A low-carbon project scheduling method for ship segment painting

Abstract

The application discloses a kind of for ship section painting plan scheduling method, consider VOCs exhaust treatment equipment consumption electric energy and the carbon emission caused by LNG gas, consider the constraint of human resources and establish the multi-schedule plan scheduling model of two kinds of tasks including sand washing and spraying.A kind of improved artificial bee colony algorithm is proposed to effectively obtain approximate optimal solution within reasonable time, and a three-dimensional coding solution mechanism is designed based on the model.In the algorithm, the search efficiency of the algorithm is increased by mixing greedy random adaptive search algorithm and variable neighborhood search algorithm, which can be well used for ship section painting plan scheduling problem.

Description

Technical Field

[0001] This invention relates to the field of shipbuilding, and more particularly to a low-carbon planning and scheduling method for painting ship sections. Background Technology

[0002] Reducing environmental pollution and achieving green manufacturing has become one of the most pressing issues for modern manufacturing. Planning is a crucial element in manufacturing systems, and production scheduling is an effective way to save energy in manufacturing. By selecting different workshops or machines and optimizing the production sequence, energy savings can be achieved without increasing additional energy consumption. More and more scholars are dedicated to researching energy-saving issues in production scheduling and have achieved considerable results.

[0003] Ship painting is a labor-intensive production system. Compared to classic planning and scheduling problems, the planning and scheduling of ship section painting requires consideration of human resource allocation. Furthermore, with the advancement of green ship technologies and concepts, VOCs treatment equipment, as a major energy-consuming device in the ship painting process, generates significant carbon emissions from electricity and LNG. Therefore, researching the planning and scheduling of low-carbon ship section painting has important practical significance. Summary of the Invention

[0004] This invention provides a low-carbon planning and scheduling method for ship section painting, which can quickly obtain a two-week planning and scheduling arrangement that comprehensively considers three objectives: completion time, unbalanced workload, and carbon emissions.

[0005] To achieve the above objectives, the present invention provides a low-carbon planning and scheduling method for ship section painting, comprising:

[0006] Establish a multi-objective mathematical model for scheduling ship section painting plans, considering maximum completion time, unbalanced workload, and carbon emissions.

[0007] The planning and scheduling results are represented by a three-dimensional coding method that includes process sequence vectors, shift allocation vectors, and personnel allocation vectors.

[0008] An improved artificial bee colony algorithm, which combines a hybrid greedy random adaptive search algorithm and a variable neighborhood search algorithm, is used to solve the mathematical model of multi-objective ship section painting schedule, and the final schedule result is obtained.

[0009] A further improvement of this invention lies in the fact that the mathematical model for solving the multi-objective ship section painting schedule takes the minimum maximum completion time, the minimum unbalanced workload, and the minimum carbon emissions as the solution objectives.

[0010] A further improvement of the present invention is that the constraints of the mathematical model for scheduling the multi-objective ship section painting plan include:

[0011] Each process can and should be handled by only one work group;

[0012] The sum of the specific number of workers assigned to each work group is less than the total number of workers;

[0013] Priority constraints between processes;

[0014] The preceding and following processes in the same segment must wait at least until the lower limit of the drying time of the preceding process;

[0015] The start date of a segment and the completion date of the final process must be within the given time window for that segment.

[0016] A further improvement of the present invention is that: in the process sequence vector, each element is a process number, and the position of the element in the process sequence vector indicates the execution order of the corresponding process;

[0017] The elements of the work group allocation vector correspond one-to-one with the process sequence vector, and each element represents the work group corresponding to the corresponding process in the process sequence vector.

[0018] In the personnel allocation vector, each element represents a work group, and the value of the element represents the actual number of workers in the work group.

[0019] A further improvement of the present invention is that the improved artificial bee colony algorithm includes an initialization phase, a hiring phase, a following phase, and a scouting phase.

[0020] A further improvement of this invention lies in the use of a greedy random adaptive search algorithm in the initialization phase of the improved artificial bee colony algorithm, specifically including:

[0021] First, randomly generate multiple sets of personnel allocation vectors and corresponding process sequence vectors; check each set of vectors, and if they do not meet the constraints, adjust the vectors to meet the constraints.

[0022] For each set of vectors, one of the three solution objectives is selected. Based on the selected solution objective, a class allocation vector for that set of vectors is constructed using a greedy random adaptive algorithm. If the constructed class allocation vector does not meet the constraints, the class allocation vector is adjusted to meet the constraints, and the corresponding solution is obtained. Finally, each solution is optimized through neighborhood search.

[0023] A further improvement of the present invention is that a crossover operator between solutions is used in the hired bee phase of the improved artificial bee colony algorithm to enhance the diversity of the population search.

[0024] A further improvement of this invention is that, in the follower bee stage of the improved artificial bee colony algorithm, the VNS method is used for neighborhood search to improve local search capability.

[0025] A further improvement of this invention lies in the fact that, during the scout bee phase of the improved artificial bee colony algorithm, a new solution is freely sought through a greedy random adaptive search. The solution of this invention has the following technical advantages: this method can effectively obtain an approximate optimal solution within a reasonable time, and a three-dimensional encoded solution mechanism is designed based on the model. The algorithm combines a greedy random adaptive search algorithm and a variable neighborhood search algorithm, increasing the search efficiency and making it well-suited for the ship section painting scheduling problem.

[0026] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0027] Figure 1 This is a flowchart of the algorithm of this invention;

[0028] Figure 2 This is a curve showing the change in LNG gas consumption during the spraying process;

[0029] Figure 3 A schematic diagram of a three-dimensional vector representation method for scheduling results;

[0030] Figure 4 This is a diagram illustrating the decomposition and mutation during the employment phase;

[0031] Figure 5 VNS includes 8 neighborhood search operators across three dimensions.

[0032] Figure 6 It is a Gantt chart of scheduling results. Detailed Implementation

[0033] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0034] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the illustrations only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0035] Some exemplary embodiments of the invention have been described for illustrative purposes. It should be understood that the invention may be implemented in other ways not specifically shown in the accompanying drawings.

[0036] like Figure 1 As shown, an embodiment of the present invention provides a low-carbon planning and scheduling method for ship section painting, comprising:

[0037] The problem is defined as a scheduling problem for painting ship sections. Ship sections require a sandblasting process as the first step, followed by painting, by a painting team. Depending on the requirements, a section may have 2-5 painting processes. The number of workers allocated to each team affects the work rate, and the sequence of processes also affects the workload of different teams. Furthermore, VOCs exhaust gas treatment equipment must be activated daily to treat the exhaust gases generated during the painting process. Therefore, this invention proposes a multi-objective mathematical model that comprehensively considers maximum completion time, team workload balance, and total carbon emissions.

[0038] The symbols and interpretations of the numbers, sets, parameters, and decision variables used in this model are shown in Table 1.

[0039] The three objective functions in the mathematical model are as follows:

[0040] (1) Completion time, expressed by the following formula:

[0041]

[0042] The completion time formula indicates that the objective is to minimize the total completion time of all plans. All planned days before the last day are considered as the maximum working time DH for calculation, regardless of the actual completion time.

[0043] Table 1. Symbols in the mathematical model

[0044]

[0045] (2) The unbalanced workload of the work group is expressed by the following formula:

[0046]

[0047]

[0048]

[0049] The formula for the unbalanced workload in work groups indicates that objective 2 is to minimize the difference between the workload of each work group and the average workload of the work group, so as to balance the overall workload. First, the average working time of workers in each work group is calculated as the workload of the work group. Then, the average workload of all work groups is calculated, and finally, the unbalanced workload is obtained.

[0050] (3) Total carbon emissions

[0051] Carbon emissions from ship section painting operations mainly come from the energy consumption of VOCs exhaust gas treatment equipment in the painting workshop. Energy consumption includes both electricity consumption and LNG gas consumption. The power consumption of electricity is constant by default when the VOCs exhaust gas treatment equipment is turned on. LNG gas consumption can be divided into three stages: the initial stage, the stable stage, and the final stage.

[0052] Changes in LNG gas consumption as follows Figure 2 As shown, the red line represents the initial stage, the green line represents the stable stage, and the blue line represents the final stage. The initial stage begins simultaneously with the spraying operation. As the VOCs gas concentration increases, the LNG gas combustion consumption rate also increases. In the stable stage, LNG gas consumption remains constant. The final stage begins when all spraying tasks for the day are completed. The VOCs exhaust gas treatment equipment continues to run for a period of time, and the LNG gas consumption rate first decreases and then stabilizes at the basic consumption rate. Finally, the equipment is shut down and restarted when the spraying operation begins the next day.

[0053] The formula for calculating carbon emissions is as follows:

[0054] Min f3=ε·Q E +σ·Q LNG

[0055]

[0056]

[0057] The carbon emission formula indicates that objective 3 aims to minimize the sum of carbon emissions from electricity consumption and gas consumption. Based on the carbon emissions per kilowatt-hour of electricity consumption, e is generally set to 0.7559, and based on the carbon emissions per cubic meter of LNG combustion, σ is generally set to 2.1650. The total electricity consumption (kilowatt-hours) and the total LNG gas consumption (cubic meters) are calculated separately and then added together. In this model, w is set according to actual conditions. E =20, w LNG1 =15, w LNG2 =30.

[0058] The constraints included in the mathematical model are as follows:

[0059] Each process can be handled by one and only one work group, with the sandblasting process handled by the sandblasting work group and the spraying process handled by the spraying work group. The constraint formula is as follows:

[0060]

[0061]

[0062]

[0063] The sum of the specific number of workers assigned to each shift is less than the total number of workers, as constrained by the following formula:

[0064]

[0065]

[0066] In the model, the actual time of a process is obtained by dividing the total budgeted working hours of the process by the number of workers in the team responsible for that process. The constraint formula is as follows:

[0067]

[0068] Each process has start and end time constraints, and each process must be completed within the maximum working time of the day. The priority relationships between different processes are constrained, and the constraint formula is as follows:

[0069]

[0070]

[0071]

[0072]

[0073] The time constraints between workstations must be considered when assigning tasks to different work groups on a given day. The constraint formula is as follows:

[0074]

[0075]

[0076]

[0077] For processes within the same segment, the time between the preceding and following processes must be at least the minimum drying time of the preceding process. The constraint formula is as follows:

[0078]

[0079] The start date of a segment and the completion date of the last process must be within the given time window for that segment, as constrained by the following formula:

[0080]

[0081]

[0082] An improved Artificial Bee Colony Algorithm (IABC) is proposed. The Artificial Bee Colony Algorithm (ABC) is a swarm intelligence optimization algorithm that simulates the nectar-collecting mechanism of bees to solve complex multi-dimensional optimization problems. In the ABC algorithm, the location of each nectar source represents a feasible solution. The artificial bee colony is divided into three categories: hired bees, follower bees, and scout bees. Hired bees search for new nectar sources based on already discovered nectar source information; follower bees search around the vicinity of nectar sources based on nectar source information shared by hired bees; and scout bees freely search for new valuable nectar sources using random searches. This invention proposes an improved artificial bee colony algorithm based on the ideas of the artificial bee colony algorithm, as detailed below:

[0083] In the initialization phase, a three-dimensional encoding method was designed to generate a stable initial population through a Greedy Random Adaptive Search (GRASP) initialization strategy. In the hired bee phase, crossover operators between nectar sources were used to enhance the diversity of the population search. In the follower bee phase, an efficient Variable Neighborhood Search (VNS) algorithm was designed to improve the local search capability of the IABC (Independent Flowchart of the Bees). In the scout bee phase, new nectar sources were freely searched using the GRASP method, increasing the global scope of the search while preventing bees from falling into a state of blind randomness. The algorithm flowchart is as follows. Figure 1 As shown.

[0084] A three-dimensional coding method was designed for the three sub-problems involved in scheduling: process scheduling, shift arrangement, and worker allocation. The determination of these three sub-problems guarantees a unique solution. To effectively allocate computational resources, corresponding three-dimensional coding methods were designed for each of the three sub-problems based on their characteristics. The feasible solution encoding of SBPSP consists of three vectors: process sequence vector (PV), shift allocation vector (GV), and worker allocation vector (WV). In PV, each element represents a process number, indicating the temporal relationship between all processes; in GV, each element represents a shift number, and the position of each element corresponds to the process number in the sequence to which that element belongs; in WV, each element represents the actual number of workers in the shift, and the position of each element corresponds to the shift number in the sequence to which that element belongs. Figure 3 The image shows an example of a three-bit encoding method for the solution.

[0085] In the initialization phase, a GRASP (Greedy Random Adaptive Search) algorithm was designed. First, the Work Value (WV) and Product Value (PV) are randomly generated. Then, based on model constraints, processes violating process priority constraints are adjusted to follow their preceding processes, thereby adjusting the PV to a PV that can find a feasible solution. Simultaneously, an objective is randomly selected with equal probability from three solution objectives. One-third of the initial population adopts the minimum completion time search strategy, one-third adopts the minimum job imbalance search strategy, and one-third adopts the minimum carbon emission search strategy. Based on the selected objective, the algorithm constructs the GV using a greedy random adaptive algorithm and ultimately finds a feasible solution that satisfies the constraints by adjusting the GV. Finally, the solution is found through neighborhood search optimization. The search operators used in the neighborhood search optimization are detailed in the VNS method of the bee-following stage.

[0086] In the hired bee phase, hired bees search among discovered nectar sources to try and find better ones. Based on a three-dimensional encoding method, a combination method between the encodings is designed. For GV and PV, considering the characteristics of the problem, two different solution combination methods are proposed to improve the efficiency of the hired bee search. Simultaneously, a mutation operator is introduced for WV to improve the search effectiveness of the algorithm, performing hired bee searches in these three dimensions. An example of GV combination (CGV), PV combination (CPV), and WV mutation (MWV) is shown below. Figure 4 As shown.

[0087] During the follower bee phase, the follower bee searches near the nectar source based on the nectar source information shared by the hired bee. The VNS method, with its strong search capabilities, allows the hired bee to reliably search within the neighborhood of the nectar source, ensuring that the nectar source moves in a better direction in each iteration. Based on a three-dimensional encoding method, this invention designs eight neighborhood search operators in the follower bee phase. The VNS method uses these eight neighborhood search operators to perform neighborhood searches in three dimensions: PV neighborhood search, GV neighborhood search, and PV neighborhood search. Figure 5 The diagram illustrates eight neighborhood search operators across three dimensions for the VNS. Graphs (a) to (d) show the neighborhood search for the PV, including four types: PV neighborhood structure point exchange, PV neighborhood structure segment exchange, PV neighborhood structure insertion, and PV neighborhood structure flipping. Graphs (e) to (g) show the neighborhood search for the GV, including three types: GV neighborhood structure partial exchange, GV neighborhood structure full exchange, and GV neighborhood structure change. The PV neighborhood structure redistribution process is shown in Figure (h), which allocates a portion of the flexible personnel from one shift to another within feasible limits.

[0088] During the scout bee phase, the scout bee invokes the GRASP algorithm in each iteration to globally search for new nectar sources. If the scout bee discovers a high-quality nectar source, it transforms into a follower bee and continues to mine that source. If a follower bee fails to find a new nectar source after `Limit` consecutive attempts in an iteration, it temporarily transforms into a scout bee to perform a global search, and reverts to a follower bee at the start of the next iteration. If it fails to find a new nectar source after `G_Limit` iterations, it permanently transforms into a scout bee.

[0089] The algorithm finds an optimal non-dominated solution set where no two solutions are better than each other in every objective dimension; this is called the Pareto front. A crowding distance judgment function is used, and the objective values ​​f of the two solutions are shown in the following formula. 1 with f 2 Distance between:

[0090]

[0091] Each newly generated non-dominated solution is compared with the solutions in the current Pareto front to determine whether to include it. If the new non-dominated solution dominates other solutions in the current Pareto front, those solutions are replaced, and the new solution is inserted. If the new non-dominated solution cannot dominate other solutions in the Pareto front and the current Pareto front has reached a specified size, a Pareto front update operation is performed, the calculation steps of which are as follows:

[0092] First, sort each objective in ascending order, calculate the maximum and minimum values ​​of the objective, and normalize each objective dimension, projecting it into the interval (0, 1). Second, calculate the distance between any two solutions using the crowding distance judgment function. Third, sort all solutions according to the crowding distance and remove the solution with the smallest distance from the Pareto front.

[0093] The Gantt chart of a solution obtained by this algorithm for a given example is shown below. Figure 6 As shown. The timeframe for each planned schedule is approximately 13 days, consistent with the shipyard's current two-week rolling schedule. Work groups G1 and G2 belong to the sand work group set G. S Teams G3 to G7 belong to the spray painting team group G. P At the beginning of the first day, the sandblasting team carried out the sandblasting operation first. After a section was sandblasted, the spraying team immediately sprayed the sandblasted section. It can be seen that the same color blocks representing the same section were sprayed right after the sandblasting end time.

[0094] The comparative analysis of this computational example is shown in the table below. This invention compares the IABC algorithm with NSGA-II, SS, and the original ABC algorithm. Numerical experiments were conducted on a total of 15 examples for each algorithm, with each example run 10 times and the average of various evaluation metrics taken. Three metrics were used to evaluate the algorithm results: Mean Ideal Distance (MID), Non-Dominated Solution Dispersion (DNS), and Inverse Generation Distance (IGD). It can be seen that the IABC algorithm consistently outperforms other algorithms in both MID and IGN metrics, indicating that the IABC algorithm has better solution performance.

[0095]

[0096] While the embodiments disclosed in this invention are as described above, the content is merely for the purpose of facilitating understanding of the invention and is not intended to limit the invention. Any person skilled in the art to which this invention pertains may make any modifications and variations in form and detail of the implementation without departing from the spirit and scope disclosed herein; however, the scope of patent protection for this invention shall still be determined by the scope defined in the appended claims.

Claims

1. A low-carbon planning and scheduling method for ship section painting, characterized in that... include: Establish a multi-objective mathematical model for scheduling ship section painting plans, considering maximum completion time, unbalanced workload, and carbon emissions. The planning and scheduling results are represented by a three-dimensional coding method that includes process sequence vectors, shift allocation vectors, and personnel allocation vectors. An improved artificial bee colony algorithm, which combines a hybrid greedy random adaptive search algorithm and a variable neighborhood search algorithm, is used to solve the mathematical model of multi-objective ship section painting schedule, and the final schedule result is obtained. In solving the mathematical model for multi-objective ship section painting schedule, the objectives are to minimize the maximum completion time, minimize the unbalanced workload, and minimize carbon emissions. The constraints of the mathematical model for the multi-objective ship section painting schedule include: Each process can and should be handled by only one work group; The sum of the specific number of workers assigned to each work group is less than the total number of workers; Priority constraints between processes; The preceding and following processes in the same segment must wait at least until the lower limit of the drying time of the preceding process; The start date of a segment and the completion date of the last process must be within the given time window for that segment. In the process sequence vector, each element is a process number, and the position of the element in the process sequence vector indicates the execution order of the corresponding processes; The elements of the work group allocation vector correspond one-to-one with the process sequence vector, and each element represents the work group corresponding to the corresponding process in the process sequence vector. In the personnel allocation vector, each element represents a work group, and the value of the element represents the actual number of workers in the work group.

2. The low-carbon planning and scheduling method for ship section painting according to claim 1, characterized in that: The improved artificial bee colony algorithm includes an initialization phase, a hired bee phase, a follower bee phase, and a scout bee phase.

3. A low-carbon planning and scheduling method for ship section painting according to claim 2, characterized in that, In the initialization phase of the improved artificial bee colony algorithm, a greedy random adaptive search algorithm is used, which specifically includes: First, randomly generate multiple sets of personnel allocation vectors and corresponding process sequence vectors; check each set of vectors, and if they do not meet the constraints, adjust the vectors to meet the constraints. For each set of vectors, one of the three solution objectives is selected. Based on the selected solution objective, a class allocation vector for that set of vectors is constructed using a greedy random adaptive algorithm. If the constructed class allocation vector does not meet the constraints, the class allocation vector is adjusted to meet the constraints, and the corresponding solution is obtained. Finally, each solution is optimized through neighborhood search.

4. A low-carbon planning and scheduling method for ship section painting according to claim 3, characterized in that, In the hired bee phase of the improved artificial bee colony algorithm, a crossover operator between different solutions is used to enhance the diversity of the population search.

5. A low-carbon planning and scheduling method for ship section painting according to claim 2, characterized in that, In the follower bee phase of the improved artificial bee colony algorithm, the VNS method is used for neighborhood search to improve local search capability.

6. A low-carbon planning and scheduling method for ship section painting according to claim 2, characterized in that, In the scout bee phase of the improved artificial bee colony algorithm, a new solution is freely sought through a greedy random adaptive search.

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