周 聰，姜繼嬌*，殷 茗

基于混合蛙跳算法的異地分布式協(xié)同開(kāi)發(fā)的任務(wù)分配優(yōu)化

周 聰1，姜繼嬌1*，殷 茗2

（1.西北工業(yè)大學(xué)管理學(xué)院，陜西 西安 710072；2.西北工業(yè)大學(xué)軟件與微電子學(xué)院，陜西 西安 710072）

異地分布式協(xié)同開(kāi)發(fā)已經(jīng)成為大型復(fù)雜產(chǎn)品開(kāi)發(fā)策略的一部分，復(fù)雜產(chǎn)品在動(dòng)態(tài)環(huán)境下，針對(duì)不同團(tuán)隊(duì)的技術(shù)水平、專(zhuān)業(yè)方向、所在的地理位置等外部條件進(jìn)行實(shí)時(shí)任務(wù)分配這一問(wèn)題，本文采用無(wú)約束化的編碼方式并結(jié)合變異、交叉的遺傳操作，建立基于混合蛙跳算法的異地分布式多團(tuán)隊(duì)開(kāi)發(fā)環(huán)境中的任務(wù)分配模型。該模型，參考Scrum產(chǎn)品的開(kāi)發(fā)框架對(duì)任務(wù)進(jìn)行分解，以協(xié)同生產(chǎn)企業(yè)的敏捷性與其地理位置為優(yōu)化目標(biāo)，實(shí)現(xiàn)在異地分布式環(huán)境中的任務(wù)智能分配。通過(guò)模擬我國(guó)某飛機(jī)發(fā)動(dòng)機(jī)任務(wù)分配的過(guò)程，驗(yàn)證算法的性能。結(jié)果表明，與原始的混合蛙跳算法相比，本文所提的改進(jìn)混合蛙跳算法具有較好的全局搜索能力與求解的精度。

復(fù)雜產(chǎn)品；異地分布式協(xié)同開(kāi)發(fā)；混合蛙跳算法；敏捷性

0 引言

目前，異地分布式協(xié)同開(kāi)發(fā)(Geographically Distributed Collaborative Development，GDCD)已經(jīng)成為大型復(fù)雜產(chǎn)品開(kāi)發(fā)策略的主流趨勢(shì)[1]。大型復(fù)雜產(chǎn)品的客戶(hù)需求、產(chǎn)品組成、產(chǎn)品設(shè)計(jì)、產(chǎn)品制造及項(xiàng)目管理復(fù)雜，涉及機(jī)械、控制、電子、液壓、氣動(dòng)和軟件等多學(xué)科領(lǐng)域，每個(gè)子系統(tǒng)都由多學(xué)科領(lǐng)域的零部件組成，與外界存在復(fù)雜的交互關(guān)系。GDCD 可以幫助企業(yè)進(jìn)行大型復(fù)雜產(chǎn)品開(kāi)發(fā)時(shí)達(dá)到更好的靈活性及成本控制，現(xiàn)有研究主要集中于異地分布式團(tuán)隊(duì)之間的協(xié)作和溝通問(wèn)題[2][3][4][5]。

異地分布式開(kāi)發(fā)需要敏捷性[6]，以快速適應(yīng)不穩(wěn)定的市場(chǎng)環(huán)境與需求變動(dòng)。大型復(fù)雜產(chǎn)品 GDCD 過(guò)程中需要充分利用分散企業(yè)的資源，進(jìn)行產(chǎn)品開(kāi)發(fā)過(guò)程，參與者復(fù)雜，信息交換內(nèi)容廣泛。人們建立敏捷開(kāi)發(fā)團(tuán)隊(duì)往往是受到利益驅(qū)動(dòng)，例如生產(chǎn)率提高、創(chuàng)新及員工滿(mǎn)意等。隨著產(chǎn)品復(fù)雜性和技術(shù)環(huán)境正以不可預(yù)測(cè)的速率進(jìn)行變化，多個(gè)企業(yè)進(jìn)行復(fù)雜航空產(chǎn)品異地分布式協(xié)同開(kāi)發(fā)的敏捷性已經(jīng)成為了提升產(chǎn)品開(kāi)發(fā)績(jī)效的關(guān)鍵。敏捷過(guò)程更加強(qiáng)調(diào)感官與反應(yīng)、自組織、跨職能團(tuán)隊(duì)及持續(xù)適應(yīng)力[7]，而且組織所具有的敏捷性可以快速適應(yīng)這種迅速變化的外部環(huán)境[8]。但異地分布式敏捷開(kāi)發(fā)相對(duì)于集中式開(kāi)發(fā)會(huì)存在更多阻力[9]。現(xiàn)有研究主要集中在應(yīng)用實(shí)踐[10]、協(xié)作與溝通[11]、方法工具[12]、知識(shí)管理[13]、大規(guī)模項(xiàng)目[14]、團(tuán)隊(duì)[15]及風(fēng)險(xiǎn)[16]等方面。近年的研究表明，任務(wù)分配被認(rèn)為是異地分布式開(kāi)發(fā)過(guò)程中的關(guān)鍵環(huán)節(jié)。項(xiàng)目中不同的人員從事相同的任務(wù)，其生產(chǎn)效率差距可達(dá) 10-40 倍[17]。Lin 等[18]認(rèn)為任務(wù)分配可減少異地團(tuán)隊(duì)間的溝通成本，使成員把精力投入到開(kāi)發(fā)中。Paasivaara等[19]指出了 GDCD 團(tuán)隊(duì)進(jìn)行的開(kāi)發(fā)必然受制于團(tuán)隊(duì)之間的協(xié)同關(guān)系，異地分布式團(tuán)隊(duì)間高效的協(xié)同控制，直接影響到合作伙伴的核心能力的充分發(fā)揮及有效地實(shí)現(xiàn)優(yōu)勢(shì)互補(bǔ)，進(jìn)而影響到項(xiàng)目的整體獲益。任務(wù)分配問(wèn)題的研究大部分主要集中在人工智能領(lǐng)域，例如多 Agent系統(tǒng)[20]、機(jī)器人[21]等。異地分布式開(kāi)發(fā)環(huán)境下的任務(wù)分配是在不同地理、時(shí)區(qū)和文化的團(tuán)隊(duì)之間進(jìn)行，團(tuán)隊(duì)相互之間并不熟悉，如何在動(dòng)態(tài)環(huán)境下，根據(jù)不同團(tuán)隊(duì)的技術(shù)水平、專(zhuān)業(yè)方向、所在地理位置等內(nèi)外部條件進(jìn)行實(shí)時(shí)任務(wù)分配，這對(duì)大型復(fù)雜產(chǎn)品進(jìn)行異地分布式敏捷協(xié)同開(kāi)發(fā)具有重要意義。因此，異地分布式開(kāi)發(fā)的任務(wù)分配，是本研究要考慮的重要問(wèn)題，任務(wù)分配有助于合理優(yōu)化開(kāi)發(fā)資源。針對(duì)異地分布式開(kāi)發(fā)的任務(wù)分配問(wèn)題，現(xiàn)有學(xué)者已經(jīng)展開(kāi)了初步的研究。例如，Ruano-Mayoral 等[22]提出了一個(gè)全球開(kāi)發(fā)項(xiàng)目任務(wù)包二階段分配框架，提出了任務(wù)分配的決策影響因子，實(shí)施結(jié)果表明了任務(wù)規(guī)劃的準(zhǔn)確性、效果和滿(mǎn)意度；Almeida等[23]提出了一個(gè)異地分布式開(kāi)發(fā)認(rèn)知映射和 MACBETH 的多維決策模型；Lamersdorf 和 Münch[24]提出了全球開(kāi)發(fā)的一個(gè)客戶(hù)化多維需求任務(wù)分配模型，運(yùn)用了改進(jìn) Bokhari 算法，該模型在多個(gè)典型假設(shè)場(chǎng)景和實(shí)際分布決策問(wèn)題獲得了應(yīng)用效果；張立等[25]提出了一種將心智模型與擴(kuò)展合同網(wǎng)機(jī)制結(jié)合的半自治多 Agent 任務(wù)分配方法，并擴(kuò)展了合同網(wǎng)機(jī)制包括發(fā)標(biāo)優(yōu)選、競(jìng)標(biāo)報(bào)價(jià)與多 Agent 任務(wù)分配過(guò)程。上述研究在分配過(guò)程框架、客戶(hù)化需求驅(qū)動(dòng)、心智模型等方面提供了很好的研究借鑒，但是，當(dāng)異地分布式環(huán)境采用敏捷開(kāi)發(fā)，如何在異地分布式敏捷開(kāi)發(fā)環(huán)境中進(jìn)行任務(wù)分配優(yōu)化，還沒(méi)有進(jìn)行深入研究。本文嘗試構(gòu)建基于混合蛙跳算法與遺傳算法的綜合算法，求解異地分布式協(xié)同開(kāi)發(fā)過(guò)程中的任務(wù)分配問(wèn)題。蛙跳算法已經(jīng)在圖形分割[26]、車(chē)輛路徑[27]、旅行商問(wèn)題[28]、資源分配[29]等問(wèn)題中得到應(yīng)用。

本文在異地分布式敏捷團(tuán)隊(duì)任務(wù)分配的特點(diǎn)，采用了基于實(shí)數(shù)的編碼方式，用一種粒子代表子任務(wù)-協(xié)同生產(chǎn)企業(yè)的決策方案，滿(mǎn)足問(wèn)題的約束條件，并基于混合蛙跳算法與遺傳算法的融合算法求解大型復(fù)雜產(chǎn)品開(kāi)發(fā)異地分布式任務(wù)分配問(wèn)題，構(gòu)建混合蛙跳和遺傳算法融合的團(tuán)隊(duì)內(nèi)部的任務(wù)分配模型。該融合算法將全局尋優(yōu)能力強(qiáng)的混合蛙跳算法與局部尋優(yōu)能力強(qiáng)的遺傳算法融合在一個(gè)算法框架中，取長(zhǎng)補(bǔ)短，而該融合算法的優(yōu)勢(shì)是先利用混合蛙跳算法對(duì)離散問(wèn)題的強(qiáng)大解決能力，建立團(tuán)隊(duì)間任務(wù)分配的初始全局最優(yōu)解群，對(duì)混合蛙跳算法中青蛙例子編碼進(jìn)行定義并改進(jìn)算法的局部搜索機(jī)制，然后利用遺傳算法進(jìn)行全局最優(yōu)解群中的局部最優(yōu)細(xì)化搜索，期望最終能達(dá)到異地分布式多團(tuán)隊(duì)敏捷開(kāi)發(fā)任務(wù)精細(xì)化分配的結(jié)果。該綜合算法具有很好的全局收斂能力與運(yùn)算精度，進(jìn)一步為實(shí)際中的任務(wù)分配提供參考。

1 混合蛙跳算法任務(wù)分配優(yōu)化模型

1.1 模型總體思路

混合蛙跳算法中，每種任務(wù)分配方案對(duì)應(yīng)一只青蛙，每只青蛙是由選取的協(xié)同生產(chǎn)企業(yè)的基因序列組成，尋找最佳青蛙就是搜索最優(yōu)的任務(wù)分配方案的過(guò)程，每只青蛙的優(yōu)劣都是由本文優(yōu)化模型的適應(yīng)度函數(shù)決定的，青蛙的適應(yīng)度函數(shù)對(duì)應(yīng)于任務(wù)分配優(yōu)化問(wèn)題的目標(biāo)函數(shù)。

圖1 異地分布式協(xié)同開(kāi)發(fā)的任務(wù)分配優(yōu)化模型

Figure 1 Task allocation optimization model of geographically distributed collaborative

1.1.1青蛙個(gè)體的表達(dá)

1.1.2優(yōu)化過(guò)程

1.2 關(guān)鍵技術(shù)

1.2.1個(gè)體更新策略

本文的青蛙個(gè)體更新策略借鑒John Holland所提的遺傳算法，其計(jì)算原理是在解域中，以目標(biāo)函數(shù)為基礎(chǔ)，不斷向最優(yōu)解靠近，是一種以一定概論為基礎(chǔ)的全局尋優(yōu)的過(guò)程。遺傳算法過(guò)程中主要包括了以下三個(gè)算子：選擇；交叉；變異。本文主要借鑒了遺傳算法中的交叉與變異這兩個(gè)算子。

（1）學(xué)習(xí)策略

圖2 交叉操作

Figure 2 Crossover operation

（2）變異策略

圖3 變異方式

Figure 3 Mutation methods

1.2.2適應(yīng)度函數(shù)

（1）協(xié)同企業(yè)敏捷性度量方式

圖4 敏捷指標(biāo)

Figure 4 Agile metrics

其次，計(jì)算14個(gè)敏捷指標(biāo)的優(yōu)劣度權(quán)重，具體的算法步驟如下：

1）初步權(quán)重。采用層次分析法計(jì)算出每個(gè)專(zhuān)家對(duì)虛擬企業(yè)敏捷的14個(gè)指標(biāo)的權(quán)重、灰色優(yōu)度與灰色劣度，即為初步權(quán)重；

計(jì)算各個(gè)可供選擇的協(xié)同生產(chǎn)企業(yè)敏捷性中的成本(C)、時(shí)間(T)、魯棒性(R)、可適應(yīng)范圍(T)的具體步驟如下：

Step0 準(zhǔn)備工作。計(jì)算各個(gè)打分專(zhuān)家的權(quán)重，以及每個(gè)指標(biāo)的優(yōu)劣度權(quán)重（14個(gè)）。

Step1 專(zhuān)家打分。組織本次虛擬企業(yè)敏捷性評(píng)價(jià)的專(zhuān)家，為其提供虛擬企業(yè)的資料，對(duì)專(zhuān)家進(jìn)行訪(fǎng)談和填表，評(píng)分表采用百分制。

表1 專(zhuān)家咨詢(xún)表

（2）協(xié)同生產(chǎn)企業(yè)與核心企業(yè)間距離的度量方式

L為協(xié)同企業(yè)距離核心企業(yè)的距離。由協(xié)同企業(yè)所處位置與核心企業(yè)之間的直線(xiàn)位置直接測(cè)量得出。

2 優(yōu)化步驟

任務(wù)分配空間優(yōu)化模型，把每種可能的任務(wù)分配想象為一只青蛙，通過(guò)計(jì)算機(jī)的高速迭代，尋找青蛙在解空間中的最優(yōu)，得到任務(wù)分配的最優(yōu)方案，優(yōu)化步驟如下：

（1）任務(wù)分解

當(dāng)項(xiàng)目或產(chǎn)品開(kāi)發(fā)過(guò)程中涉及多個(gè)團(tuán)隊(duì)時(shí)，Scrum 可以幫助敏捷團(tuán)隊(duì)與其他團(tuán)隊(duì)的協(xié)調(diào)與合作。因此本文結(jié)合敏捷理論將一個(gè)產(chǎn)品任務(wù)可分解為若干個(gè)子任務(wù)，每個(gè)子任務(wù)按照相似的特征及其之間的關(guān)系進(jìn)行開(kāi)發(fā)。生產(chǎn)子任務(wù)的團(tuán)隊(duì)都要完成特定的子任務(wù)，而子任務(wù)也是一個(gè)完整帶有獨(dú)立專(zhuān)家和產(chǎn)品經(jīng)理角色的產(chǎn)品。

首先，核心企業(yè)確定其生產(chǎn)子任務(wù)。對(duì)總?cè)蝿?wù)進(jìn)行分解，由核心企業(yè)根據(jù)該產(chǎn)品完整的設(shè)計(jì)以及工藝，先對(duì)產(chǎn)品項(xiàng)目進(jìn)行初步的拆分，確定核心企業(yè)的生產(chǎn)部分。其次，確定協(xié)同企業(yè)生產(chǎn)任務(wù)。子任務(wù)的分解方式，借鑒SCRUM迭代式的增量軟件開(kāi)發(fā)過(guò)程，把任務(wù)分解成多個(gè)具有優(yōu)先權(quán)重的子任務(wù)，每個(gè)子任務(wù)都是一個(gè)“用戶(hù)故事”，完成整個(gè)任務(wù)就是多個(gè)子任務(wù)的迭加，Scrum迭代任務(wù)分解方式使子任務(wù)之間具有靈活性，核心企業(yè)在生產(chǎn)過(guò)程中可以隨時(shí)根據(jù)客戶(hù)需求、技術(shù)變更等外界變化，及時(shí)調(diào)整后續(xù)子任務(wù)的分解及分配方式，且在變更過(guò)程中對(duì)已完成的子任務(wù)不會(huì)造成返工等影響，減少變更過(guò)程中不影響整體任務(wù)的生產(chǎn)時(shí)間或效率。

（2）確定優(yōu)化模型參數(shù)。

（3）種群初始化

在本次研究中，子任務(wù)的生產(chǎn)企業(yè)構(gòu)成青蛙的基因，每只青蛙對(duì)應(yīng)一種解。初始種群決定了優(yōu)化搜索的起點(diǎn)與范圍，在很大程度上影響著優(yōu)化結(jié)果的質(zhì)量，為了避免人為的干擾，初始青蛙由子任務(wù)隨機(jī)分配選擇生產(chǎn)商，以青蛙基因中每個(gè)可供選擇的子任務(wù)的企業(yè)為基礎(chǔ)，隨機(jī)選取只青蛙作為初始解。

（4）排序分組及組內(nèi)局部?jī)?yōu)化。

圖5 組內(nèi)優(yōu)化過(guò)程

Figure 5 Intra-group optimization process

（5）全局優(yōu)化。

（6）解析成圖并進(jìn)行結(jié)果分析。

蛙群在滿(mǎn)足終止條件后，對(duì)青蛙的空間分布進(jìn)行解析，并將優(yōu)化后的數(shù)字信息還原為任務(wù)分配策略。該模型在多目標(biāo)控制下把任務(wù)分配優(yōu)化的數(shù)量結(jié)構(gòu)進(jìn)行了空間布局，符合任務(wù)分配優(yōu)化的應(yīng)用需要。

3 案例分析

為了驗(yàn)證本文所提任務(wù)分配方法的有效性，本文以課題小組參與的航空基金項(xiàng)目案例為基礎(chǔ)，通過(guò)Matlab語(yǔ)言在 Intel Core i5 CPU 2.20GHz,內(nèi)存32GB的PC機(jī)上進(jìn)行實(shí)驗(yàn)。假設(shè)航空某廠生產(chǎn)4中不同型號(hào)的發(fā)動(dòng)機(jī)，記為M1、M2、M3、M4,每個(gè)型號(hào)發(fā)動(dòng)機(jī)的訂單結(jié)構(gòu)為圖6。這4中型號(hào)的發(fā)動(dòng)機(jī)按照SCRUM敏捷開(kāi)發(fā)框架分解為8個(gè)子任務(wù)，其余由協(xié)同企業(yè)提供，

為了說(shuō)明本文所提算法的有效性，同時(shí)與原混合蛙跳算法（SFLA）進(jìn)行對(duì)比分析。

圖6 M1、M2、M3、M4型號(hào)發(fā)動(dòng)機(jī)的訂單結(jié)構(gòu)

Figure 6 Order structure for M1,M2,M3,M4 engines

表2 協(xié)同生產(chǎn)企業(yè)敏捷性得分

Table 2 Agility score of collaborative development enterprises

表3 協(xié)同生產(chǎn)企業(yè)與核心企業(yè)間的距離

表4 M1、M2、M3、M4型號(hào)任務(wù)參數(shù)

3.1 參數(shù)設(shè)定

表5 子任務(wù)對(duì)應(yīng)可選生產(chǎn)企業(yè)

混合蛙跳算法以協(xié)同企業(yè)敏捷性與其所處地理位置為優(yōu)化目標(biāo)，利用Matlab（2014a）進(jìn)行仿真實(shí)驗(yàn)，設(shè)定全局迭代次數(shù)為100次，局部迭代次數(shù)為5次，初始種群為50組，每組青蛙25，即初始種群規(guī)模為1250。

3.2 運(yùn)算結(jié)果分析

此次研究同時(shí)考慮了協(xié)同企業(yè)的敏捷性與其所處的地理位置，建立多目標(biāo)的任務(wù)分配優(yōu)化模型，從模型的優(yōu)化結(jié)果看，分別用改進(jìn)后的混合蛙跳算法與原始混合蛙跳算法對(duì)此問(wèn)題進(jìn)行20次的獨(dú)立求解。

本文所提到的改進(jìn)混合蛙跳算法在問(wèn)題求解的平均第29次，就出現(xiàn)了回歸，平均最優(yōu)值為0.12，具體如表6所示。改進(jìn)后的混合蛙跳算法優(yōu)化結(jié)果比混合蛙跳算法優(yōu)化結(jié)果相對(duì)減少0.06。改進(jìn)后的混合蛙跳算法平均進(jìn)化到32代就已經(jīng)達(dá)到了最優(yōu)，而原混合蛙跳算法在38代才達(dá)到了最優(yōu)，由此可見(jiàn)，改進(jìn)后的混合蛙跳算法在求解問(wèn)題時(shí)收斂速度更快，比SFLA相對(duì)提高了17%。其中一次的優(yōu)化結(jié)果如圖6所示。

圖6所示實(shí)驗(yàn)結(jié)果的收斂曲線(xiàn)中，在算法迭代第32次時(shí)所得到的任務(wù)分配方案是型號(hào)為M1發(fā)動(dòng)機(jī)的子任務(wù)對(duì)應(yīng)的生產(chǎn)企業(yè)為[0,0,21,24],型號(hào)為M2發(fā)動(dòng)機(jī)的子任務(wù)對(duì)應(yīng)的生產(chǎn)企業(yè)為[0,8,22],型號(hào)為M3發(fā)動(dòng)機(jī)的子任務(wù)對(duì)應(yīng)的生產(chǎn)企業(yè)為[2,0,13,26],型號(hào)為M4發(fā)動(dòng)機(jī)的子任務(wù)對(duì)應(yīng)的生產(chǎn)企業(yè)為[0,8,24,0],此時(shí)在滿(mǎn)足型號(hào)需求的約束下，各協(xié)同企業(yè)與核心企業(yè)的距離最短，企業(yè)敏捷性最小。

圖7 改進(jìn)后混合蛙跳算法與混合蛙跳算法最優(yōu)值隨迭代次數(shù)變化的對(duì)比

Figure 7 Comparison of the optimal value of the improved Shuffled Frog Leading Algorithm and Shuffled Frog Leading Algorithm with the number of iterations

表6 改進(jìn)后混合蛙跳算法與原混合蛙跳算法迭代100次對(duì)比

4 結(jié)論與討論

本文針對(duì)異地分布式協(xié)同開(kāi)發(fā)的任務(wù)分配問(wèn)題，提出了一種改進(jìn)的混合蛙跳算法，通過(guò)以無(wú)約束的編碼方式使其適應(yīng)任務(wù)分配問(wèn)題的求解，針對(duì)算法中局部搜索的能力，結(jié)合交叉、變異的遺傳操作特點(diǎn)，對(duì)混合蛙跳算法進(jìn)行改進(jìn)。以子任務(wù)個(gè)數(shù)為8，可供選擇的協(xié)同生產(chǎn)企業(yè)個(gè)數(shù)為29的任務(wù)分配為例，通過(guò)Matlab進(jìn)行仿真實(shí)驗(yàn)，驗(yàn)證了算法有效性。

經(jīng)過(guò)案例研究表明，算法中的青蛙可以通過(guò)自主學(xué)習(xí)實(shí)現(xiàn)自主的更新，使其適應(yīng)度值增加，青蛙通過(guò)局部與全局的信息交換與尋優(yōu)，能盡快的找到解空間中的最優(yōu)解。協(xié)同生產(chǎn)企業(yè)的敏捷性與其所處的地理位置緊湊度這兩個(gè)方面對(duì)解的優(yōu)劣進(jìn)行評(píng)價(jià)，對(duì)空間結(jié)構(gòu)與數(shù)量結(jié)構(gòu)進(jìn)行有效的耦合，使協(xié)同企業(yè)盡量集中。但本文是以Scrum的敏捷框架為基礎(chǔ)進(jìn)行任務(wù)的分解，產(chǎn)品的最終交付一次次疊加的成果，在此基礎(chǔ)上為了進(jìn)一步提高任務(wù)分配的效率，下一步研究方向可以使用并行的分布式計(jì)算方式。

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Task assignment optimization for distributed cooperative development based on shuffled frog leaping algorithms

ZHOUCong1,JIANG Jijiao1*, YIN Ming2

2. School of ManagementNorthwestern Polytechnical UniversityXi’an 710072，China; Software and Microelectronics Northwestern Polytechnical UniversityXi’an 710072，China)

Geographically distributed collaborative development has become part of the development strategy for large and complex products. Complex products are composed of multiple subsystems, and each subsystem involves multiple disciplines, which makes the complex interaction between large complex R&D product enterprises and the outside world. In different stages of complex product development, a single enterprise is often limited by technology and resources, and cannot complete the entire process of product development independently. This requires mutual cooperation between enterprises, resource sharing, and risk sharing. Geographically distributed collaborative development can integrate the resources of different geographies, enterprises, and teams to reduce risks, but it also brings about coordination and cooperation issues between geographically distributed teams. In response to this phenomenon, this paper studies the problem of task assignment for large and complex products in a geographically distributed agile development environment.

This paper mainly does the following work: First, it proposes a task allocation optimization model for geographically distributed agile development based on hybrid shuffled frog-leaping algorithm. This model uses the scrum of scrums agile development model as the basic framework for the development and production of large and complex products, and decomposes the R&D and production tasks of complex products then takes the maximum agility and minimum geographic compactness of the enterprise of complex aviation products as the objective function. Second, the unconstrained coding method is used to encode the model solution, which the "cross" and "mutation" operators are introduced in the learning strategy of the hybrid shuffled frog-leaping algorithm to optimize the local and global search mechanism of the hybrid shuffled frog-leaping algorithm and improve the efficiency and convergence accuracy of the algorithm. Third, taking an aircraft engine R&D enterprise as an example, MATLAB software is used to simulate the example, and the convergence between the improved hybrid shuffled frog-leaping algorithm and the original hybrid shuffled frog-leaping algorithm is compared under the same experimental background. The experimental results show that the improved hybrid shuffled frog-leaping algorithm in this study is better and has stronger convergence ability in the task allocation process. Through the research of this paper, the following conclusions can be drawn. Aiming the goal of the two aspects of agility of the collaborative production enterprise and the compactness of its geographical location, we assign the tasks. The spatial structure and the quantitative structure are effectively coupled to make the best of collaborative enterprise. Centralization, as far as possible, can avoid the decrease in product production efficiency caused by the change in the geographic location of the collaborative production enterprise and project tasks. It has certain practical significance; Secondly, the improved hybrid shuffled frog-leaping algorithm obtains a task allocation scheme that is more in line with the actual task allocation of large and complex aviation products than the traditional hybrid shuffled frog-leaping algorithm. The improved hybrid shuffled frog-leaping algorithm can achieve autonomous updates through self-learning to increase the degree of value fitness so that the optimal solution in the solution space can be found as quick as possible. Thus, it has certain theoretical significance.

Complex product; Geographically distributed collaborative development; Shuffled frog-leaping algorithm; Agility

C935

A

1004-6062(2020)06-0148-008

10.13587/j.cnki.jieem.2020.06.015

2018-07-16

2019-01-04

Supported by the Humanities and Social Sciences of Ministry of Education Fund Project (16YJA630068, 18YJA630043), the Aeronautical Science Fund of China (2016ZG53071), theNatural Science Basic Research Plan in Shaanxi Province of China (2018JM7008)and the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University (ZZ2018036)

2018-07-16

2019-01-04

教育部人文與社會(huì)科學(xué)基金項(xiàng)目（16YJA630068、18YJA630043）；航空科學(xué)基金資助項(xiàng)目（2016ZG53071）；陜西省自然科學(xué)基礎(chǔ)研究計(jì)劃項(xiàng)目（2018JM7008）；西北工業(yè)大學(xué)研究生創(chuàng)意創(chuàng)新種子基金資助（ZZ2018036）

姜繼嬌（1979—），男，山東巨野人；西北工業(yè)大學(xué)管理學(xué)院管理科學(xué)與工程系主任，副教授；研究方向：項(xiàng)目管理與人力資源管理。

中文編輯：杜 健；英文編輯：Boping Yan