WO2021212649A1 - 一种入侵杂草算法求解资源受限项目调度方法 - Google Patents

一种入侵杂草算法求解资源受限项目调度方法 Download PDF

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WO2021212649A1
WO2021212649A1 PCT/CN2020/097665 CN2020097665W WO2021212649A1 WO 2021212649 A1 WO2021212649 A1 WO 2021212649A1 CN 2020097665 W CN2020097665 W CN 2020097665W WO 2021212649 A1 WO2021212649 A1 WO 2021212649A1
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activity
weed
project
population
weeds
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袁泉
曾文驱
史海欧
农兴中
王建
张耘琳
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广州地铁设计研究院股份有限公司
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • 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
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
    • G06Q10/06311—Scheduling, planning or task assignment for a person or group
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00—Arrangements for program control, e.g. control units
    • G06F9/06—Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/46—Multiprogramming arrangements
    • G06F9/50—Allocation of resources, e.g. of the central processing unit [CPU]
    • G06F9/5005—Allocation of resources, e.g. of the central processing unit [CPU] to service a request
    • G06F9/5027—Allocation of resources, e.g. of the central processing unit [CPU] to service a request the resource being a machine, e.g. CPUs, Servers, Terminals
    • G06F9/5038—Allocation of resources, e.g. of the central processing unit [CPU] to service a request the resource being a machine, e.g. CPUs, Servers, Terminals considering the execution order of a plurality of tasks, e.g. taking priority or time dependency constraints into consideration
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/004—Artificial life, i.e. computing arrangements simulating life
    • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • 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
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • 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
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
    • G06Q10/06312—Adjustment or analysis of established resource schedule, e.g. resource or task levelling, or dynamic rescheduling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • 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
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
    • G06Q10/06313—Resource planning in a project environment
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • 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
    • G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
    • G06Q50/08—Construction
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00—Arrangements for program control, e.g. control units
    • G06F9/06—Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/46—Multiprogramming arrangements
    • G06F9/48—Program initiating; Program switching, e.g. by interrupt
    • G06F9/4806—Task transfer initiation or dispatching
    • G06F9/4843—Task transfer initiation or dispatching by program, e.g. task dispatcher, supervisor, operating system
    • G06F9/4881—Scheduling strategies for dispatcher, e.g. round robin, multi-level priority queues
    • G06F9/4887—Scheduling strategies for dispatcher, e.g. round robin, multi-level priority queues involving deadlines, e.g. rate based, periodic
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications

Definitions

  • the invention relates to the technical field of construction project scheduling.
  • Resource-constrained project scheduling problem has been proved to be a kind of complex and strong NP-hard problem.
  • the algorithms for solving RCPSP and its extension problems can be divided into three categories: precise algorithms, heuristic algorithms, and meta-heuristic algorithms (intelligent algorithms).
  • precise algorithms can obtain theoretical optimal solutions, they only Applicable to small-scale solutions, from which approximate algorithms have begun to be applied to solve large-scale RCPSP problems.
  • the scheduling generation plan was proposed in 1963, various heuristic algorithms have been applied to this problem one after another, but they do not have the ability to optimize, and are often affected by the problem itself and fail to get a satisfactory solution.
  • IWO Invasive Weed Optimization
  • the present invention designs a right-shift decoding strategy to correct the illegal solutions that appear in the process of weed seed generation, which improves the efficiency of algorithm solving while ensuring the optimization effect, and realizes the resource of invading weed algorithm.
  • Restricted project scheduling problems especially large-scale resource-constrained project scheduling problems.
  • the purpose of the present invention is to provide a resource-constrained project scheduling method based on an intrusion weed algorithm, which can effectively solve the technical problem of avoiding illegal solution defects in the resource-constrained project scheduling problem.
  • an invading weed algorithm to solve resource-constrained project scheduling method including the following steps:
  • Resource-constrained project scheduling problem is the scheduling problem of how to optimize certain management objectives under resource-constrained conditions for projects with many immediate-sequence-constrained activities. The specific description is as follows:
  • the activities 0 and n+1 in the set are virtual activities, which only represent the beginning and end of the project, and the time It has nothing to do with resources;
  • j represents some other activity in the activity set except virtual activity, j ⁇ J, the immediately preceding activity set of j is denoted by P j, the immediately following activity set of j is denoted by S j;
  • t j is the activity
  • formula (1) is the objective function, that is, to minimize the total project duration
  • formula (2) is a decision variable
  • formula (3) means that each activity must be completed within its prescribed duration
  • formula (4) means that activity j once starts , Then it cannot be interrupted before completion
  • Equations (5) and (6) indicate that the duration and resource demand of virtual activities 0 and n+1 are both 0
  • Equation (7) is the constraint of immediately before and after, and activity j must It can start after all the immediately preceding activities are completed
  • formula (8) is the resource constraint, and the demand for a certain resource for all activities being executed at time d is not greater than the maximum supply of the resource per unit time.
  • Step 1 Parameter setting:
  • the nonlinear harmonic index is N;
  • Step two population initialization:
  • the first layer of code is a decimal code representing the position of the weeds. It generates n+1 random numbers between 0 and 1 to form the weeds.
  • the second level of encoding is an integer encoding representing the sequence of activities, where the integer corresponding to each random number from small to large in the code represents an activity sequence number, and the set of activity sequence numbers composed of all the activity sequence numbers is called Is an activity sequence; the process of generating the activity sequence in the second layer of coding based on the weed position code in the first layer of coding is called translation; the activity sequence corresponding to each individual weed is a feasible solution for project scheduling, and its The corresponding position code represents the position of the feasible solution in the solution space; due to the immediate or immediate limitation between the project activities, the generated activity sequence needs to be adjusted by the right shift decoding strategy to make it conform to The legal and feasible solution of the immediately-before or immediately-behind constraint restriction is as follows:
  • Step 3 Calculate the fitness value of weeds:
  • Step 4 Calculate the number of seeds reproduced by each individual weed in the population, and update the standard deviation of this iteration;
  • the number of seeds produced by each individual weed during the reproduction process is proportional to the fitness value f of the weed, and the calculation formula is as follows:
  • f max is the maximum value of weed fitness in the population
  • f min is the minimum value of weed fitness in the population
  • the seeds produced by weed propagation are scattered around the weeds in a normal distribution with a mean value of 0 and a standard deviation of ⁇ for colonization expansion.
  • Step 5 The weeds reproduce to produce seeds, which grow into weeds and merge with the original weed population to form a new weed population;
  • the weeds are propagated, and the new position obtained in the solution space is called the seed, and its corresponding position
  • the coding is the position coding of the seed, that is, the position coding of the seed is obtained according to the position coding of the weed and the random step length D representing the distance between the seed and the weed; then the same operation as in step 2 is performed to code the position of the seed Translated into an active sequence, and right-shifted decoding to make it a legal and feasible solution, the seed grows into a weed; at this time, the position code of the seed becomes the position code of the weed, which is composed of the active sequence after right-shifting decoding Two-layer coding of new weed individuals; finally, all newly generated weeds grown from seeds are merged with the original weed population to obtain a new weed population;
  • Step 6 Determine whether the weed population size reaches Q max , if it reaches Q max, go to step 7; otherwise go to step 3;
  • Step 7 Calculate the fitness value of the weeds in the population, and select Q size individuals according to the law of survival and competition;
  • the maximum population size must be set to limit the reproduction of weeds, and some individuals should be eliminated through the principle of survival of the fittest to retain elite individuals; according to the fitness of the weeds Value judgment, select Q size individuals with high fitness values to form a new population, and enter a new iterative process;
  • Step 8 Determine whether the number of iterations reaches iter max , if it reaches iter max, output the optimal solution, and the algorithm ends; otherwise, go to step 4.
  • This method designs a right-shift decoding strategy, which effectively solves the problem that weed algorithm cannot avoid illegal solutions when solving project scheduling problems.
  • the prior art usually adopts a method of directly discarding the illegal solution and continuously generating new solutions in a continuous loop until a legal and feasible solution is obtained.
  • the method adopted in the present invention greatly improves the solving efficiency of the algorithm, and makes the algorithm simpler and easier to implement.
  • Figure 1 shows the reproduction process of the weeds of the present invention.
  • Figure 2 is a flow chart of the invading weed algorithm of the present invention.
  • Resource-constrained project scheduling problem is the scheduling problem of how to optimize certain management objectives under resource-constrained conditions for projects with many immediate-sequence-constrained activities. The specific description is as follows:
  • the activities 0 and n+1 in the set are virtual activities, which only represent the beginning and end of the project, and the time It has nothing to do with resources;
  • j represents some other activity in the activity set except virtual activity, j ⁇ J, the immediately preceding activity set of j is denoted by P j, the immediately following activity set of j is denoted by S j;
  • t j is the activity
  • formula (1) is the objective function, that is, to minimize the total project duration
  • formula (2) is a decision variable
  • formula (3) means that each activity must be completed within its prescribed duration
  • formula (4) means that activity j once starts , Then it cannot be interrupted before completion
  • Equations (5) and (6) indicate that the duration and resource demand of virtual activities 0 and n+1 are both 0
  • Equation (7) is the constraint of immediately before and after, and activity j must It can start after all the immediately preceding activities are completed
  • formula (8) is the resource constraint, and the demand for a certain resource for all activities being executed at time d is not greater than the maximum supply of the resource per unit time.
  • the data brought in includes the duration t j of each activity, the set of immediately preceding activities P j , the set of subsequent activities S j , the resource demand per unit time r jq and the maximum supply of each resource per unit time b q , and then obtain a complete mathematical model of resource-constrained project scheduling problem optimization for solving specific examples.
  • Step 1 Parameter setting:
  • Step two population initialization:
  • the first layer of code is a decimal code representing the position of the weeds. It generates n+1 random numbers between 0 and 1 to form the weeds.
  • the second level of encoding is an integer encoding representing the sequence of activities, where the integer corresponding to each random number from small to large in the code represents an activity sequence number, and the set of activity sequence numbers composed of all the activity sequence numbers is called Is an activity sequence; the process of generating the activity sequence in the second layer of coding based on the weed position code in the first layer of coding is called translation; the activity sequence corresponding to each individual weed is a feasible solution for project scheduling, and its The corresponding position code represents the position of the feasible solution in the solution space; due to the immediate or immediate limitation between the project activities, the generated activity sequence needs to be adjusted by the right shift decoding strategy to make it conform to The legal and feasible solution of the immediately-before or immediately-behind constraint restriction is as follows:
  • Step 3 Calculate the fitness value of weeds:
  • Step 4 Calculate the number of seeds reproduced by each individual weed in the population, and update the standard deviation of this iteration;
  • the number of seeds produced by each individual weed during the reproduction process is proportional to the fitness value f of the weed, and the calculation formula is as follows:
  • f max is the maximum value of weed fitness in the population
  • f min is the minimum value of weed fitness in the population
  • the seeds produced by weed propagation are scattered around the weeds in a normal distribution with a mean value of 0 and a standard deviation of ⁇ for colonization expansion.
  • Step 5 The weeds reproduce to produce seeds, which grow into weeds and merge with the original weed population to form a new weed population;
  • the weeds are propagated, and the new position obtained in the solution space is called the seed, and its corresponding position
  • the coding is the position coding of the seed, that is, the position coding of the seed is obtained according to the position coding of the weed and the random step length D representing the distance between the seed and the weed; then the same operation as in step 2 is performed to code the position of the seed Translated into an active sequence, and right-shifted decoding to make it a legally feasible solution, the seed grows into a weed; at this time, the position code of the seed becomes the positional code of the weed, which is composed of the active sequence after right-shifting decoding Two-layer coding of new weed individuals; finally, all newly generated weeds grown from seeds are merged with the original weed population to obtain a new weed population;
  • Step 6 Determine whether the weed population size reaches Q max , if it reaches Q max, go to step 7; otherwise go to step 3;
  • Step 7 Calculate the fitness value of the weeds in the population, and select Q size individuals according to the law of survival and competition;
  • the maximum population size must be set to limit the reproduction of weeds, and some individuals should be eliminated through the principle of survival of the fittest to retain elite individuals; according to the fitness of the weeds Value judgment, select Q size individuals with high fitness values to form a new population, and enter a new iterative process;
  • Step 8 Judge whether the number of iterations reaches iter max , if it reaches iter max, the optimal solution is output and the algorithm ends; otherwise, go to step 4.
  • T 1 is the average value of the total construction period obtained by the genetic algorithm
  • T 2 is the average value of the total construction period obtained by the IWO algorithm.

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Abstract

一种入侵杂草算法求解资源受限项目调度方法，涉及建筑工程项目调度活动的调度技术领域。该方法首先建立资源受限的项目调度模型，将实际工程中的项目调度问题转化为组合优化的数学模型问题；其次以最小化项目总工期为优化目标，同时考虑项目活动的紧前紧后约束与多种可更新资源约束，构建项目调度模型；最后采用入侵杂草算法进行大规模项目调度情况下的求解。在求解过程中，设计了一种右移解码策略，用以修正在杂草种子产生的过程中所出现的非法解，保证所有解都严格遵从项目活动的紧前紧后约束，同时提高了算法的求解效率。通过本方法所得的资源受限项目调度方案可有效缩短大规模项目的总工期。

Description

一种入侵杂草算法求解资源受限项目调度方法 技术领域
本发明涉及建筑工程项目调度技术领域。
背景技术
建筑项目在设计和建设过程中往往涉及业主单位、总包单位、设计单位、施工单位、运维单位等多家单位，同时涉及建筑、结构、通风、给排水、安控、地质等几十个专业的项目设计与实施等方面的协调，这些单位和专业之间在施工图设计、施工建设和建筑运维中会产生庞大的信息，这些信息可以通过BIM系统获取，但是由于各个部门的不同专业涉及的资源是有限的，动态变化的信息对各个子项目及其活动中，产生的资源配置和调度带来了新挑战，往往需要根据信息不断进行各子项目及其活动展开重调度。由于子项目和细分的活动数量大致使整个调度规模庞大，传统的资源受限项目调度求解算法在效率和精度上都受到考验，需要一套行之有效的资源受限项目调度求解算法以提高项目整体效率。
资源受限项目调度问题已被证明为一类复杂的强NP-hard问题。从求解角度来看，解决RCPSP及其扩展问题的算法可分为三大类：精确算法、启发式算法和元启发式算法(智能算法)，其中精确算法虽然能得到理论最优解，但仅适用于小规模求解，由此近似算法开始被应用于求解大规模RCPSP问题。自1963年调度生成方案后被提出后，各种启发式算法也相继被应用到该问题，但其不具备优化能力，往往受到问题本身的影响而得不到满意解。元启发式算法和智能算法的应用使问题的求解得到了新的发展，如引入局部搜索中的模拟退火算法(Simulated Annealing，SA)来求解RCPSP，进化算法(如遗传算法，Genetic Algorithm，GA)和群体智能算法(如蚁群优化算法，Ant Colony Optimization，ACO)都在求解RCPSP问题上得到了广泛的应用。
入侵杂草算法(Invasive Weed Optimization，IWO)是一种新颖且简单有效的数值优化算法，最早由Lucas和Mehrabian于2006年提出，该算法受到杂草侵略性繁殖的启发，其优化过程模拟杂草的殖民化过程，具有很强的鲁棒性、自适应性和随机性，研究表明入侵杂草算法在求解大规模调度问题时有着优异的表现。但对于项目调度问题，一般的入侵杂草算法在产生种子的过程中无法避免非法解的产生，导致算法效率较低。本发明针对这一问题设计了一种右移解码策略来修正在杂草种子产生的过程中所出现的非法解，在保证优化效果的同时提高了算法求解效率，实现了入侵杂草算法求解资源受限项目调度问题，尤其是大规模资源受限项目调度问题。
发明内容
本发明的目的是提供一种入侵杂草算法求解资源受限项目调度方法，它能有效地解决资源受限项目调度问题中避免产生非法解缺陷的技术问题。
本发明的目的是通过以下技术方案来实现的：一种入侵杂草算法求解资源受限项目调度方法，包括以下步骤：
一、建立资源受限项目调度目标优化的数学模型
资源受限项目调度问题所研究的是具有众多紧前紧后顺序约束活动的项目在资源受限的情况下如何使某些管理目标最优的调度问题，其具体描述如下：
首先，假设一个项目由活动集合J＝{0,1,2,…,n+1}组成，该集合中的活动0和活动n+1为虚活动，仅代表项目的开始和结束，与时间和资源无关；j表示活动集合中除虚活动之外的其他某个活动，j∈J，j的紧前活动集合用P j表示，j的紧后活动集合用S j表示；t j表示活动j的持续时间，st j表示活动j的作业开始时间；项目所需共有k种资源，q表示其中的一种资源，用r jq表示活动j对资源q在单位时间的需求量，b q为资源q在单位时间的最大供应量；对项目持续时间进行离散化处理，d＝{1,2,…,T}为离散的时间节点，T表示项目总工期，A d＝{j|st j<d≤st j+t j}为d时刻正在执行的活动集合；其次，在上述假设的基础上建立资源受限项目调度目标优化的数学模型：
min T＝st n+1           (1)
Figure PCTCN2020097665-appb-000001
Figure PCTCN2020097665-appb-000002
Figure PCTCN2020097665-appb-000003
t 0＝t n+1＝0           (5)
r 0q＝r (n+1)q＝0,q＝1,2,...,k          (6)
Figure PCTCN2020097665-appb-000004
Figure PCTCN2020097665-appb-000005
其中：式(1)为目标函数，即最小化项目总工期；式(2)为决策变量；式(3)表示每项活动必须在其规定持续时间完成；式(4)表示活动j一旦开始，则在完成之前不能中断；式(5)和(6)表示虚活动0和n+1的持续时间和资源需求量都为0；式(7)为紧前、紧后约束，活动j必须在其全部紧前活动完成后才能开始；式(8)为资源约束，d时刻正在执行的所有活动对某种资源的需求量不大于该资源单位时间的最大供应量。
二、入侵杂草算法优化求解：包括以下步骤
步骤一、参数设置：
设置初始种群大小为Q size，最大种群数量为Q max，最大种子数量为s max，最小种子数量为s min，初始标准差为σ init，最终标准差为σ final，最大迭代次数为iter max，非线性调和指数为N；
步骤二、种群初始化：
首先，对杂草种群进行初始化，其中每个杂草个体包含两层编码，第一层编码为代表杂草位置的小数编码，它生成n+1个0到1之间的随机数组成杂草的位置编码；第二层编码为代表活动序列的整数编码，其中每个随机数在该编码中由小到大的位置所对应的整数代表一个活动序号，所有活动序号所组成的活动序号集合称为一个活动序列；根据第一层编码中杂草位置编码生成第二层编码中活动序列的过程，称为转译；每个杂草个体对应的活动序列即为项目调度的一个可行解，而其所对应的位置编码则代表了该可行解在解空间中的位置；由 于项目活动间存在紧前或紧后的限制，需要对产生的活动序列通过右移解码策略进行调整，使其变为符合紧前或紧后约束限制的合法可行解，方法如下：
从活动序列的左边第一位起，依次判断该活动之后的序列中是否存在其紧前活动，若没有，则说明该活动的紧前或紧后活动均已结束，可以开始此活动，其活动序号在序列中的位置不变；若该活动之后的序列中存在其紧前活动，则说明该活动的紧前活动没有全部结束，不可以开始此活动，将其活动序号向右移动至序列的最后一位，直至对序列中所有活动进行判断之后，得到满足紧前或紧后约束限制的完整活动序列，即为该项目的一个合法可行解；按以上种群初始化操作生成Q size个满足合法可行解的杂草个体，组成初始杂草种群；
步骤三、计算杂草适应度值：
以目标函数的倒数1/T乘以系数C作为适应度函数Fitness，即Fitness＝C/T，C为常数，计算种群中所有杂草个体的适应度值；
步骤四、计算种群中每个杂草个体所繁殖的种子个数，并更新本次迭代的标准差；
每个杂草个体在繁殖过程中所产生的种子数量weed与杂草的适应度值f成正比，计算公式如下：
Figure PCTCN2020097665-appb-000006
f max为种群中杂草适应度值的最大值，f min为种群中杂草适应度值的最小值；
杂草繁殖所产生的种子按均值为0，标准差为σ的正态分布散布在杂草周围进行殖民扩张，种子与杂草之间的距离称为随机步长D＝[-σ,σ]，σ随着迭代的进行不断变化，其计算公式如下：
Figure PCTCN2020097665-appb-000007
式中，iter为当前迭代次数；
步骤五、杂草繁殖产生种子，种子长成杂草并与原杂草种群合并生成新的杂草种群；
首先根据公式(9)和公式(10)计算所得杂草繁殖的种子数weed和正态分布标准差σ，对杂草进行繁殖，在解空间中得到的新位置称为种子，其对应的位置编码则是种子的位置编码，即根据杂草的位置编码和产生的代表种子与杂草间距离的随机步长D，得到种子的位置编码；然后进行与步骤二相同的操作，将种子位置编码转译为活动序列，并进行右移解码使其成为合法可行解，则种子长成杂草；此时，种子的位置编码则变为了杂草的位置编码，同右移解码后的活动序列一起组成了新杂草个体的两层编码；最后将所有新生成的由种子长成的杂草与原杂草种群合并，得到新的杂草种群；
步骤六、判断杂草种群规模是否达到Q max，若达到则转步骤七；否则转步骤三；
步骤七、计算种群中杂草的适应度值，按生存竞争法则选出Q size个个体；
随着杂草的不断繁殖，种群数量超过了环境的承载能力，则需设置最大种群规模对杂草的繁殖进行限制，通过优胜劣汰的准则来淘汰一部分个体以保留精英个体；根据杂草的适应度值进行判断，选择适应度值高的Q size个个体组成新的种群，进入新的迭代过程；
步骤八、判断迭代次数是否达到iter max，若达到则输出最优解，算法结束；否则转步骤四。
与现有技术相比，本发明的有益效果是：
1)由于入侵杂草算法优化的局限性，现有技术尚未将入侵杂草算法应用到项目调度领域，本方法通过对算法编码与解码方式的改进，首次将入侵杂草算法应用到求解资源受限的项目调度问题，其优化效果明显，较其他智能算法同样有一定的优越性，且当项目规模增大时优化效果更为明显。
2)本方法设计了一种右移解码策略，有效的解决了杂草算法在求解项目调度问题时无法规避产生非法解的问题。而现有技术在处理该类问题的非法解时，通常采用直接舍弃非法解而不断循环产生新解直至得到合法可行解为止的方法。本发明中所采用的方法较现有技术方法，大大提高了算法的求解效率，使得算法更加简单易行。
附图说明
图1为本发明杂草繁殖过程。
图2为本发明入侵杂草算法流程图。
具体实施方式
采用标准算例库PSPLIB中的算例，在活动数量为30、60、90、120的4种工况下随机选取5组初始输入数据。该算例库中的项目涉及四种可更新资源，每项活动单位时间对一种或多种资源有一定的需求量，每种资源设有单位时间的最大供应量。
具体实施方案如下：
一、确定资源受限项目调度问题的描述和假设，建立资源受限项目调度目标优化的数学模型
资源受限项目调度问题所研究的是具有众多紧前紧后顺序约束活动的项目在资源受限的情况下如何使某些管理目标最优的调度问题，其具体描述如下：
首先，假设一个项目由活动集合J＝{0,1,2,…,n+1}组成，该集合中的活动0和活动n+1为虚活动，仅代表项目的开始和结束，与时间和资源无关；j表示活动集合中除虚活动之外的其他某个活动，j∈J，j的紧前活动集合用P j表示，j的紧后活动集合用S j表示；t j表示活动j的持续时间，st j表示活动j的作业开始时间；项目所需共有k种资源，q表示其中的一种资源，用r jq表示活动j对资源q在单位时间的需求量，b q为资源q在单位时间的最大供应量；对项目持续时间进行离散化处理，d＝{1,2,…,T}为离散的时间节点，T表示项目总工期，A d＝{j|st j<d≤st j+t j}为d时刻正在执行的活动集合；其次，在上述假设的基础上建立资源受限项目调度目标优化的数学模型：
minT＝st n+1          (1)
Figure PCTCN2020097665-appb-000008
Figure PCTCN2020097665-appb-000009
Figure PCTCN2020097665-appb-000010
t 0＝t n+1＝0             (5)
r 0q＝r (n+1)q＝0,q＝1,2,...,k           (6)
Figure PCTCN2020097665-appb-000011
Figure PCTCN2020097665-appb-000012
其中：式(1)为目标函数，即最小化项目总工期；式(2)为决策变量；式(3)表示每项活动必须在其规定持续时间完成；式(4)表示活动j一旦开始，则在完成之前不能中断；式(5)和(6)表示虚活动0和n+1的持续时间和资源需求量都为0；式(7)为紧前、紧后约束，活动j必须在其全部紧前活动完成后才能开始；式(8)为资源约束，d时刻正在执行的所有活动对某种资源的需求量不大于该资源单位时间的最大供应量。
根据PSPLIB中所选取的算例，将n＝30、n＝60、n＝60、n＝90四种工况下的初始输入数据带入到公式(1)-(10)中。带入的数据除n外还包括每项活动的持续时间t j、紧前活动集合P j、紧后活动集合S j、单位时间资源需求量r jq以及每种资源的单位时间最大供应量b q，进而得到完整的求解具体算例的资源受限项目调度问题优化数学模型。
二、入侵杂草算法优化求解，具体如下：
步骤一、参数设置：
设置初始种群大小Q size＝5，最大种群数量Q max＝20，最大种子数量s max＝10，最小种子数量s min＝0，初始标准差σ init＝100，最终标准差σ final＝0.01，最大迭代次数iter max＝50，非线性调和指数N＝3；
步骤二、种群初始化：
首先，对杂草种群进行初始化，其中每个杂草个体包含两层编码，第一层编码为代表杂草位置的小数编码，它生成n+1个0到1之间的随机数组成杂草的位置编码；第二层编码为代表活动序列的整数编码，其中每个随机数在该编码中由小到大的位置所对应的整数代表一个活动序号，所有活动序号所组成的活动序号集合称为一个活动序列；根据第一层编码中杂草位置编码生成第二层编码中活动序列的过程，称为转译；每个杂草个体对应的活动序列即为项目调度的一个可行解，而其所对应的位置编码则代表了该可行解在解空间中的位置；由于项目活动间存在紧前或紧后的限制，需要对产生的活动序列通过右移解码策略进行调整，使其变为符合紧前或紧后约束限制的合法可行解，方法如下：
从活动序列的左边第一位起，依次判断该活动之后的序列中是否存在其紧前活动，若没有，则说明该活动的紧前或紧后活动均已结束，可以开始此活动，其活动序号在序列中的位置不变；若该活动之后的序列中存在其紧前活动，则说明该活动的紧前活动没有全部结束，不可以开始此活动，将其活动序号向右移动至序列的最后一位，直至对序列中所有活动进行判断之后，得到满足紧前或紧后约束限制的完整活动序列，即为该项目的一个合法可行解；按以上种群初始化操作生成Q size个满足合法可行解的杂草个体，组成初始杂草种群；
步骤三、计算杂草适应度值：
以目标函数的倒数1/T乘以系数C作为适应度函数Fitness，即Fitness＝C/T，C为常数，计算种群中所有杂草个体的适应度值；
步骤四、计算种群中每个杂草个体所繁殖的种子个数，并更新本次迭代的标准差；
每个杂草个体在繁殖过程中所产生的种子数量weed与杂草的适应度值f成正比，计算公式如下：
Figure PCTCN2020097665-appb-000013
f max为种群中杂草适应度值的最大值，f min为种群中杂草适应度值的最小值；
杂草繁殖所产生的种子按均值为0，标准差为σ的正态分布散布在杂草周围进行殖民扩张，种子与杂草之间的距离称为随机步长D＝[-σ,σ]，σ随着迭代的进行不断变化，其计算公式如下：
Figure PCTCN2020097665-appb-000014
式中，iter为当前迭代次数；
步骤五、杂草繁殖产生种子，种子长成杂草并与原杂草种群合并生成新的杂草种群；
首先根据公式(9)和公式(10)计算所得杂草繁殖的种子数weed和正态分布标准差σ，对杂草进行繁殖，在解空间中得到的新位置称为种子，其对应的位置编码则是种子的位置编码，即根据杂草的位置编码和产生的代表种子与杂草间距离的随机步长D，得到种子的位置编码；然后进行与步骤二相同的操作，将种子位置编码转译为活动序列，并进行右移解码使其成为合法可行解，则种子长成杂草；此时，种子的位置编码则变为了杂草的位置编码，同右移解码后的活动序列一起组成了新杂草个体的两层编码；最后将所有新生成的由种子长成的杂草与原杂草种群合并，得到新的杂草种群；
步骤六、判断杂草种群规模是否达到Q max，若达到则转步骤七；否则转步骤三；
步骤七、计算种群中杂草的适应度值，按生存竞争法则选出Q size个个体；
随着杂草的不断繁殖，种群数量超过了环境的承载能力，则需设置最大种群规模对杂草的繁殖进行限制，通过优胜劣汰的准则来淘汰一部分个体以保留精英个体；根据杂草的适应度值进行判断，选择适应度值高的Q size个个体组成新的种群，进入新的迭代过程；
步骤八、判断迭代次数是否达到iter max，若达到则输出最优解，算法结束；否则转步骤四。
三、进行数值实验和结果分析
通过Matlab2014b平台进行数值实验，采用入侵杂草算法(IWO)对算例库中资源受限的项目调度问题进行求解，并与现有最优解以及遗传算法(GA)所求解的结果进行对比。在每种工况下运算10次，记录运算所得最优解(UB)、最劣解(LB)以及10次运算结果的均值(average)。实验结果如表1所示，其中opt为标准算例库PSPLIB的现有最优解，GAP为两种算法的差值百分比。
Figure PCTCN2020097665-appb-000015
式中，T 1为遗传算法得到的总工期均值，T 2为IWO算法得到的总工期均值。
表1 4种规模下的实验结果
Figure PCTCN2020097665-appb-000016
Figure PCTCN2020097665-appb-000017
实验结果表明，4种规模下IWO在10次运算内均求得最优解，对比GA的求解情况，两种算法在30规模下的所有运算结果均达到最优解，而随着项目规模的增大，IWO的求解结果逐渐优于GA，10次运算结果均值的差值百分比逐渐增大，60规模下的平均差值百分比为1.15％，90规模下为2.97，120规模下为4.91，且GA在120的规模下10次运算之内无法保证可以达到最优解。由此可见，本申请提出的入侵杂草算法求解资源受限项目调度问题的方法是有效的，尤其是随着项目规模的增大，算法的优化效果更显著。

Claims (1)

  1. 一种入侵杂草算法求解资源受限项目调度方法，包括以下过程：
    一、首先，假设一个项目由活动集合J＝{0,1,2,…,n+1}组成，该集合中的活动0和活动n+1为虚活动，仅代表项目的开始和结束，与时间和资源无关；j表示活动集合中除虚活动之外的其他某个活动，j∈J，j的紧前活动集合用P j表示，j的紧后活动集合用S j表示；t j表示活动j的持续时间，st j表示活动j的作业开始时间；项目所需共有k种资源，q表示其中的一种资源，用r jq表示活动j对资源q在单位时间的需求量，b q为资源q在单位时间的最大供应量；对项目持续时间进行离散化处理，d＝{1,2,…,T}为离散的时间节点，T表示项目总工期，A d＝{j|st j<d≤st j+t j}为d时刻正在执行的活动集合；其次，在上述假设的基础上建立资源受限项目调度目标优化的数学模型：
    min T＝st n+1    (1)
    Figure PCTCN2020097665-appb-100001
    Figure PCTCN2020097665-appb-100002
    Figure PCTCN2020097665-appb-100003
    t 0＝t n+1＝0   (5)
    r 0q＝r (n+1)q＝0,q＝1,2,...,k     (6)
    Figure PCTCN2020097665-appb-100004
    Figure PCTCN2020097665-appb-100005
    其中：式(1)为目标函数，即最小化项目总工期；式(2)为决策变量；式(3)表示每项活动必须在其规定持续时间完成；式(4)表示活动j一旦开始，则在完成之前不能中断；式(5)和(6)表示虚活动0和n+1的持续时间和资源需求量都为0；式(7)为紧前、紧后约束，活动j必须在其全部紧前活动完成后才能开始；式(8)为资源约束，d时刻正在执行的所有活动对某种资源的需求量不大于该资源单位时间的最大供应量；
    二、入侵杂草算法优化求解：包括以下步骤
    步骤一、参数设置：
    设置初始种群大小为Q size，最大种群数量为Q max，最大种子数量为s max，最小种子数量为s min，初始标准差为σ init，最终标准差为σ final，最大迭代次数为iter max，非线性调和指数为N；
    步骤二、种群初始化：
    首先，对杂草种群进行初始化，其中每个杂草个体包含两层编码，第一层编码为代表杂草位置的小数编码，它生成n+1个0到1之间的随机数组成杂草的位置编码；第二层编码为代表活动序列的整数编码，其中每个随机数在该编码中由小到大的位置所对应的整数代表一个活动序号，所有活动序号所组成的活动序号集合称为一个活动序列；根据第一层编码中杂草位置编码生成第二层编码中活动序列的过程，称为转译；每个杂草个体对应的活动序列即 为项目调度的一个可行解，而其所对应的位置编码则代表了该可行解在解空间中的位置；由于项目活动间存在紧前或紧后的限制，需要对产生的活动序列通过右移解码策略进行调整，使其变为符合紧前或紧后约束限制的合法可行解，方法如下：
    从活动序列的左边第一位起，依次判断该活动之后的序列中是否存在其紧前活动，若没有，则说明该活动的紧前或紧后活动均已结束，可以开始此活动，其活动序号在序列中的位置不变；若该活动之后的序列中存在其紧前活动，则说明该活动的紧前活动没有全部结束，不可以开始此活动，将其活动序号向右移动至序列的最后一位，直至对序列中所有活动进行判断之后，得到满足紧前或紧后约束限制的完整活动序列，即为该项目的一个合法可行解；按以上种群初始化操作生成Q size个满足合法可行解的杂草个体，组成初始杂草种群；
    步骤三、计算杂草适应度值：
    以目标函数的倒数1/T乘以系数C作为适应度函数Fitness，即Fitness＝C/T，C为常数，计算种群中所有杂草个体的适应度值；
    步骤四、计算种群中每个杂草个体所繁殖的种子个数，并更新本次迭代的标准差；
    每个杂草个体在繁殖过程中所产生的种子数量weed与杂草的适应度值f成正比，计算公式如下：
    Figure PCTCN2020097665-appb-100006
    f max为种群中杂草适应度值的最大值，f min为种群中杂草适应度值的最小值；
    杂草繁殖所产生的种子按均值为0，标准差为σ的正态分布散布在杂草周围进行殖民扩张，种子与杂草之间的距离称为随机步长D＝[-σ,σ]，σ随着迭代的进行不断变化，其计算公式如下：
    Figure PCTCN2020097665-appb-100007
    式中，iter为当前迭代次数；
    步骤五、杂草繁殖产生种子，种子长成杂草并与原杂草种群合并生成新的杂草种群；
    首先根据公式(9)和公式(10)计算所得杂草繁殖的种子数weed和正态分布标准差σ，对杂草进行繁殖，在解空间中得到的新位置称为种子，其对应的位置编码则是种子的位置编码，即根据杂草的位置编码和产生的代表种子与杂草间距离的随机步长D，得到种子的位置编码；然后进行与步骤二相同的操作，将种子位置编码转译为活动序列，并进行右移解码使其成为合法可行解，则种子长成杂草；此时，种子的位置编码则变为了杂草的位置编码，同右移解码后的活动序列一起组成了新杂草个体的两层编码；最后将所有新生成的由种子长成的杂草与原杂草种群合并，得到新的杂草种群；
    步骤六、判断杂草种群规模是否达到Q max，若达到则转步骤七；否则转步骤三；
    步骤七、计算种群中杂草的适应度值，按生存竞争法则选出Q size个个体；
    随着杂草的不断繁殖，种群数量超过了环境的承载能力，则需设置最大种群规模对杂草的繁殖进行限制，通过优胜劣汰的准则来淘汰一部分个体以保留精英个体；根据杂草的适应度值进行判断，选择适应度值高的Q size个个体组成新的种群，进入新的迭代过程；
    步骤八、判断迭代次数是否达到iter max，若达到则输出最优解，算法结束；否则转步骤四。
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