A Multi-Mode Project Scheduling Method Based on Hybrid Heuristic Ant Colony System

Abstract

The present invention discloses a multi-mode project scheduling method based on a hybrid heuristic ant colony system. First, a benchmark sequence that satisfies the execution order of activities in the activity-on-arrow network diagram is randomly generated. Then, an actual scheduling plan that satisfies the activity-on-arrow network diagram is gradually constructed according to the benchmark sequence. Next, the paths of ants are updated through hybrid heuristic information. After that, asynchronous simulation processing is performed on the cost and execution time parameters, and the correlation coefficient between solutions is calculated. Finally, simulation is carried out in the next generation according to the correlation coefficient between solutions in the previous generation. The method of the present invention utilizes the characteristics of uncertain parameters in multi-mode medical project scheduling optimization and the high dependence of uncertainty on the context to design and improve the algorithm. On the premise of ensuring the evaluation accuracy, it reduces the consumption of computing resources and improves the optimization efficiency of the ant colony system.

Description

Technical Field

[0001] The present invention belongs to the technical field of operations research, and particularly relates to a multi-mode project scheduling method based on a hybrid heuristic ant colony system. Background Art

[0002] The project scheduling problem is one of the most important research topics in the field of project management and is widely applied in software science, logistics scheduling, construction science, ship scheduling, medical services and other fields. Domestic and foreign scholars earliest carried out corresponding research on the resource-constrained project scheduling problem. Subsequently, some scholars considered that in real life, the activity patterns in most projects are more than one, so they carried out research on the resource-constrained multi-mode project scheduling problem. And by adding the consideration of the net present value of the cash flow in the objective function, it was extended to the multi-mode project scheduling problem considering the net present value of the discounted cash flow. Another part of the scholars carried out research on the uncertain single-mode project scheduling problem aiming at the uncertainty in the project scheduling problem in real life and extended it to the multi-mode situation. The specific research progress is as follows:

[0003] (1) Resource-constrained project scheduling problem

[0004] The resource-constrained project scheduling problem (RCPSP) is the most classic project scheduling model in the industrial field. Generally, given a project composed of n activities, the goal of RCPSP is to arrange the execution order of each activity according to the precedence constraints and resource limitations to minimize the project duration. This problem has been proved to be an NP-hard problem, that is, any NP problem can be reduced to this problem under polynomial-time many-one reduction, logarithmic-space many-one reduction or polynomial-time Turing reduction. Generally speaking, the most commonly used method to solve RCPSP is to first find a basic activity list that satisfies the activity precedence order, and then allocate feasible processing times for each activity according to the order in the activity list. At present, scholars have proposed a series of methods for how to find the activity list that meets the constraint conditions, mainly divided into exact methods such as the branch and bound method, and meta-heuristic methods such as genetic algorithms, ant colony algorithms, tabu search, simulated annealing, etc.

[0005] (2) Resource-constrained multi-mode project scheduling problem

[0006] In the traditional resource-constrained project scheduling problem, each activity can only be implemented in a single mode. In reality, however, activities can generally be carried out through different alternative modes. For example, in the normal mode, an activity can be completed by 5 employees and 2 machines in five months. But in the case of extremely urgent time, an emergency mode can be launched, increasing the number of employees to 8 and the number of machines to 4, and shortening the project duration to three months. Therefore, different execution modes represent different trade-offs between time, cost, and resources for an activity. The resource-constrained project scheduling problem considering multiple execution modes is called the multi-mode RCPSP (Multi-Mode RCPSP, MRCPSP). To handle the time / cost / resource trade-offs between different modes, MRCPSP not only has to find a basic activity list that satisfies the activity precedence order, but also has to find the corresponding execution mode for each activity. Therefore, the computational complexity of MRCPSP increases significantly. Kolisch has proven in the monograph "KOLISCH R. Projectscheduling under resource constraints-Efficient heuristics for severalproblem classes[M]. Project Scheduling under Resource Constraints—EfficientHeuristics for Several Problem Cases, 1995" that for MRCPSP with multiple non-renewable resources, finding a feasible solution is already an NP-complete problem, let alone finding an optimal feasible solution. Currently, the existing MRCPSP methods are mainly meta-heuristic methods, such as hybrid genetic algorithms, ant colony algorithms, simulated annealing, etc.

[0007] (3) Multi-Mode Project Scheduling Problem of Net Present Value of Discounted Cash Flow

[0008] Traditional RCPSP and MRCPSP only consider the minimization of construction period, while ignoring the impact of economic aspects. In recent years, economic considerations are increasingly considered to be the key to project scheduling. The most commonly used economic quantitative standard is the Net Present Value (NPV) of discounted cash flow. NPV refers to the difference between cash inflows and outflows, which considers the time value of money by discounting cash flows. Compared with the traditional standard that only considers construction period, the use of NPV standard will result in higher computational costs when evaluating the objective function because the objective function is nonlinear. Therefore, the model using NPV standard becomes more complicated and is called MRCPSP with discounted cashflows (MRCPSP with discounted cashflows, MRCPSPDCF). In MRCPSPDCF, since the evaluation of NPV involves the time and cost of the project, it is more difficult to design an effective heuristic method for the problem. The meta-heuristic methods currently designed for this problem include genetic algorithms, algorithms combining simulated annealing with taboo search, ant colony algorithms, etc.

[0009] (4) Uncertain single-mode project scheduling problem

[0010] The scheduling models in previous studies are all based on the premise that environmental parameters such as activity duration and cost are determined before scheduling. However, in practical applications, due to unexpected situations, it is often almost impossible to determine all environmental parameters of a project a priori. In general, as a practical scheduling model for project selection and planning, uncertainty is a factor that cannot be ignored. Since the actual duration may be longer or shorter than expected, it is difficult to complete the project exactly as planned. Since the disrupted duration may exceed the deadline and cause a deficit, the activity list generated by deterministic scheduling may no longer be applicable in this case. Scheduling under uncertainty is a challenging research field that has attracted increasing attention. Several types of scheduling models and algorithms have been proposed to solve single-mode RCPSP under uncertainty.

[0011] (5) Uncertain multi-mode project scheduling problem

[0012] In recent years, scholars have further combined the situation of parameter uncertainty with the multi-mode problem and considered the MRCPSP under parameter uncertainty. Among them, Asta et al. applied the Monte Carlo simulation method to the MRCPSP under parameter uncertainty in the literature "Asta S, Karapetyan D, Kheiri A, et al. Combining Monte-Carlo and hyper-heuristic methods for the multi-mode resource-constrained multi-project scheduling problem[J]. Information Sciences, 2016, 373(10): 476-498.", and combined it with novel neighborhood movement strategies, memetic algorithms, and hyper-heuristic methods, using the computing power of multi-core machines to improve the speed of iterative execution. Wang et al. designed a genetic tabu hybrid search heuristic algorithm in the literature "Wang Yanting, He Zhengwen, Liu Renjing. Optimization of reactive multi-mode project scheduling under stochastic duration[J]. Journal of Systems & Management, 2017, 26(1): 85-93.", and under the condition of random interruption of activity duration, by measuring the impacts of three objectives of cost, robustness, and completion time and different combinations of two resource allocations on the loss cost, completion time, and number of interruptions in the project scheduling process, to determine the optimal scheduling strategies in different situations. Xie et al. also studied the MRCPSP under the condition of uncertain activity duration in the literature "Xie Fang, Li Hongbo, Bai Qingguo. Stochastic multi-mode resource-constrained project scheduling[J]. Chinese Journal of Management Science, 2020.", and established a Markov decision process model for this problem. To achieve the efficient solution of the model, an approximate dynamic programming algorithm based on Rollout was designed to dynamically give a scheduling plan according to the latest project status during the project execution process, so as to effectively optimize the expected project duration. Summary of the Invention

[0013] To overcome the deficiencies of the prior art, the present invention provides a multi-mode project scheduling method based on a hybrid heuristic ant colony system. First, a baseline sequence that satisfies the execution sequence of activities in the activity-on-arrow network diagram is randomly generated, and then an actual scheduling plan that satisfies the activity-on-arrow network diagram is gradually constructed according to the baseline sequence. Next, the paths of ants are updated through hybrid heuristic information, and then asynchronous simulation processing is performed on the cost and execution time parameters to calculate the correlation coefficient between solutions. Finally, simulation is performed in the next generation according to the correlation coefficient between solutions in the previous generation. The method of the present invention utilizes the characteristics of uncertain parameters in the optimization of multi-mode medical project scheduling and the high dependence of uncertainty on the context to design and improve the algorithm, reducing the consumption of computing resources and improving the optimization efficiency of the ant colony system while ensuring the evaluation accuracy.

[0014] The technical solution adopted by the present invention to solve its technical problems includes the following steps:

[0015] Step 1: Randomly generate a benchmark sequence that satisfies the execution order of activities in the activity-on-arrow network diagram;

[0016] Record the predecessor activities of each activity, and randomly select a pattern according to pheromone and heuristic information among the activities where all predecessor activities have been selected until the benchmark sequence is completed, ensuring that each predecessor activity does not appear after the successor activity;

[0017] Step 2: Gradually construct a scheduling plan that satisfies the activity-on-arrow network diagram according to the benchmark sequence;

[0018] Combine each activity with the corresponding pattern to obtain a benchmark pattern, and obtain a scheduling plan according to the execution time, required resources, and resource usage limitations corresponding to the benchmark pattern, and calculate the total duration required for the scheduling plan;

[0019] Step 3: Use the ant colony algorithm to update the paths of ants through hybrid heuristic information;

[0020] Update the optimal path of the ants by simultaneously considering the hybrid heuristic information of time, cost, and resources;

[0021] The hybrid heuristic information h(i) of the i-th pattern is as follows:

[0022]

[0023] Among them, and are the expected cost and expected execution time of pattern i respectively, r i is the resources required for pattern i, and α is a set parameter;

[0024] Step 4: Asynchronously simulate and process the two uncertain parameters of cost and execution time;

[0025] For the uncertain cost parameters corresponding to each pattern in the multi-mode medical project scheduling problem, since they follow a normal distribution, directly take the expected cost for the evaluation of fitness values;

[0026] For the uncertain execution time corresponding to each pattern in the multi-mode medical project scheduling problem, perform Monte Carlo simulation on the parameter values to evaluate the fitness values;

[0027] Step 5: After updating the solutions in each generation of the ant colony algorithm, calculate the correlation coefficient between the solutions, thereby judging the current evolutionary stage, and setting the number of simulations required for the fitness value evaluation in the next generation;

[0028] By calculating the correlation relationship between solutions in each generation, the evolutionary stage of the solutions is judged; the correlation relationship r between two solutions X and Y is given by formula (2):

[0029]

[0030] where n is the number of simulations in this generation, X l and Y l are the fitness values of the two solutions in the l-th simulation respectively, and are the average values of the two solutions in the simulations of this generation respectively; by calculating the correlation coefficient between the fitness values of the two solutions in the n simulation scenarios of this generation, the correlation degree between the two solutions in this generation is obtained; by calculating the pairwise correlation coefficients between all solutions in this generation and taking the average value, the average correlation coefficient between the solutions in this generation is obtained

[0031]

[0032] where NP is the total number of ants in the ant colony system, r kj is the correlation coefficient between the k-th ant and the j-th ant; by calculating the average correlation coefficient between pairs of solutions in each generation, the current evolutionary stage can be judged, so as to set the corresponding number of simulations;

[0033] Step 6: Perform simulations in the next generation according to the correlation coefficient between solutions in the previous generation of the ant colony algorithm;

[0034] According to the correlation coefficient calculated in the previous generation and the set number of simulations, perform two-stage simulations in the next generation and calculate the corresponding fitness values; in the initial stage of the ant colony system, set the number of simulations to n according to the characteristics of the problem; after each generation loop ends, calculate the average correlation coefficient between the solutions in the current ant colony. When the value of the average correlation coefficient is less than the threshold ξ, the number of simulations in the next generation remains unchanged, still n; until in a certain generation, the value of the average correlation coefficient is greater than the threshold ξ, it is determined that the ant colony system has evolved to the next stage.

[0035] Preferably, the ξ is set to 0.7.

[0036] The beneficial effects of the present invention are as follows:

[0037] 1) The method of the present invention increases the search ability of ants in the ant colony system by mixing heuristic information. This system uses the characteristics of the multi-mode project scheduling optimization problem to design and improve the algorithm, and improves the search ability of ants in the ant colony system.

[0038] 2) The method of the present invention sets an asynchronous fitness value evaluation method for different coefficients, improves the accuracy of fitness value estimation, avoids additional simulations, and determines the evolutionary stage of the system based on the correlation coefficient between solutions, and sets corresponding simulation times for different stages to further reduce unnecessary simulations. This method utilizes the characteristics of uncertain parameters in multimode medical project scheduling optimization and the high dependence of uncertainty on the context to design and improve the algorithm. On the premise of ensuring the evaluation accuracy, it reduces the consumption of computing resources and improves the optimization efficiency of the ant colony system. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a flowchart of an embodiment of the present invention.

[0040] Figure 2 It is a activity-on-arrow network diagram of an embodiment of the present invention.

[0041] Figure 3 It is a schematic diagram of the actual scheduling plan of an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0042] The present invention will be further described below with reference to the drawings and embodiments.

[0043] For the scheduling model considering economic impacts, it is very difficult to accurately predict the inflow and outflow of cash. In this sense, the handling of uncertainty is more important in project scheduling models using the NPV criterion, but the research in this aspect is relatively lacking, and the handling of uncertainty in existing research is not yet mature. In response to this, the present invention conducts research on the multimode project scheduling problem of the net present value of discounted cash flow in an uncertain environment, designs a hybrid heuristic ant colony system, and combines it with an asynchronous two-stage simulation method based on the correlation coefficient. The proposed algorithm can not only improve the search ability of the ant colony algorithm, but also reduce unnecessary resource consumption and improve the optimization efficiency of the algorithm.

[0044] The present invention proposes a multimode project scheduling method based on a hybrid heuristic ant colony system, which can not only improve the search ability of the algorithm, but also improve the optimization efficiency of the algorithm. The content of the present invention is as follows:

[0045] 1. Randomly generate a benchmark sequence that satisfies the execution sequence of activities in the activity-on-arrow network diagram, ensuring that each predecessor activity does not appear after the successor activity.

[0046] 2. Gradually construct an actual scheduling plan that satisfies the activity-on-arrow network diagram according to the benchmark sequence.

[0047] 3. Update the paths of ants by mixing heuristic information. Since there are trade - offs among time, cost, and resources in the multi - mode medical project scheduling problem with resource constraints, mixing heuristic information can better combine information from various aspects and improve the search ability of ants.

[0048] 4. According to the characteristics of the two uncertain parameters, cost and execution time, in the problem, perform asynchronous simulation processing on the two parameters. For the uncertain cost parameter corresponding to each mode in the multi - mode medical project scheduling problem, since it follows a normal distribution, the expected cost can be directly taken for fitness value evaluation during the optimization process. For the uncertain execution time corresponding to each mode in the problem, since its impact on fitness evaluation is very large and it does not follow a normal distribution, Monte Carlo simulation needs to be performed on the parameter values for fitness value evaluation.

[0049] 5. After updating the solutions in each generation, calculate the correlation coefficient between the solutions to determine the current evolutionary stage and set the number of simulations required for fitness value evaluation in the next generation.

[0050] 6. Conduct simulations in the next generation according to the correlation coefficient between the solutions in the previous generation. For those with a relatively low correlation coefficient between solutions, it is generally considered that they are still in the initial stage of evolution and more simulations are needed to accurately evaluate the quality of the solutions. For those with a relatively high correlation coefficient between solutions, it is generally considered that they are in the later stage of evolution. Since the correlation coefficient between solutions is very good at this stage, only a small number of Monte Carlo simulations are needed to accurately evaluate the quality of the solutions. Specific embodiments:

[0052] 1. Taking the activity - on - arrow network diagram given in Figure 2 as an example, first randomly generate a baseline sequence that satisfies the precedence relationship of activities in the activity - on - arrow network diagram. To ensure that the generated sequence satisfies the sequence constraints of activities, record the predecessor activities of each activity and randomly select according to pheromone and heuristic information among the activities whose all predecessor activities have been selected until the construction of activities in the baseline sequence is completed. Suppose the constructed precedence relationship of activities is (A, B, D, C, E). After construction, for each activity, select the corresponding mode according to pheromone and heuristic information. Suppose the modes selected for each activity are (1, 2, 2, 1, 2) respectively. Then the final obtained baseline sequence is:

[0053]

[0054] 2. Gradually transform the constructed benchmark sequence into an actual scheduling plan that meets the requirements of the activity-on-arrow network diagram. Combine each activity with its corresponding mode, and the resulting benchmark mode is (A1, B2, D2, C1, E2). Assume that the execution times corresponding to these five modes are (5, 5, 4, 3, 3) respectively, and the required resources are (2, 3, 3, 2, 2) respectively. The limit of available resources is 5. The scheduling plan is given in Figure 3 . And it is calculated that the total duration required for the scheduling plan is 16.

[0055] 3. Update the optimization path of the ants by simultaneously considering the hybrid heuristic information of time, cost, and resources. Since in the considered multimode medical project scheduling problem, the fitness value is affected by time, cost, and resources simultaneously. Therefore, when updating the path, using the hybrid heuristic information that simultaneously considers these three parameters can enable the ants in the ant colony system to better find the optimal path. The hybrid heuristic information h(i) of the i-th mode is as follows:

[0056]

[0057] Among them, and are the expected cost and expected execution time of mode i respectively, r i is the resource required for mode i, and α is a parameter set according to the actual situation of the problem. Through the given hybrid heuristic information, the search ability of the ants can be enhanced, helping the ants to find excellent paths with lower costs, shorter execution times, and less resource consumption faster.

[0058] 4. In the uncertain multi-modal medical project scheduling problem, the two parameters, cost c and execution time d, in each mode are uncertain. Based on existing expert experience, it is known that the cost c follows a normal distribution, and the mean and variance of the cost c in each mode can be estimated. Since the impact of the cost c on the fitness value is consistent with the change in the cost itself, when calculating the expected fitness value, directly taking the expected value of the cost for calculation can not only reduce the computing resources consumed by simulating the mode cost, but also obtain a more accurate result than only performing a small number of simulations. For the execution time d, this parameter does not follow a normal distribution, but according to existing expert experience, the possible values and probabilities of the execution time d can be given. Different from the cost c, the impact of the value of the execution time d on the fitness value is inconsistent with the change in its own value. When the execution time of each mode changes, on the one hand, the thread allocation for each mode when converting the benchmark sequence into the actual scheduling plan may also change, resulting in a completely different calculation of the fitness value. On the other hand, it is very likely that the overall scheduling time exceeds the expected time, and a penalty coefficient needs to be multiplied when calculating the fitness value, greatly reducing the fitness value. Therefore, for the parameter of the execution time d, the mean of the scheduling plan cannot be simply calculated by taking its expected value, but Monte Carlo simulation needs to be carried out to truly reflect the impact of the change in the execution time on the fitness value.

[0059] 5. By calculating the correlation relationship between solutions in each generation, the evolutionary stage in which the solutions are located is judged. The correlation relationship r between two solutions X and Y is given by formula (3):

[0060]

[0061] where n is the number of simulations in this generation, X i and Y i are the fitness values of the two solutions in the i-th simulation respectively, and are the average values of the two solutions in the simulations of this generation respectively. By calculating the correlation coefficient between the fitness values of the two solutions in the n simulation scenarios of this generation, the degree of correlation between the two solutions in this generation can be obtained. By calculating the pairwise correlation coefficients between all solutions in this generation and taking the average value, the average correlation coefficient between the solutions in this generation can be obtained

[0062]

[0063] where NP is the total number of ants in the ant colony system, r ijis the correlation coefficient between the i-th ant and the j-th ant. By calculating the average correlation coefficient between pairs of solutions in each generation, the current evolutionary stage can be determined, and the corresponding number of simulation runs can be set.

[0064] 6. According to the correlation coefficients calculated in the previous generation and the set number of simulation runs, perform a two-stage simulation in the next generation to calculate the corresponding fitness values. In the initial stage of the ant colony system, the number of simulation runs is set to n according to the characteristics of the problem. After each generation loop ends, calculate the average correlation coefficient between the solutions in the current ant colony. When the value is less than a certain threshold ξ (according to the definition of the correlation coefficient, when the correlation coefficient between two solutions is greater than 0.7, it is considered that the two solutions are highly correlated. Therefore, in the present invention, ξ is set to 0.7), the number of simulation runs in the next generation remains unchanged and is still n. Until in a certain generation, the value is greater than the threshold ξ, it is considered that the ant colony system has evolved to the next stage. In this stage, since the correlation coefficient between the solutions is very high, that is to say, the correlation between the fitness value of the solution and the situation is very high. Since in the ant colony system, only by judging the quality of the solutions can evolution be carried out, without the need to obtain a very accurate estimated value of the fitness expectation. Therefore, in this stage, only a small number of simulations (set to 1 in the present invention) need to be carried out in the same situation to accurately judge the quality between the solutions, thereby supporting the evolution of the ant colony system. This two-stage simulation strategy for the correlation coefficient can reduce unnecessary simulations in the later stage of evolution, save computing resources, and improve the optimization efficiency of the ant colony system.

Claims

1. A multi-mode project scheduling method based on a hybrid heuristic ant colony system, characterized in that It includes the following steps: Step 1: Randomly generate a benchmark sequence that satisfies the execution sequence of activities in the activity-on-arrow network diagram; Record the predecessor activities of each activity, and randomly select a pattern according to pheromone and heuristic information among the activities where all predecessor activities have been selected until the benchmark sequence is completed, ensuring that each predecessor activity does not appear after the successor activity; Step 2: Gradually construct a scheduling plan that satisfies the activity-on-arrow network diagram according to the benchmark sequence; Combine each activity with the corresponding pattern to obtain a benchmark pattern, and obtain a scheduling plan according to the execution time, required resources, and resource usage limitations corresponding to the benchmark pattern, and calculate the total duration required for the scheduling plan; Step 3: Use the ant colony algorithm to update the paths of ants through hybrid heuristic information; Update the optimization paths of ants by simultaneously considering hybrid heuristic information of time, cost, and resources; The hybrid heuristic information h(i) of the i-th pattern is as follows: wherein, and are the expected cost and expected execution time of mode i, respectively, r i is the resource required for mode i, and α is a setting parameter; Step 4: Asynchronously simulate the two uncertain parameters of cost and execution time; For the uncertain cost parameters corresponding to each pattern in the multi-mode medical project scheduling problem, since they follow a normal distribution, directly take the expected cost for fitness value evaluation; For the uncertain execution time corresponding to each pattern in the multi-mode medical project scheduling problem, perform Monte Carlo simulation on the parameter values for fitness value evaluation; Step 5: After updating the solutions in each generation of the ant colony algorithm, calculate the correlation coefficient between the solutions to judge the current evolutionary stage and set the number of simulations required for fitness value evaluation in the next generation; Judge the evolutionary stage of the solutions by calculating the correlation relationship between the solutions in each generation; the correlation relationship r between two solutions X and Y is given by formula (2): where n is the number of simulations in this generation, and X l and Y l are the fitness values of the two solutions in the l-th simulation respectively, and are the average values of the two solutions in the simulations of this generation respectively; the correlation degree between the two solutions in this generation is obtained by calculating the correlation coefficient between the fitness values of the two solutions in the n simulation scenarios of this generation; by calculating the pairwise correlation coefficients between all solutions in this generation and taking the average value, the average correlation coefficient between the solutions in this generation is obtained where NP is the total number of ants in the ant colony system, and r kj is the correlation coefficient between the k-th ant and the j-th ant; by calculating the average correlation coefficient between pairs of solutions in each generation, the current evolutionary stage can be determined, and thus the corresponding number of simulation runs can be set. Step 6: Perform simulation in the next generation according to the correlation coefficient between the solutions in the previous generation of the ant colony algorithm; According to the correlation coefficient calculated in the previous generation and the set number of simulations, perform two-stage simulation in the next generation and calculate the corresponding fitness value; in the initial stage of the ant colony system, set the number of simulations to n according to the characteristics of the problem; after each generation cycle, calculate the average correlation coefficient between the solutions in the current ant colony. When the value of the average correlation coefficient is less than the threshold ξ, the number of simulations in the next generation remains unchanged, still n; until in a certain generation, the value of the average correlation coefficient is greater than the threshold ξ, it is determined that the ant colony system has evolved to the next stage.

2. A multimode project scheduling method based on a hybrid heuristic ant colony system according to claim 1, characterized in that, The ξ is set to 0.7.

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