Project dynamic multi-objective tradeoff optimization method based on MATLAB

Abstract

The invention discloses a project dynamic multi-objective tradeoff optimization method based on MATLAB, and relates to the technical field of project management, and the method comprises the following steps: firstly, setting a plurality of project constraint conditions, arranging and inputting initialization parameters, adjusting the weight and introducing disturbance according to needs, respectively calling NSGA-II and MOEA / D global search, obtaining a next-generation elite solution set, and carrying out the global search of the next-generation elite solution set; the method aims at optimal balance of project construction period-efficiency-cost, construction period fluctuation constraint conditions, quality assurance constraint conditions, process fluctuation constraint conditions and other constraint conditions, a non-dominated sorting genetic algorithm II (NSGA-II) and a decomposition-based multi-objective evolutionary algorithm (MOEA / D) are used as contrasts, and then PS local search is called in a next-generation elite solution set. The method comprises the following steps of: constructing a project dynamic multi-target tradeoff algorithm, performing mixed application with a pattern Search (PS) algorithm, performing optimization in combination with a pattern search enhancement technology and a multi-stage optimization strategy, and constructing the project dynamic multi-target tradeoff algorithm to ensure the feasibility and practicability of project management.

Description

Technical Field

[0001] The invention relates to the technical field of project management, and in particular to a project dynamic multi-objective trade-off optimization method based on MATLAB. Background Art

[0002] With the increasingly significant development trend of scale and diversification in the construction industry, especially the increasingly widespread application of new construction technologies and materials, the frequency and probability of dynamic changes in the project environment have increased significantly, and there is an urgent need to improve the control ability and response speed of project management in dynamic changes.

[0003] Project management is a process to ensure that projects are completed with high quality within the scheduled time and budget. It involves a series of means such as planning, organization, leadership and control to coordinate related activities. Although the existing research in the field of project management has achieved remarkable results, with the increasing precision requirements and uncertainty of project management, the following key issues are still facing urgent solutions: 1. Intensified changes in project environment: Risk factors such as social events, systemic disruptions and fluctuations in raw material prices have significantly increased the frequency and probability of changes in project environment, requiring project managers to have the ability to respond quickly. Traditional management methods can no longer meet current needs in terms of decision-making efficiency; 2. Rapid changes in project scenarios and requirements: With the continuous advancement of technology and the rapid changes in market demand, many innovative project management technologies and tools are out of touch with theory and practice, and cannot adapt and self-adjust according to the scenarios and requirements of actual projects. In addition, in actual applications, complex optimization models are limited in data acquisition and computing resources, which seriously affects their practicality; 3. Scattered and redundant project information: The project information lacks a unified integrated platform and smooth information communication channels, resulting in untimely information updates and low collaboration efficiency; In order to effectively solve the key problems in the above-mentioned project management, the present invention provides a project dynamic multi-objective trade-off optimization method based on MATLAB. Summary of the invention

[0004] The purpose of the present invention is to provide a project dynamic multi-objective trade-off optimization method based on MATLAB to solve the problems raised in the above background technology.

[0005] To achieve the above object, the present invention provides the following technical solution: a project dynamic multi-objective trade-off optimization method based on MATLAB, comprising the following steps: S1. In construction project management, multiple project constraints are set, which mainly include: stage efficiency constraints, construction period fluctuation constraints, quality assurance constraints and process fluctuation constraints: S2, sort and input initialization parameters, adjust weights and introduce perturbations as needed; S3, call NSGA-II and MOEA / D global search respectively to obtain the next generation elite solution set; S4, calling PS local search in the next generation elite solution set to obtain the optimal solution; S5. Perform multi-stage optimization on the next generation elite solution set, each stage including adaptive perturbation, pattern search optimization, local search strategy and random perturbation, and gradually refine the search scope.

[0006] Preferably, the stage efficiency constraint condition is: the project stage efficiency is divided into three levels: high, medium and low, and different compression and extension ratios are set: The lower limit of high efficiency process (ie efficiency>100): ; Upper limit: ; In the formula, i_di is the duration vector of the stage process, lb and ub represent the lower limit and upper limit of the stage duration respectively, 0.9 and 1.1 represent the lower limit and upper limit boundary multiples of the stage duration i_di allowed to change respectively, which are adjusted according to the actual situation of the project, and the medium efficiency and low efficiency processes are set in the same way; For medium efficiency processes (50<efficiency≦100), the lower limit compression ratio is 0.85 and the upper limit extension ratio is 1.15; The lower limit compression ratio of low-efficiency processes (efficiency ≦50) is 0.8, and the upper limit extension ratio is 1.2.

[0007] Preferably, the construction period fluctuation constraint condition is set as: ; In the formula, Var represents the variance, which is a preset small constant.

[0008] Preferably, the quality assurance constraint condition is used to avoid excessive compression of the construction period resulting in a decrease in project quality, and an excessive compression penalty condition is set to ensure project quality. The excessive compression penalty condition is: ; In the formula, k1 is the penalty coefficient, i_d i is the duration vector of the phase process.

[0009] Preferably, the process fluctuation constraint condition is used to keep the duration change between adjacent stages smooth and avoid frequent changes in resource scheduling. A continuous process fluctuation penalty condition is set to constrain process fluctuations. The continuous process fluctuation penalty condition is: ; In the formula, k2 is the penalty coefficient, i_d i is the duration vector of the phase process.

[0010] Preferably, the process fluctuation constraint condition further sets an efficiency loss penalty condition, and the efficiency loss penalty condition is: ; In the formula, k3 is the penalty coefficient, i_d i is the duration vector of the phase process.

[0011] Preferably, the adaptive perturbation dynamically adjusts the perturbation amplitude according to the number s of the current stage, and the solution x after the perturbation perturbed It is expressed as: ; In the formula, r is a start Random vectors of the same dimension, ⊙ represents element-by-element multiplication, x start is the initial solution.

[0012] Preferably, the pattern search optimization uses a pattern search algorithm to optimize the perturbed solution, and the optimized solution x ps It is expressed as: ; In the formula, lb and ub represent the lower and upper limits of the stage duration, respectively, and x perturbed is the solution after perturbation.

[0013] Preferably, the local search strategy is used to further improve the quality of the solution, and the improved solution xi is expressed as: ; In the formula, lb and ub represent the lower and upper limits of the phase duration, respectively, i_d i is the duration vector of the phase process.

[0014] Preferably, the random perturbation is added at the end of the local search strategy periodically, and the random perturbation is used to avoid falling into the local optimum. The solution x after the random perturbation η is rp It is expressed as: ; In the formula, x start为 The initial solution, ⊙ represents element-by-element multiplication, r is a start Random vector of the same dimension.

[0015] The impact assessment of process duration changes on efficiency is introduced and incorporated into the optimization target. The efficiency impact assessment is expressed by the following formula: ; Where wi is the weight of the i-th project stage, and ei is the efficiency of the i-th project stage.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention sets a series of constraints such as stage efficiency constraints, duration fluctuation constraints, quality assurance constraints, and process fluctuation constraints, so as to balance the efficiency of each stage in the project, limit duration fluctuations, avoid quality degradation caused by excessive compression, and maintain the smoothness of duration changes in adjacent stages, so that the algorithm can achieve the optimal balance of project duration-efficiency-cost, while ensuring the feasibility and practicality of project management; 2. The present invention cleverly integrates NSGA-Ⅱ, MOEA / D and PS algorithms, and optimizes by combining pattern search enhancement technology and multi-stage optimization strategy to construct a dynamic multi-objective trade-off algorithm for the project, thereby achieving the optimal balance among project duration, cost and efficiency. This method effectively improves the optimization quality and efficiency, has significant economic benefits, and at the same time ensures the rationality of the optimization range and the feasibility of the optimization scheme. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is the algorithm process diagram of the present invention; Figure 2 A first result diagram of running the program code of the present invention; Figure 3 This is a second result diagram of the program code of the present invention. DETAILED DESCRIPTION

[0018] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] See also Figures 1 to 3 , the present invention provides a technical solution: A project dynamic multi-objective trade-off optimization method based on MATLAB, comprising the following steps: S1. In construction project management, multiple project constraints are set, wherein the project constraints mainly include: stage efficiency constraints, construction period fluctuation constraints, quality assurance constraints, and process fluctuation constraints; The construction projects mainly include: anti-pullout pile construction, foundation construction, cushion construction, raft waterproofing layer construction, raft construction, installation and embedding, negative three-story floor and column wall construction and installation and embedding, negative two-story floor and column wall construction and installation and embedding, negative one-story floor and column wall construction and installation and embedding, 1st-3rd floor slab and column wall construction and installation and embedding, 4th-Rth floor slab and column wall construction and installation and embedding, structure layer construction and installation and embedding, roofing construction and installation and embedding, installation of secondary piping, water and electricity installation, fire protection installation, secondary structure construction and elevator installation: S2, sort and input initialization parameters, adjust weights and introduce perturbations as needed; The input initialization parameters include: the initial total construction period is 353 days, the initial original cost is 140 million yuan, the delay penalty cost is 150,000 yuan, the early incentive fee is 100,000 yuan, the basic daily cost is 100,000 yuan, and the overtime cost is 15,000 yuan; the initial parameters of the above construction project are as follows:

[0020] The parameter structure code is as follows:

[0021] S3, call NSGA-II and MOEA / D global search respectively to obtain the next generation elite solution set; S4, calling PS local search in the next generation elite solution set to obtain the optimal solution; S5. Perform multi-stage optimization on the next generation elite solution set, each stage including adaptive perturbation, pattern search optimization, local search strategy and random perturbation, and gradually refine the search scope.

[0022] The corresponding codes of steps S3 and S4 are as follows:

[0023] In this scheme, PS is a non-gradient optimization method, which is suitable for optimization problems with non-differentiable or non-continuous objective functions. It gradually approaches the optimal solution by adjusting the grid step size, and is good at finding the local optimal solution near the initial solution; NSGA-II and MOEA / D are global search algorithms, which are good at locating the global optimal solution; among them, NSGA-II can find uniformly distributed Pareto front solutions through fast non-dominated sorting and crowding comparison, which is suitable for dealing with multi-objective problems with complex Pareto fronts; and MOEA / D is based on the idea of ​​decomposition, and guides the search by adjusting the weights of sub-problems, which is suitable for high-dimensional problems and problems with complex objective structures. In terms of computational efficiency, PS has significant advantages in dealing with complex problems, while NSGA-II and MOEA / D are less efficient than PS in dealing with certain specific types of problems. When used in combination, PS can be used as an efficient local search tool to further optimize the solution of NSGA-II or MOEA / D. In terms of robustness, the PS algorithm has less dependence on the initial solution. However, NSGA-II and MOEA / D may be affected by the initial population in some cases, resulting in unstable solution quality. Combining the global search capability of NSGA-II or MOEA / D with the local search capability of PS can enhance the robustness of the hybrid algorithm. In terms of algorithm implementation, the PS algorithm has a small amount of code, while the implementation complexity of NSGA-II and MOEA / D is slightly higher. Combining PS with NSGA-II or MOEA / D can facilitate the integration of hybrid models.

[0024] In summary, the hybrid algorithm combines the advantages of global search and local search, can quickly locate potential optimal solutions and optimize the quality of solutions, and is suitable for complex and changeable optimization problems to improve the scientific nature of the results.

[0025] Example 1 Considering the potential for stage efficiency adjustment, the stage efficiency constraints are set as follows: the project stage efficiency is divided into three levels: high, medium and low, and different compression and extension ratios are set: The lower limit of high efficiency process (ie efficiency>100): ; Upper limit: ; In the formula, i_d iis the duration vector of the stage process, lb and ub represent the lower and upper limits of the stage duration respectively, 0.9 and 1.1 represent the lower and upper boundary multiples of the stage duration i_di allowed to change respectively, which are adjusted according to the actual situation of the project, and the medium efficiency and low efficiency processes are set in the same way. The lower limit compression ratio of the medium efficiency process (50<efficiency≦100) is 0.85, and the upper limit extension ratio is 1.15; the lower limit compression ratio of the low efficiency process (efficiency≦50) is 0.8, and the upper limit extension ratio is 1.2; Part of the code for setting stage efficiency constraints is as follows:

[0026] In order to maintain the stability of resource allocation and the continuity of the project and avoid the instability of resource allocation, the duration fluctuation constraint is set as follows: ; In the formula, Var represents variance, is a preset small constant, i_d i is the duration vector of the phase process, In order to avoid the quality degradation of the project due to excessive compression of the construction period, it is necessary to set quality assurance constraints. Setting excessive compression penalty conditions can be used to ensure project quality. The excessive compression penalty conditions are set as follows: ; In the formula, k1 is the penalty coefficient, i_d i is the duration vector of the phase process; Some of the code for setting the over-compression penalty condition is as follows:

[0027] In order to keep the duration changes between adjacent stages smooth and avoid frequent changes in resource scheduling, it is necessary to set process fluctuation constraints. Continuous process fluctuation penalty conditions can be set to achieve the purpose of constraining process fluctuations: ; In the formula, k2 is the penalty coefficient, i_d i is the duration vector of the phase process, Part of the code for setting the penalty conditions for continuous process fluctuations is as follows:

[0028] In order to fit the actual project influencing factors, the process fluctuation constraint condition also sets the efficiency loss penalty condition, which is: ; In the formula, k3 is the penalty coefficient, i_d i is the duration vector of the phase process, Some of the codes for setting the efficiency loss penalty conditions are as follows:

[0029] In this embodiment, by setting project constraints, the algorithm can achieve the optimal balance of project duration-efficiency-cost, while ensuring the feasibility and practicality of project management. This method can balance the efficiency of each stage of the project, limit duration fluctuations, avoid quality degradation caused by excessive compression, and maintain the smoothness of duration changes in adjacent stages by setting a series of project constraints such as stage efficiency constraints, duration fluctuation constraints, quality assurance constraints, and process fluctuation constraints.

[0030] Example 2 Adaptive perturbation dynamically adjusts the perturbation amplitude according to the number s of the current stage, thereby increasing the diversity of solutions. The perturbed solution x perturbed It can be expressed as: ; In the formula, r is a start Random vectors of the same dimension, ⊙ represents element-by-element multiplication, x start is the initial solution.

[0031] The following is some code to set up adaptive perturbations:

[0032] Pattern search optimization uses the pattern search algorithm to optimize the perturbed solution. The optimized solution x ps It is expressed as: ; In the formula, lb and ub represent the lower and upper limits of the stage duration, respectively, and x perturbed is the solution after perturbation.

[0033] The quality of the solution is further improved by the local search strategy. i It is expressed as: ; In the formula, lb and ub represent the lower and upper limits of the phase duration, respectively, i_d i is the duration vector of the phase process.

[0034] Part of the code for the local search strategy is as follows:

[0035] At the end of the stage, random perturbations are added to avoid falling into the local optimum. The solution x after random perturbations is rp It is expressed as: ; In the formula, x start为 The initial solution, ⊙ represents element-by-element multiplication, r is a start Random vector of the same dimension.

[0036] The following is the partial code for adding random perturbations:

[0037] The impact of process duration changes on efficiency is introduced and incorporated into the optimization goal. The efficiency impact evaluation can be expressed by the following formula: ; In the formula, w i is the weight of the i-th project stage, e i is the efficiency of the i-th project stage.

[0038] In this embodiment, NSGA-II and MOEA / D algorithms are utilized, and the NSGA-II-PS and MOEA / D-PS algorithms are hybrid optimized by combining pattern search enhancement technology and multi-stage optimization strategy to enhance project management flexibility and response speed and better cope with environmental changes. In the design and optimization of NSGA-II-PS and MOEA / D-PS algorithms, enhanced pattern search is designed to improve the search efficiency and robustness of PS, and an innovative multi-stage adaptive search strategy including adaptive perturbation, pattern search optimization, local search strategy and random perturbation is proposed, thereby enhancing the effect of local search.

[0039] The present invention comprehensively considers the complex relationship between processes and the potential impact of schedule adjustment on efficiency as well as various practical constraints, cleverly integrates NSGA-Ⅱ, MOEA / D and PS algorithms, and optimizes by combining pattern search enhancement technology and multi-stage optimization strategy to build a dynamic multi-objective trade-off algorithm for the project, achieving the optimal balance of project schedule, cost and efficiency. The algorithm effectively improves the optimization quality and efficiency, has significant economic benefits, and ensures the rationality of the optimization range and the feasibility of the optimization scheme.

[0040] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A project dynamic multi-objective trade-off optimization method based on MATLAB, characterized in that: The following steps are involved: S1. In project management, multiple project constraints are set, which mainly include: stage efficiency constraints, construction period fluctuation constraints, quality assurance constraints and process fluctuation constraints: S2, sort and input initialization parameters, adjust weights and introduce perturbations as needed; S3, call NSGA-II and MOEA / D global search respectively to obtain the next generation elite solution set; S4, calling PS local search in the next generation elite solution set to obtain the optimal solution; S5. Perform multi-stage optimization on the next generation elite solution set, each stage including adaptive perturbation, pattern search optimization, local search strategy and random perturbation, and gradually refine the search scope.

2. A project dynamic multi-objective trade-off optimization method based on MATLAB according to claim 1, characterized in that: The stage efficiency constraint condition is: the project stage efficiency is divided into three levels: high, medium and low, and different compression and extension ratios are set: High efficiency process lower limit: ； Upper limit: ； In the formula, i_di is the stage duration, lb and ub represent the lower limit and upper limit of the stage duration respectively, and 0.9 and 1.1 represent the lower limit and upper limit boundary multiples of the allowable variation of the stage duration i_di respectively.

3. The project dynamic multi-objective trade-off optimization method based on MATLAB according to claim 1 is characterized in that: The construction period fluctuation constraint condition is set as: ； In the formula, Var represents variance, is a preset small constant, i_d i is the duration vector of the phase process.

4. The project dynamic multi-objective trade-off optimization method based on MATLAB according to claim 1 is characterized in that: The quality assurance constraint condition is used to avoid excessive compression of the construction period resulting in a decrease in project quality. The excessive compression penalty condition is set to ensure project quality. for: ； In the formula, k1 is the penalty coefficient, i_d i is the duration vector of the phase process.

5. The project dynamic multi-objective trade-off optimization method based on MATLAB according to claim 1 is characterized in that: The process fluctuation constraint condition is used to keep the duration change between adjacent stages smooth and avoid frequent changes in resource scheduling. The continuous process fluctuation penalty condition is set to constrain the process fluctuation. for: ； In the formula, k2 is the penalty coefficient, i_d i is the duration vector of the phase process.

6. A project dynamic multi-objective trade-off optimization method based on MATLAB according to claim 5, characterized in that: The process fluctuation constraint condition also sets an efficiency loss penalty condition, and the efficiency loss penalty condition for: ； In the formula, k3 is the penalty coefficient, i_d i is the duration vector of the phase process.

7. The project dynamic multi-objective trade-off optimization method based on MATLAB according to claim 1 is characterized in that: The adaptive perturbation dynamically adjusts the amplitude of the perturbation according to the number s of the current stage, and the solution x after the perturbation perturbed It is expressed as: ； In the formula, r is a start Random vectors of the same dimension, ⊙ represents element-by-element multiplication, x start is the initial solution.

8. The project dynamic multi-objective trade-off optimization method based on MATLAB according to claim 7 is characterized in that: The pattern search optimization uses a pattern search algorithm to optimize the perturbed solution. The optimized solution x ps It is expressed as: ； In the formula, lb and ub represent the lower and upper limits of the stage duration, respectively, and x perturbed is the solution after perturbation.

9. A MATLAB-based project dynamic multi-objective trade-off optimization method according to claim 8, characterized in that: The local search strategy is used to further improve the quality of the solution. The improved solution xi is expressed as: ； In the formula, lb and ub represent the lower and upper limits of the stage duration respectively, i_d i is the duration vector of the phase process.

10. A MATLAB-based project dynamic multi-objective trade-off optimization method according to claim 9, characterized in that: The random perturbation is added at the end of the local search strategy periodically. The random perturbation is used to avoid falling into the local optimum. The solution x after the random perturbation η rp It is expressed as: ； In the formula, x start为 The initial solution, ⊙ represents element-by-element multiplication, r is a start Random vectors of the same dimension; The impact assessment of process duration changes on efficiency is introduced and incorporated into the optimization target. The efficiency impact assessment is expressed by the following formula: ； Where wi is the weight of the i-th project stage, and ei is the efficiency of the i-th project stage.

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