Multi-target traffic network optimization method based on adaptive constraint relaxation strategy

Abstract

The invention discloses a multi-target traffic network optimization method based on an adaptive constraint relaxation strategy. The method comprises the following steps: inputting a plurality of targets of traffic network optimization; initializing a convergence file and a guide file; performing population initialization; iterating: selecting a parent from the convergence file by using a tournament selection mechanism; performing variation on the selected parent by simulating binary crossover and polynomial variation to generate offspring; updating the archive by using a self-adaptive constraint relaxation method, and updating the convergence archive through a local convergence index and diversity comprehensive selection method; and after iteration is finished, outputting an optimized traffic network optimization solution. Through the ACR method, the adaptability of constraint processing is enhanced, and dynamic balance between exploration and utilization is achieved; a diversity comprehensive selection mechanism is introduced, the diversity of solutions is kept, and thorough exploration and robust convergence are ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of traffic network optimization, and particularly relates to a multi-objective traffic network optimization method based on an adaptive constraint relaxation strategy. Background Art

[0002] Constrained multi-objective optimization problems (CMOPs) exist in the field of traffic network optimization, where multiple conflicting objectives and constraints need to be considered simultaneously. The main conflicting objectives include: minimizing travel time vs. reducing operating costs, maximizing traffic efficiency vs. ensuring fairness, infrastructure investment vs. environmental protection, real-time response to dynamic demands vs. system stability, etc. The core constraint conditions include road capacity and flow limitations, budget and resource limitations, user demand volatility, etc. The traffic demand varies significantly between peak and off-peak hours, and the optimization model needs to take into account the dynamic adjustment ability, such as coping with demand uncertainty through robust optimization.

[0003] Due to the existence of multiple objective functions and a large number of constraints, these problems are inherently complex. Effectively solving these problems is crucial for finding solutions that are not only optimal but also feasible in real-world scenarios.

[0004] In recent years, significant progress has been made in developing algorithms for solving CMOPs. A popular approach in the evolutionary computation (EC) community is to utilize a co-evolutionary framework that combines an auxiliary archive to help quickly identify solutions on the unconstrained Pareto front, thus keeping the evolutionary process away from local optima. However, these auxiliary archives traditionally do not consider constraints but focus on the unconstrained Pareto front (UPF) to guide the evolutionary process. This strategy has been proven effective in dealing with some benchmark problems. However, since the auxiliary archives do not consider constraints, these methods may lead to unnecessary waste of computational resources.

[0005] In addition, there is a significant gap in the existing research in addressing the balance between solution diversity and convergence. Although these archives help quickly identify potential solutions, they often pay little attention to solution diversity in the decision space, resulting in a poor solution distribution, especially when facing problems characterized by a discontinuous Pareto front (PF). Moreover, the reliance on these auxiliary archives may inadvertently overlook solutions residing on the constrained Pareto front (CPF), not only spreading incorrect information but also wasting valuable computational resources. Summary of the Invention

[0006] The necessity of balancing these two conflicting objectives (convergence and diversity) constitutes the key of this application. This application uses a nuanced approach that takes into account the randomness of constraints and promotes adaptive local convergence to overcome the drawbacks found in current state-of-the-art algorithms. When there are multiple separated feasible regions, most of the previous constrained multi-objective algorithms (CMOEA) have difficulty obtaining the entire PF because of the lack of population diversity in the decision space. On the other hand, many algorithms tend to introduce leading archives. In the final stage, such as when population 2 is far from the true CPF. In this case, population 2 will cause a waste of computing resources and even provide incorrect information.

[0007] To address these deficiencies and promote a harmonious balance between solution diversity and convergence, thereby improving the effectiveness and efficiency of the optimization process, this application fully considers the nuances related to CMOP, integrates innovative strategies to more subtly guide the evolutionary process towards the optimal solution, while ensuring a robust representation of the solution space.

[0008] To achieve the above object, the multi-objective traffic network optimization method based on the adaptive constraint relaxation strategy disclosed in this application includes the following steps: Input multiple objectives for traffic network optimization; Initialize the convergence archive and the guiding archive ; The convergence archive and the guiding archive are used as repositories for solutions, with the former focusing on convergence and the latter on diversity; calculate the fitness of the solutions in the convergence archive to guide the selection process, ensuring that solutions with higher convergence potential are given priority; Population initialization; Perform iterations: select parents from the convergence archive using the tournament selection mechanism; the selected parents are mutated through simulated binary crossover and polynomial mutation to generate offspring; update the archives using the adaptive constraint relaxation method, that is, in the early generations, explore various solutions without considering constraints, and use the multi-objective evolutionary algorithm to update the guiding archive to quickly search for the Pareto front; in the later generations, use the adaptive constraint relaxation method to converge, aiming to improve the utilization rate of function evaluations; at the same time, the convergence archive is updated through the local convergence index and the diversity comprehensive selection method; After the iteration ends, output the optimized traffic network optimization solution.

[0009] Furthermore, the use of the adaptive constraint relaxation method to converge includes: determining whether to consider constraints ; The computing expression of the constraint is: ; ; ; where and represent the average distance between solutions in the convergence archive and the distance between the guiding archive and the convergence archive; indicates that the distance between two archives is less than a preset threshold, are the i-th and j-th solutions in the convergence archive respectively, is is the Euclidean distance of, is the solution in.

[0010] Furthermore, the multi-objective evolutionary algorithm at least includes one of a feasibility-driven multi-objective evolutionary algorithm, an objective and feasibility balanced multi-objective evolutionary algorithm, an evolutionary operator modified multi-objective evolutionary algorithm, and a multi-objective evolutionary algorithm based on a hybrid strategy; the early stage is the stage where the number of iterations is less than or equal to half of the maximum number of iterations.

[0011] Furthermore, the local convergence index is expressed as follows: ; ; ; ; ; represents the neighborhood solution set of; and are the local domination relationship and the constraint domination relationship respectively, is the local domination strength, are the constraint violation degrees of the i-th and j-th solutions respectively.

[0012] Furthermore, the diversity comprehensive selection process includes: After obtaining the local optimal solution through the local convergence index, truncate the population size to ; Calculate using the crowding distance-based method: ; where represents the Euclidean distance between solutions and ; When the number of remaining solutions is greater than , the largest solution will be discarded; this process is iteratively executed until the population size is equal to .

[0013] The beneficial effects of this application include: Develop the ACR method to enhance the adaptability of constraint handling and achieve a dynamic balance between exploration and exploitation; Introduce a diversity comprehensive selection mechanism to maintain the diversity of solutions and ensure thorough exploration and robust convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 The pseudocode of the method of this application.

[0015] Figure 2 The method flowchart of this application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0016] The present invention will be further described below with reference to the accompanying drawings, but the present invention is not limited in any way. Any transformation or replacement based on the teachings of the present invention falls within the protection scope of the present invention.

[0017] Constrained multi-objective evolutionary algorithms (CMOEA) play a key role in solving complex optimization problems, as these optimization problems require balancing multiple objectives and constraints. These algorithms are essential in fields such as engineering, economics, and environmental science, as solutions in these fields must be both optimal and feasible. However, existing CMOEA often struggle to maintain a balance between convergence and diversity, especially when faced with complex constraints and discontinuous feasible regions. This imbalance can lead to suboptimal solutions and inefficient resource utilization.

[0018] To address these challenges, this application introduces the Adaptive Constraint Relaxation (ACR) method, which dynamically adjusts constraint handling based on the evolutionary state. This adaptability enables this application to effectively navigate the search space and balance the requirements of early exploration and late exploitation. By doing so, this application effectively avoids common pitfalls such as premature convergence and local optima. In addition, this application employs a diversity comprehensive selection mechanism that uses local convergence metrics to maintain a diverse set of solutions. This mechanism ensures that the algorithm thoroughly explores the solution space, prevents it from getting stuck in narrow regions, and promotes a well-distributed Pareto front.

[0019] Before introducing the embodiments of this application, some terms related to this application will be explained.

[0020] 1. Minimizing the CMOP can be formulated as follows: ; where is the decision space The decision vector in is the target vector. and are the lower bound and the upper bound respectively. and respectively are the th inequality and equality constraints, and their numbers are and respectively. The constraint violation for the th constraint is usually calculated as follows: ; The overall constraint violation is defined as ; The constrained multi-objective optimization problem includes the unconstrained Pareto front (UPF) and the constrained Pareto front (CPF). There are two disconnected CPFs, and solution A is non-dominated for both the CPF and the UPF.

[0021] Given a decision variable vector (i.e., a solution), it is only feasible when the overall constraint violation is zero. For two feasible solutions, and , if for and for, then it is said to dominate . When no other feasible solution dominates this solution, this solution is called Pareto optimal. All Pareto optimal solutions in the decision space constitute the Pareto optimal set.

[0022] The image of all Pareto optimal solutions in the objective space is the Pareto front (PF). For distinction, the constrained PF (CPF) and the unconstrained PF (UPF) are usually used to represent the PF of the constrained and unconstrained multi-objective optimization problems. When solving the CMOP, the goal is to approximate the PF with a set of well-converged and well-distributed feasible solutions.

[0023] The pseudo-code of the algorithm provided in this application refers to Figure 1 . Referring to Figure 2 , the structure of the framework of this application is the same as that of a typical EA, including population initialization, offspring generation, and environmental selection. There are two main differences: this application uses two archives for co-evolution and is divided into two stages. The framework starts with initializing two key archives: the convergence archive ( ) and the guiding archive ( ) These archives serve as repositories for solutions, with the former focusing on convergence and the latter on diversity. The fitness of solutions in the convergence archive is calculated to guide the selection process, ensuring that solutions with higher convergence potential are prioritized.

[0024] The algorithm proceeds iteratively, using a tournament selection mechanism to select parents from the convergence archive. The selected parents are mutated through simulated binary crossover (SBX) and polynomial mutation (PM) to generate offspring. The framework is divided into two distinct phases: in the early generations ( ), the guiding archive is updated using a normal MOEA. This phase emphasizes exploring various solutions without considering constraints in order to quickly search the Pareto front. In the later generations, the focus shifts to using an adaptive constraint relaxation method for convergence, aiming to improve the utilization of function evaluations.

[0025] Homologously, the convergence archive is updated through local convergence metrics and diversity-based environmental selection methods. This ensures that the final solutions are not only convergent but also diverse, thus addressing the dual objectives of the optimization process. By carefully balancing exploration and exploitation in these two phases, this application effectively navigates the complex landscape of CMOP, providing a powerful and adaptive method that can improve the quality and diversity of the obtained solutions.

[0026] In one embodiment, the solution update in the guiding archive - the adaptive constraint relaxation method includes: Using an auxiliary archive that does not consider constraints can effectively help cross infeasible regions, thereby improving the search ability of CMOEA. However, in the later stage of evolution, once the UPF is different from the CPF, the information from these auxiliary archives will not only mislead the algorithm but also waste computational budget. To address this issue, this application proposes an adaptive constraint relaxation (ACR) method. The main idea of ACR is to control whether the leading archive considers constraints by evaluating the current evolutionary state.

[0027] Specifically, in the first phase, the leading archive helps the algorithm converge to the true Pareto front without considering constraints. When the evolution enters the second phase, the algorithm will decide whether to consider constraints based on the value of. Specifically, the calculation expression of is: ; ; ; where and represent the average distance between solutions in the convergence archive and the distance between the guiding file and the converging file. Indicates that the distance between the two files is less than a given threshold. In this case, more exploration is needed, so the guiding file will not consider the constraints. Instead, the guiding file is far from the converging file, and the constraints should be considered to avoid wasting computing resources.

[0028] ACR can dynamically adjust constraint handling according to the evolutionary state. In the initial stage, it relaxes the constraints to enhance the exploration ability, enabling the algorithm to traverse infeasible regions that may contain promising solutions. By dynamically shifting the focus, ACR helps to efficiently explore the search space and converge towards the feasible region as the process progresses. This ensures that the search remains adaptive and responsive to the problem environment. Additionally, ACR optimizes the use of computing resources by adaptively guiding the efforts at different stages of the search, thereby improving the overall algorithm efficiency.

[0029] Here, the key role played by the converging file in ACREA is discussed. This file is a repository of solutions that have demonstrated good convergence characteristics. This application analyzes the solution update mechanism in this file, highlighting the strategies implemented to maintain a harmonious balance between convergence and diversity.

[0030] Within the scope of the converging file, the local convergence metric is an important tool for guiding the evolutionary process. In this section, the function of this metric will be explored in depth, showing how it helps to guide the solution search towards the optimal front while avoiding local optima.

[0031] In one embodiment, the method for selecting based on the local convergence metric in the converging file includes: The local convergence metric proposed for multi-modal multi-objective optimization problems can effectively enhance the population diversity in the decision space. However, since it is proposed for unconstrained problems, directly applying the local convergence metric to constrained optimization problems has serious problems. For unconstrained problems and local optimal solutions , the solution is the current non-dominated solution. In this case, performing environmental selection using the local convergence metric will save the solution . However, for constrained optimization problems, the solution will not be considered because it is infeasible.

[0032] To avoid this problem, both global constraint violation and local dominance information should be considered. Specifically, the comparison of constraint violations should be considered globally, while the convergence information should be considered locally, such as the normal definition of the local convergence metric. Based on this motivation, in one embodiment, this application proposes a new CMOP local convergence metric, which can be expressed as follows: ; ; ; ; ; Specifically, represents the neighborhood solution set; and are the local domination relationship and the constraint domination relationship respectively. can be regarded as the local domination strength.

[0033] By adopting an improved local convergence index, the present application can select potential feasible optimal solutions. For solutions , and , only and can survive because is infeasible. For solutions , and , only can be retained according to the local convergence index. It can be seen that solution has no neighbors. Then, if the original local convergence index is used, solution is the local optimal solution and thus can survive. However, since is infeasible and non-dominant for the non-constrained problem, it will release incorrect information to mislead the evolution. By adopting a novel local convergence index, will not be able to survive because it is constraint-dominated by other solutions.

[0034] The diversity comprehensive mating selection process is a key step in the present application, which helps to generate offspring with good diversity properties, thus ensuring rich diversity in the solution space, promoting broader exploration and more powerful representation of potential solutions.

[0035] After obtaining the local optimal solution through the local convergence index, the population size needs to be truncated to . The method based on crowding distance is adopted: ; where represents the Euclidean distance between solutions and .

[0036] Specifically, when the number of remaining solutions is greater than , the solutions with the largest will be discarded. This process will be iteratively executed until the population size is equal to 。

[0037] In the experiments of this application, the population size of the algorithm is set to 100, and the maximum number of function evaluations is set to . All experiments are run on PlatEMO, with the PC being an AMD R9-5900X @ 3.70 GHz and 64G RAM.

[0038] The Inverted Generational Distance (IGD) is chosen to evaluate the performance of the algorithm. Specifically, given a set of points uniformly sampled along the PF and a set of feasible objective vectors obtained by CMOEA, the IGD value is calculated as follows: ; where is the Euclidean distance between and

[0039] Note that for CMOEA, a smaller IGD value is required. It should be noted that only feasible solutions can be used to calculate the IGD value.

[0040] In one embodiment, the multi-objective evolutionary algorithm includes at least one of a feasibility-driven multi-objective evolutionary algorithm, an objective and feasibility balanced multi-objective evolutionary algorithm, an evolutionary operator modified multi-objective evolutionary algorithm, and a hybrid-strategy-based multi-objective evolutionary algorithm.

[0041] Feasibility-driven CMOEAs usually prioritize feasible solutions over infeasible solutions and mainly utilize feasibility information during the evolutionary search process. Overall, although feasibility-driven CMOEAs can effectively ensure the feasibility of solutions, their exploration ability may be limited and they may perform poorly on complex or highly constrained problems.

[0042] Objective and feasibility balanced CMOEAs advocate maintaining a dynamic balance between objectives and constraints, being biased towards optimizing objectives in the initial stage and turning to optimizing constraints later, and can dynamically adjust the focus between objectives and constraints, thus achieving a more balanced search process. However, their complexity and resource requirements may be limiting factors and it may be difficult to find the best balance between feasibility and objective improvement, especially in highly complex problems.

[0043] The evolutionary operator modified CMOEA focuses on the design of evolutionary operators, effectively navigating complex environments through customized operators to enhance exploration and convergence. This approach typically leads to higher-quality solutions. However, the increased complexity and the need for problem-specific customization may increase computational costs and limit general applicability.

[0044] The CMOEA based on hybrid strategies employs multiple constraint handling techniques (CHT). The hybrid strategy can be embodied in different stages of the algorithm, across different populations, or in response to different tasks.

[0045] The above multi-objective evolutionary algorithms are prior arts in this field and will not be elaborated in this application.

[0046] In summary, the above embodiments are one implementation manner of the present invention, but the implementation manners of the present invention are not limited by the said embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made under the premise of departing from the spirit and principle of the present invention shall be equivalent replacement manners and are all included in the protection scope of the present invention.

Claims

1. A multi-objective traffic network optimization method based on an adaptive constraint relaxation strategy, characterized in that Including the following steps: Input multiple objectives for traffic network optimization; Initialize the convergence archive and the guide archive ; The convergence archive and the guide archive are used as repositories for solutions, with the former focusing on convergence and the latter on diversity; Calculate the fitness of solutions in the convergence archive to guide the selection process, ensuring that solutions with higher convergence potential are given priority; Population initialization; Perform iterations: Select parents from the convergence archive using the tournament selection mechanism; The selected parents are mutated through simulated binary crossover and polynomial mutation to generate offspring; Update the archive using the adaptive constraint relaxation method, that is, in the early generations, explore various solutions without considering constraints, and use the multi-objective evolutionary algorithm to update the guiding archive for a quick search of the Pareto front; In the later generations, use the adaptive constraint relaxation method to converge, aiming to improve the utilization rate of function evaluations; At the same time, the convergence archive is updated through the local convergence index and the diversity comprehensive selection method; After the iterations end, output the optimized traffic network optimization solution.

2. The multi-objective traffic network optimization method based on an adaptive constraint relaxation strategy according to claim 1, wherein The use of the adaptive constraint relaxation method for convergence includes: determining whether to consider constraints ; the constraint has a calculation expression as follows: ； ； ； where and represent the average distance between solutions in the convergence archive and the distance between the guiding archive and the convergence archive; indicates that the distance between the two archives is less than a preset threshold, are the i-th and j-th solutions in the convergence archive respectively, is the Euclidean distance of and is the solution in the guiding archive.

3. The multi-objective traffic network optimization method based on an adaptive constraint relaxation strategy according to claim 1, characterized in that The multi-objective evolutionary algorithm at least includes one of the feasibility-driven multi-objective evolutionary algorithm, the objective and feasibility balanced multi-objective evolutionary algorithm, the evolutionary operator modified multi-objective evolutionary algorithm, and the multi-objective evolutionary algorithm based on a hybrid strategy; The early generations refer to the stage where the number of iterations is less than or equal to half of the maximum number of iterations.

4. The multi-objective traffic network optimization method based on the adaptive constraint relaxation strategy according to claim 2, wherein The local convergence index is expressed as follows: ； ； ； ； ； representation neighborhood solution set; and are local domination relation and constraint domination relation respectively, is local domination strength, are the constraint violation degrees of the i-th and j-th solutions respectively.

5. The multi-objective traffic network optimization method based on an adaptive constraint relaxation strategy according to claim 4, wherein The diversity comprehensive selection process includes: After obtaining the local optimal solution through the local convergence index, truncate the population size to ; Calculate using the crowding distance-based method: ； wherein represents the solution and Euclidean distance; When the number of remaining solutions is greater than then the largest solution will be discarded; this process is iteratively executed until the population size is equal to .

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