S101，预先设置所述一个任务中多个目标同时要达到的预设要求，也就是说在某些问题的优化过程中，有多个目标同时要达到的预设要求，其中一个任务只是泛指的概念，可以表示各种问题；
S102，获取所述一个任务中多个不相关的目标，建立每一个目标对应的目标函数；
S103，将多个不相关的目标函数进行映射转换。
本发明实施例中，以两个目标函数(双目标的优化)来进行说明，假设两个目标函数分别表示为f 1和f 2，且目标函数f 1和f 2为两个不相关的目标函数，则定义：
Figure PCTCN2017119312-appb-000017
其中，h 1和h 2为定义的中间变量，a 1,a 2,b 1,和b 2为实数，且
Figure PCTCN2017119312-appb-000018
并且当
Figure PCTCN2017119312-appb-000019
则
Figure PCTCN2017119312-appb-000020
，即
Figure PCTCN2017119312-appb-000021
步骤S200，将目标函数通过映射转换到一组具有相关性或者相似性的任务系列中对多个不相关的目标函数进行关联。
具体地，步骤S200具体包括如下步骤：
S201，当将多个不相关的目标函数进行映射转换后，多个不相关的目标函数集中到一组具有相关性或者相似性的任务系列中；
S202，当转换得到所述任务系列后，多个不相关的目标函数完成关联操作。
本发明实施例中，对f 1和f 2建立高斯过程模型等价于对h 1和h 2建立高斯过程模型，通过f 1和f 2的分布，则获取得到h 1和h 2的分布，或者通过h 1和h 2的分布，则获取得到f 1和f 2的分布。
步骤S300，将具有相似性或相关性的任务系列进行联合建模，生成多任务高斯过程模型对目标进行预测，并输出优化结果。
具体地，步骤S300具体包括如下步骤：
S301，根据转换得到的具有相关性或者相似性的任务系列，进行高斯联合建模；
S302，当完成所述高斯联合建模后，生成多任务高斯过程模型多个目标进行预测，根据所述预设要求对多个目标进行优化。
本发明实施例中，当已知h 1和h 2的分布，对于f 1和f 2的均值和方差，则：
Figure PCTCN2017119312-appb-000022
Figure PCTCN2017119312-appb-000023
则得到：
Figure PCTCN2017119312-appb-000024
Figure PCTCN2017119312-appb-000025
f 1和f 2的高斯过程模型与h 1和h 2的高斯过程模型的估计值进行转换。
由于h 1和h 2之间具有相关性或相似性，通过对f 1和f 2映射获取h 1和h 2，通过h 1和h 2之间的相关性或相似性对h 1和h 2采用多任务高斯过程进行联合建模。
由上面可以看出，虽然f 1和f 2之间可能没有相关性或相似性，然而，h 1和h 2之间具有相关性或相似性，因此，可以考虑通过对f 1和f 2映射获取h 1和h 2，再利用h 1和h 2之间的相关性或相似性，对h 1和h 2采用MTGP进行联合建模来提高模型准确度，然后再通过逆向映射获取f 1和f 2的预测值。
例如，假设本发明的一个任务为车辆寻找最佳路线，预设要求好处是提出目标：1.路况最好，2.时间最短，3.成本最低；那么这三个就是不相关的目标，一个目标对应一个目标函数，可以分别用f1(表示路况)、f2(表示时间)、和f3(表示成本)表示，将三个标函数f1、f2、和f3通过映射进行转换得到h1、h2、和h3，那么h1、h2、和h3为一组具有相关性或者相似性的任务系列，再将具有相似性或相关性的任务系列进行联合建模，生成多任务高斯过程模型后，对多个目标进行优化，达到预设要求，为用户规划出一条符合多个目标要求的最佳路线。
进一步地，所述步骤S300还包括：对所述多任务高斯过程模型通过逆向映射获取所有目标函数的预测值，对所有目标函数进行预测。
本发明实施例中，对于双目标的优化问题，所述通过h 1和h 2之间的相关性或相似性对h 1和h 2采用多任务高斯过程进行联合建模之后还包括：通过逆向映射获取f 1和f 2的预测值。
如图2所示，图2是本发明基于昂贵多目标优化问题的优化方法的较佳实施例中基于映射和逆映射的MTGP建模及预测的示意图；在对所述目标函数进行预测时，对于任一输入矢量x*(或解)，通过建立的多任务高斯过程模型获得预测值
Figure PCTCN2017119312-appb-000026
和
Figure PCTCN2017119312-appb-000027
对
Figure PCTCN2017119312-appb-000028
和
Figure PCTCN2017119312-appb-000029
进行逆向映射则获得
Figure PCTCN2017119312-appb-000030
和
Figure PCTCN2017119312-appb-000031
其中，
Figure PCTCN2017119312-appb-000032
表示对于输入j的第i个目标值。
之所以需要进行预测，是因为在优化过程中，通常需要计算优化目标适应度函数，对于昂贵优化问题，计算适应度函数代价高，因此通过代理模型来预测目标函数，而不需要真正计算目标函数准确值，从而达到降低代价的目的。
当然，上述方案可以推广到目标函数大于两个的任何昂贵多目标优化问题中，大于两个的任何昂贵多目标优化问题采用的公式按照上述公式依次进行类推即可。
另外，生成的模型可以很容易嵌入到一些昂贵多目标优化框架中，比如MOEA/D-EGO(MOEA/D-EGO是一种针对昂贵多目标优化的算法框架，算法对每个目标函数单独建立GP模型，在预测环节对每个目标值用建立的独立模型进行预测)，从而组成昂贵多目标优化系统，具体的嵌入方法是用上述的针对多目标建立MTGP模型的方法取代MOEA/D-EGO中对每个目标建立普通GP模型的方法。
本发明的主要关键点是：在昂贵多目标优化问题中，对每个互不相关的目标函数采用映射技术，把目标映射到一组具有相似性或相关性的任务系列中，然后对具有相似性或相关性的任务系列进行GP联合建模(MTGP)，从而提高模型的准确性；另外，在预测环节，采用逆向映射把预测值从任务系列恢复到目标系列；联合建模利用了训练任务之间的相似性及拓展了训练数据量，使得建立的模型更加准确。
当然，本领域普通技术人员可以理解实现上述实施例方法中的全部或部分流程，是可以通过基于昂贵多目标优化问题的建模程序来指令相关硬件(如处理器， 控制器等)来完成，所述的程序可存储于一计算机可读取的存储介质中，所述程序在执行时可包括如上述各方法实施例的流程。其中所述的存储介质可为存储器、磁碟、光盘等。
本发明实施例还提供了一种基于昂贵多目标优化问题的优化系统，如图3所示，所系统包括：
映射模块10，用于当一个任务中多个目标同时达到预设要求时，将多个不相关的目标对应的目标函数通过映射进行转换；
关联模块20，用于将目标函数通过映射转换到一组具有相关性或者相似性的任务系列中对多个不相关的目标函数进行关联；
建模模块30，用于将具有相似性或相关性的任务系列进行联合建模，生成多任务高斯过程模型对目标进行预测，并输出优化结果；
预测模块40，用于对所述多任务高斯过程模型通过逆向映射获取所有目标函数的预测值，对所有目标函数进行预测；具体如上所述。
综上所述，本发明公开了一种基于昂贵多目标优化问题的优化方法及系统，所述方法包括：当一个任务中多个目标同时达到预设要求时，将多个不相关的目标对应的目标函数通过映射进行转换；将目标函数通过映射转换到一组具有相关性或者相似性的任务系列中对多个不相关的目标函数进行关联；将具有相似性或相关性的任务系列进行联合建模，生成多任务高斯过程模型对目标进行预测，并输出优化结果；在优化环节，利用建立的多任务高斯过程模型对每个任务进行预测，然后通过逆映射将任务预测值映射到目标预测值，达到避免计算昂贵目标函数的目的，最后输出优化结果；本发明通过将多个不相关的目标函数映射到一组存在相关性或相似性的任务系列中，然后利用MTGP将任务系列进行联合建模产生MTGP模型，有效利用任务系列之间的相似性来提高模型的准确度，同时在数据量较小时能有效增加训练的数据样本，降低了同一任务中多个不相关目标优化的成本。
应当理解的是，本发明的映射采用线性映射把目标函数映射到任务序列，从而建立任务之间的相似性，在多目标优化中，其他采用任何方法建立任务相似性，从而进行联合建模，都可看作与本方案相同；本发明的应用不限于上述的举例，对本领域普通技术人员来说，可以根据上述说明加以改进或变换，所有这些改进和变换都应属于本发明所附权利要求的保护范围。

Claims (10)

  1. 一种基于昂贵多目标优化问题的优化方法，其特征在于，所述基于昂贵多目标优化问题的优化方法包括：
    当一个任务中多个目标同时达到预设要求时，将多个不相关的目标对应的目标函数通过映射进行转换；
    将目标函数通过映射转换到一组具有相关性或者相似性的任务系列中对多个不相关的目标函数进行关联；
    将具有相似性或相关性的任务系列进行联合建模，生成多任务高斯过程模型对目标进行预测，并输出优化结果。
  2. 根据权利要求1所述的基于昂贵多目标优化问题的优化方法，其特征在于，所述将具有相似性或相关性的任务系列进行联合建模，生成多任务高斯过程模型对目标进行预测，并输出优化结果还包括：
    对所述多任务高斯过程模型通过逆向映射获取所有目标函数的预测值，对所有目标函数进行预测。
  3. 根据权利要求1所述的基于昂贵多目标优化问题的优化方法，其特征在于，所述当一个任务中多个目标同时达到预设要求时，将多个不相关的目标对应的目标函数通过映射进行转换包括以下步骤：
    预先设置所述一个任务中多个目标同时要达到的预设要求；
    获取所述一个任务中多个不相关的目标，建立每一个目标对应的目标函数；
    将多个不相关的目标函数进行映射转换。
  4. 根据权利要求3所述的基于昂贵多目标优化问题的优化方法，其特征在于，所述将目标函数通过映射转换到一组具有相关性或者相似性的任务系列中对多个不相关的目标函数进行关联包括以下步骤：
    当将多个不相关的目标函数进行映射转换后，多个不相关的目标函数集中到一组具有相关性或者相似性的任务系列中；
    当转换得到所述任务系列后，多个不相关的目标函数完成关联操作。
  5. 根据权利要求4所述的基于昂贵多目标优化问题的优化方法，其特征在于，所述将具有相似性或相关性的任务系列进行联合建模，生成多任务高斯过程模型对目标进行预测，并输出优化结果包括以下步骤：
    根据转换得到的具有相关性或者相似性的任务系列，进行高斯联合建模；
    当完成所述高斯联合建模后，生成多任务高斯过程模型多个目标进行预测， 根据所述预设要求对多个目标进行优化。
  6. 根据权利要求1所述的基于昂贵多目标优化问题的优化方法，其特征在于，当所述目标函数为两个不相关的目标函数时，两个目标函数分别表示为f 1和f 2，则定义：
    Figure PCTCN2017119312-appb-100001
    其中，h 1和h 2为定义的中间变量，a 1,a 2,b 1,和b 2为实数，且a 1≠a 2≠0,b 1≠b 2≠0,
    Figure PCTCN2017119312-appb-100002
  7. 根据权利要求6所述的基于昂贵多目标优化问题的优化方法，其特征在于，当
    Figure PCTCN2017119312-appb-100003
    则
    Figure PCTCN2017119312-appb-100004
    即
    Figure PCTCN2017119312-appb-100005
    Figure PCTCN2017119312-appb-100006
    Figure PCTCN2017119312-appb-100007
    Figure PCTCN2017119312-appb-100008
    对f 1和f 2建立高斯过程模型等价于对h 1和h 2建立高斯过程模型，通过f 1和f 2的分布，则获取得到h 1和h 2的分布，或者通过h 1和h 2的分布，则获取得到f 1和f 2的分布。
  8. 根据权利要求7所述的基于昂贵多目标优化问题的优化方法，其特征在于，当已知h 1和h 2的分布，对于f 1和f 2的均值和方差，则：
    Figure PCTCN2017119312-appb-100009
    Figure PCTCN2017119312-appb-100010
    则得到：
    Figure PCTCN2017119312-appb-100011
    Figure PCTCN2017119312-appb-100012
    f 1和f 2的高斯过程模型与h 1和h 2的高斯过程模型的估计值进行转换；h 1和h 2之间具有相关性或相似性，通过对f 1和f 2映射获取h 1和h 2，通过h 1和h 2之间的相关性或相似性对h 1和h 2采用多任务高斯过程进行联合建模；联合建模完成后，通过逆向映射获取f 1和f 2的预测值。
  9. 根据权利要求8所述的基于昂贵多目标优化问题的优化方法，其特征在于，在对所述目标函数进行预测时，对于任一输入矢量x*，通过建立的多任务高斯过程模型获得预测值
    Figure PCTCN2017119312-appb-100013
    和
    Figure PCTCN2017119312-appb-100014
    对
    Figure PCTCN2017119312-appb-100015
    和
    Figure PCTCN2017119312-appb-100016
    进行逆向映射则获得
    Figure PCTCN2017119312-appb-100017
    和
    Figure PCTCN2017119312-appb-100018
    其中，f i j表示对于输入j的第i个目标值。
  10. 一种基于昂贵多目标优化问题的优化系统，其特征在于，所系统包括：
    映射模块，用于当一个任务中多个目标同时达到预设要求时，将多个不相关的目标对应的目标函数通过映射进行转换；
    关联模块，用于将目标函数通过映射转换到一组具有相关性或者相似性的任务系列中对多个不相关的目标函数进行关联；
    建模模块，用于将具有相似性或相关性的任务系列进行联合建模，生成多任务高斯过程模型对目标进行预测，并输出优化结果；
    预测模块，用于对所述多任务高斯过程模型通过逆向映射获取所有目标函数的预测值，对所有目标函数进行预测。
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