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优先级的活动安排在本论文,生产活动的序列采用串行机制。在生产期间,有必要选择一个活动满足资源约束的条件下,逻辑关系约束。但它是随机选择一个活动中满足条件的集合。这涉及到活动的优先级调度。许多学者已经提出了许多解决方案。Priority of activities' scheduling In this dissertation, the production of activities' sequence adopts the serial mechanism. During the production, it is necessary to choose a activity which satisfy the condition of resource constraints, logical relationship constraints. But it is random to choose a activity among the assemble which satisfy the conditions. This involves Priority of activities' scheduling. Many scholars have put forward many solutions respectively. Luo(2004)put forward a kind of heuristic algorithm of priority of activities' scheduling. This algorithm emphasizes randomness. Its main principle is that due to the constraints of activities' logic relation; it will generate a lot of infeasible solution by randomly generated. The algorithm considers a activity which still has not arranged by a fixed order, and the whole selection process is generated from left to right successively. At each stage, there is a set of practical activities' scheduling, and it gives a priority of conflicting work randomly. This process has been repeated until all work has finished the selected arrangement. The essence of this method is that in the set of practical activities, chooses the activity randomly, which is without priority with the equiprobable model. The efficiency of random sampling depends mainly on random functions. Shou(2004) Mentions a solution to solve various activities' priority, which is called based on the value as regret random sampling methods. The method combines a prioritized rule commonly used in the heuristic algorithm. The prioritized rule is that examines an activity in a feasible set named Q, and make the selected probability is related with its priority, meanwhile ensure the sum of probability of all activities in the feasible set is 1. The random function is as follows: [pic] (6) [pic]is the probability of activity (i, j) selected; [pic] is the largest D-value between the priority of activity(I, j ) and other activities in set Q; [pic] is parameter, Generally, it is greater than zero and the value is often set as 1. This ensures the lowest priority activity also has certain probability to be selected; [pic] is used to control the stochastic process. According to the above definition of probability, it can choose an activity randomly in the practical set Q. The probability of activities selected is reciprocal to the priority. The smaller the priority, the probability of activities selected is larger. It can be anticipated that the prioritized rule will have effect on the project schedule by generated randomly. Therefore, the prioritized rule which is based on the random sampling is used frequently at present. This dissertation will adopt the random number based on the system time to determine the activities priority. Firstly, the random number based on the system time is produced by a random function used in the VB language, which is used as the priority of activities scheduling. When there are a lot of choices in the feasible set, the activities' scheduling will be determined by the size of the random number. 4.4 Algorithm basic step . Initialize particles' random position and speed according to the established initialization . Calculate each particle's adaptive value . For each particle, let the adaptive value compare with the best position' value which has experienced, if it is better, it will be set as the current best position. . For each particle, let the adaptive value compare with the best position' value which has experienced in the whole situation, if it is better, it will be set as the current global best position. . Make the particles' speed and location iterated according to formula . If terminal conditions are satisfied, the algorithm ends. Otherwise, return steps 2 4.5 The flow chart Based on the previous chapter, this paper the discrete particle swarm optimization algorithm to solve the maximum net present value. The main flow chart is shown in figure 4.3. [pic] Figure 4.3 Main flow chart Source: Experimental results 4.4 Results contrast and analysis 4.4.1 Illustration of calculation results The results from last iteration are set as the approximately optimal solution Because of the randomness of the algorithm; the calculation shall be carried out many times and got the statistic results. Table 4.5 shows the 10 calculation results of number 5000 in PSO. |Serial |activities' |activities|activities|activities|NPV | |number |actual start |' actual |' mode |' paid | | | |time |end time able 4.5 10 calculation results of number 5000 in PSO Source: Experimental results 4.4.2 Several conclusions from the results . Because of the large scale problems and the complexity of the variables, the optimizing performance is not stable, especially in the optimal payment schedule. . Each iterative result is not identical. There are two reasons. Firstly, it is related to the randomness of the algorithm. Every time the random Numbers are produced in different iteration. Secondly, the results effected by seeking for the optimal performance and complexity of the problem. It is difficult to get the optimal solution from combinatorial optimization problem, and it mostly only gets approximate solutions. From this point of view, this paper has got some of the approximate solution of the combinatorial optimization problem which is accord with the characteristics. . The approximate solutions of multiple optimal solutions are obtained. The NPV of the project, payment schedule and each activity' actual start time of each scheme is different, but the total time of construction and each activity' mode is the same. It can be seen from the calculated results that there are two major schemes. Each activity's start time of the first scheme is{0 0 5 5 8 8 12 12 12 18} and the other is {0 0 5 5 8 8 8 12 12 18}. . Except the virtual activities, the optimal time of each activity is {0 0 5 5 8 8 12 12 12 18}, the optimal mode of each activity is {1 2 1 2 1 2 1 1 2 2 }, the optimal payment schedule of each activity is {1 1 0 0 0 0 1 0 0 1}, The optimal time of construction is 21, the maximum net present value for the project is 1029.784. It can be seen that payment schedule has certain effect on the final result. 4.4.3 Comparison There are some different points with two optimization model [25] which combines contractor's and the client's viewpoints respectively. For example: The model of He (2006) fixes the payment on 4 landmarks (2,4,5,7); otherwise payment scheme works as a decision-making variables in this paper . The model of He (2006) considers the cost connection between events, otherwise the cost is considered in the beginning of activities which means simplified activities' connection in this paper. Those differences lead to the different of the calculation results. The results of He (2006) is that total time of construction is 19, The Net Present Value is 779.0, each activity' start time is {0 3 7 6 10 16 19}, each activity' execute mode is {2 2 1 2 1 2 1 1 2 2 }, the payment happens at the event 2,4,5,7. But the results of this research are different. Total time of construction is 21, each activity' execute mode is {1 2 1 2 1 2 1 1 2 2 }. The net present value, each activity' actual start time and end time and payment schedule is different. Then the analyzed of the two results are given. . The time of constriction and each activity' actual start time is different. The total time of constriction is longer than He'. The mainly reason is that this paper does not consider the flexible resource. It means that the maximum of resources can not be changed which may reduce the possibility of activities happened at the same time. Otherwise the model of He (2006) considers the maximum of resources can be increased. It may increase the possibility of activities happened at the same time. So the total time of construction is longer in this paper. Each activity' actual start time is also affected by the maximum resources. . Each activity' executed mode is different. The first activity does not adopt the second' mode in this paper. It is reasonable. From activity' starts time, the first and second activity start and end at the same time. The third activity happens after these two activities. If the first activity adopts the second' mode, it not only does not influence on the start time of the third activity, but also increases the cost. It is deviated from the optimization target, so there is no need for using the second execute mode. In the model of He(2006), The first activity adopts second' mode because of the different second node. The maximum resources can be increased and the possibility of activities happened at the same time may be increased too. The first activity adopts second' mode which may make the latter activities' start time ahead of the schedule. So this calculation result is reasonable too. . The net present value is different. The results are bigger than the model of He (2006). Those differences have effect on the calculation results. It can be seen from the table 4.5; Payment schedule has certain effect on the calculation results. In a word, although the calculation results are different from the results of He (2006), through the contrast analysis, it can be seen that the different influence factors will lead to different results and the difference is reasonable and explanatory. 4.5 Summary of analysis In this section, firstly, it introduces the principle and concept of the particle swarm algorithm and gives a detailed elaboration to variable and iteration involved in the algorithm. Then it presents the main flow chart. At last, it proves that it is feasible to solve the maximum net present value using discrete particle swarm algorithm. It provides a reference to solve this kind of problem and also gives a reference to actual project. 5 Discussions Pursuing the maximum net present value has emerged in network project, especially at the broad heading-just like the case -- JZDWBD-V which has been used in this dissertation. However, there are few project announced that they let the interest maximized. The truth is known that net present value problem is still at its primary stage and it is a senior stage developed in western countries where this problem has developed very mature. So whether existing method can fit the network planning of big project and help it develop becomes a question, which is also a part of question which this dissertation tends to answer. Network planning technique has widely applied and promoted. The optimization of network plan is the higher level of the application of network planning technique. It has become a necessary component in the project management, and is an important content of modern project management. Based on consulting the related literature of optimization of network planning, this dissertation mainly aims at maximizing NPV problem. In the course of the study, particle swarm algorithm is applied to solve the maximum net present value, and combines with the characteristics of problem; finally it uses the discrete particle swarm algorithm to solve the problem. Next there will be a summary of the study in this dissertation and the main exploratory conclusion. . It points out that the deficiency of network planning optimization according to the current research situation of network planning optimization. Meanwhile it puts forward that the maximizing net present value gradually become the global research hot spot in network planning optimization, but in china this problem is still in the stage of exploration. . It analyzes the previous research achievements on maximum net present value problem and try to consider various factors together, such as : resource constraints, executive mode, the owners' payment, rewards and punishment, cash inflows and outflows, etc. Then analyzes these factors one by one and form a decision variable including activity's sequences, activity's executive mode and the schedule of owners' payment. . It studies the principle of the standard particle swarm algorithm, and labors the characteristics of discrete particle swarm algorithm according to the discrete characteristics of the decision variables in this research. Besides it obtains the maximum net present value of the given case using discrete particle swarm algorithm and gives comparative analysis on the existing results. Finally , it verifies the feasibility of the algorithm. The calculation results show that the algorithm finds a couple of the approximate solution of the optimal one. It is accordance with combinatorial optimization and gives a reference on optimization of project schedule. . It adopts the serial generating mechanism in project generating schedule mechanism and let activities' execution sequence as decision variable replaced the activities' actual start time. Compared with parallel generating mechanism, Serial generating mechanism would ensure the searching optimization performance of the algorithm. . In the realization of the algorithm, according to the characteristics of problem this dissertation takes example by the successful experience on solving TSP (traveling salesman problem) by discrete particle swarm algorithm, especially on the iteration method of activities sequence, and gives the definition of the position and speed. It works out the difficulty of iterating activities sequence. 6 Conclusions and further research In this chapter, there are two problems to be handled. In the first place, the work finished in the research will be overviewed. Secondly, suggestions of future work following the work done here will be illustrated. 6.1 Conclusions The purpose of this dissertation is to explore the network planning in China: how to get the maximum net present value in big project in China and whether now existing methods fits the situation of China to improve the performance of the optimal solution. The Chinese project is used as a case- JZDWBD-V is a successful network planning by now in China. Particle swarm algorithm can be viewed as a feasible method for several reasons such as algorithm finds a couple of the approximate solution of the optimal one. So the data in this case is believed to reflect the solving of net present value of network planning in China. Some means, the case selected has be used to avoid or resolve the problems such as information security. Otherwise, some other problem such as lake of experience still need time to solve. 6.2 further research This dissertation makes some exploratory research on the maximizing NPV problems which is a area of network planning. But there still exist many improvements. . In the process of studying the maximum net present value, this paper makes a reference to some assumptions made by previous researchers. But I think some assumptions can be relaxed, such as nonrenewable resources, double constraint resources to be considered in the maximum net present value; Cash outflows occurs in the middle of activities, which can get more accurate net present value. . In the solving process of adopting discrete particle swarm algorithm to a specific example, the optimization is not as better as expectations due to the complexity of the variables. Especially, the payment schedule variables can not get a more stable solution. It can be imagined that when the scale of the problems increases, the convergence of the algorithm and searching for optimum performance need to be made further improvement. . Flexible resource is not studied in this dissertation. It is necessary to make some improvements because flexible resource can give a further optimization on total construction period. . It lacks the analysis of complexity during the process of coding. The efficiency needs to be improved further.
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