Abstract
Optimizing the allocation of higher education resources and improving the utilization efficiency of educational resources are of great significance to further promoting the balanced development of higher education quality. In order to rationalize and maximize the efficiency of the allocation of innovation and entrepreneurship education resources in colleges and universities and build an evaluation index system for the input and output of educational resources, this paper proposes to use the improved cytogenetic algorithm educational resources for resource allocation and utilization. The adaptive constraint processing technology is combined with the cytogenetic algorithm to avoid the algorithm falling into local optimum. Our method has achieved good results on high-dimensional functions. The utilization efficiency and allocation efficiency of innovation and entrepreneurship education resources in colleges and universities have increased by 21.33% and 18.92%, respectively, and tend to be in a balanced state, which can optimize the allocation of educational resources.
1. Introduction
While higher education has grown significantly in China throughout the 13th Five-Year Plan period, with the gross enrollment rate of higher education increasing from 42.7 percent in 2016 to 54.4 percent in 2020, higher education has reached the stage of universalization in its entirety. General Secretary Xi Jinping stated that the demand for higher education, as well as the need for scientific knowledge and great skills, is more pressing than ever before for the growth of the Party and the country [1–4]. It is a major concern of the Party and the state that higher education develops in a high-quality manner, as this will undoubtedly necessitate and attract more resources to invest. Improving the efficiency of resource allocation is a concrete manifestation of the modernization of higher education governance as well as an important means of achieving the modernization of higher education governance. The establishment of a performance evaluation mechanism for higher education is an essential step toward furthering the reform of higher education, according to the Ministry of Education’s 13th Five-Year Plan for Scientific and Technical Development of Higher Education, which was issued in 2016 [5, 6]. Promotion of first-class construction of our universities should be based on performance, according to the plan. Performance should be used as a lever to coordinate the overall construction of universities as well as the construction of individual disciplines [7]. In this context, the development of a comprehensive index system for evaluating the efficiency of higher education resource allocation, the scientific and precise implementation of the evaluation of resource allocation efficiency, and the formation of a data-driven education resource allocation orientation are all of great theoretical and practical importance in order to further promote a more reasonable and efficient allocation of higher education resources [8–12].
The input and output of education resources are the primary focus of research on the efficiency of resource allocation in education [13]. In order to increase the efficiency with which colleges and universities are run, it is necessary to optimize education resource allocation. The input direction and quantity of education resources are modified and optimized under the guidance of college and university development and discipline construction in order to achieve this [14, 15]. One of the most important factors in the development of high-quality higher education, the attainment of educational justice, and the improvement of public perceptions about higher education is making the most efficient use of educational resources. As the fact that China places a high value on innovation and entrepreneurship education in colleges and universities and that the total amount of educational resources invested in this area continues to grow year after year, there are still issues to be addressed, such as a lack of adequate investment in resources, unequal allocation, and inefficient utilization, in order to promote an innovation-driven development strategy and alleviate employment pressure [16–20]. The subject of how to rationalize and maximize the efficiency of resource allocation for innovation and entrepreneurship education in colleges and universities has so piqued the interest of people from all walks of life, who have been debating it for quite some time [17, 18].
At the moment, data envelopment analysis is most commonly employed in the evaluation of resource allocation efficiency in many types of schools, and it is widely utilized because of its low preconditions and ease of operation. It is frequently used because of its low preconditions and ease of operation [19, 20]. From the perspectives of policy changes, influencing factors, double-class construction, regional economy, and technical support, domestic researchers have conducted theoretical and empirical studies on the connotation of educational resources and their characteristics, as well as the problems associated with optimal resource allocation. They have also proposed corresponding recommendations for optimal resource allocation. In-depth examination of existing research findings reveals that the majority of the research content is concerned with broad educational resource allocation, with little attention being paid to the allocation of educational resources in colleges and universities, as well as other factors [21–26]. On the one hand, research objects such as universities directly under the Ministry of Education, double first-class universities, and higher vocational institutions receive the majority of attention; on the other hand, research dimensions such as production efficiency, loss efficiency, and allocation efficiency receive the least attention; and on the third hand, studies on ordinary local universities and universities in single provinces receive the least attention. The researchers’ primary focus in terms of research methodologies is linear programming methods that use data envelopment analysis to develop CCR-BCC models and evolutionary algorithms that employ genetic algorithm for research [27].
There have been a number of early stage studies undertaken by foreign researchers that have yielded extensive findings in the evaluation of resource allocation efficiency at various levels and types of education [28]. They have then applied their findings in a wide range of practices to improve the overall quality of higher education, including allocation of education funds. The overall efficiency of 45 colleges and universities in the United Kingdom was evaluated using the DEA approach, and the system’s rationality for evaluating the efficiency of college operation was confirmed by certain scholars using the method. Several additional researchers used the DEA approach to analyze the relative efficiency of 45 Canadian universities, and they discovered that the majority of them had high efficiency scores, which is regarded to be a novel way to comprehend the efficiency of Canadian higher education institutions. Based on multiple input-output indicator systems, literature [22] discovered that Australian universities have relatively good operational efficiency compared with other institutions around the world [29–35].
The following recommendations are made in response to the problems identified in the preceding study: develop an education resource input and output evaluation index system, propose a multiobjective function model to improve the efficiency of education resource utilization and allocation, and propose the optimal solution for resource allocation in the multiobjective function model sphere of education resource utilization efficiency and allocation efficiency to achieve the optimization of education resources [36–40].
2. Education Resource Allocation Optimization and Algorithm Design
2.1. Construction of Education Resource Evaluation Index System
Education efficiency is one of the metrics used to assess the success of a school’s educational program. The optimal allocation of educational resources involves determining how to reasonably allocate the limited resources of colleges and universities in order to achieve the educational efficiency of producing the greatest amount of educational output with the least amount of input per unit of time. The education system is a complicated system with a large number of different inputs and various outputs, making it difficult to quantify and measure the link between the inputs and outputs. As a result, in order to improve the efficiency of education while also optimizing resource allocation, it is important to first develop the education resource index system as well as a multiobjective optimization mathematical model.
It is necessary to choose indicators from two dimensions of resource input and output before constructing the education resource input and output index system. The education resource input and output index system is built around two problems: whether the above evaluation index system can completely support the above evaluation index system and whether the above evaluation index system can completely support the above evaluation index system. Education resources input and output index system is shown in Table 1.
In the index system of education, we can see that there are two primary indicators of educational resources input and output, six secondary indicators such as human resources and physical resources, and twelve tertiary indicators such as the number of full-time and part-time teachers and administrative teachers in Table 1.
2.2. Multiobjective Optimization Analysis and Model Construction
The following two objectives are given in order to maximize the allocation of resources:(1)In order to increase the efficiency with which resources are utilized, that is, to organize limited resources in such a way that the maximal educational product is brought into play.(2)To increase the efficiency with resources, that is, to maximize the ratio of educational resources to input resources while also taking into account the complexity and specificity of each resource as well as the degree to which it influences educational outcomes, in order to ensure that each resource is effectively allocated to the most adapted aspect of the curriculum.
First and foremost, this article investigates ways to increase the efficiency with which resources are utilized in the context of education.
Several factors influence the allocation of education resources in colleges and universities, and their allocation problems are classified as nonlinear allocation problems. The ultimate goal is to maximize educational outcomes, and the efficiency of resources utilization is defined as the ratio of educational output to educational input.in which and represent the elements of educational resources and educational achievement, respectively, and are the output and input of educational resources, respectively, and and are the weights of the input and output indicators. With a higher value , there is a higher input-output ratio, and with a better utilization efficiency of educational resources, there is a more acceptable combination of educational production variables.
According to the resources input of colleges and universities, the education resources output index system is constructed in order to construct seven resources allocation efficiency indexes, including the teacher-student ratio, the average number of administrative teachers, the average number of off-campus teachers with enterprise background, the average value of teaching instruments and equipment, and the average value of teaching instruments and equipment, among others. The following is an expression of the objective function of the Kth university’s resource allocation for educational purposes:in which is the number of students in the kth university, and denote the average value of each resource element in the kth university, and denotes the change of each resource element in the kth university.
Considering the objective function of (1) and (2) together, we get the multiobjective optimization function, which is as follows:in which is the maximum value that should be sought for each university’s educational resource utilization efficiency, and maximum educational resource allocation efficiency is the maximum value that should be sought for each university’s educational resource allocation efficiency.
The degree of influence of resource input index and output index on education is different; therefore, it is necessary to calculate the weights of each factor by the full weight method, and based on the calculation results, expert opinions are solicited on the rationality and validity of the evaluation index weights by using Delphi method, and after two rounds of solicitation, feedback, and revision of the closed-loop process, the final weights of resource input and education resource output indexes are obtained, as shown in Tables 2 and 3, respectively.
2.3. Cellular Genetic Algorithm
A minimization optimization problem with equation constraints and inequality constraints can be represented mathematically in the following way, without sacrificing generality or efficiency:in which is the objective function, is the i-th inequality constraint, and the j-th equation constraint is .
As indicated in the example of equation constraints, the general strategy is to change the equation constraints into inequality constraints by assigning a very tiny constraint tolerance to the equation constraints, as illustrated in the following example:in which is the tolerance of the equation constraint, which is typically represented by the value 0.0001 in most cases.
The notion of constraint violation degree is proposed in order to more correctly express the distance between people in a population and the feasible domain; the greater the value of this concept is, the further the individual is from the feasible domain. The expression formula for the degree of constraint violation is presented as follows:
The comparison criterion, which is made of the three criteria listed below, is used to compare feasible individuals with infeasible individuals. For example, to obtain the minimal value, the following three criteria are used:(1)Smaller goal function value is selected when both individuals are practicable.(2)In the event that both individuals are infeasible, the smaller constraint violation is chosen.(3)The feasible individual is selected if the constraint violation degree of one of the infeasible individuals is less than or equal to; otherwise, the feasible individual is selected if the constraint violation degree of one of the infeasible individuals is more than or equal to.
The following is the setting formula:where gen is the evolutionary algebra .
The drawback of the method is the low convergence accuracy and lack of diversity for complex constrained problems.
An algorithm of high quality that was developed by merging cellular automata and genetic algorithms is the cellular genetic algorithm (also known as the cellular genetic algorithm). Its fundamental principle is to distribute the population randomly in a two-dimensional topology, which restricts the competition and hybridization behavior of individuals to a local range, thereby ensuring the diversity of the population and preventing it from falling into local optimal solutions too quickly. The genetic operation of the universal cellular genetic algorithm is illustrated in Figure 1.
When dealing with limited optimization issues, the differential evolution algorithm is one of the most effective techniques available. It primarily makes use of the distance between persons as well as the directional distance while performing direct search on a population of people.
Here are three general differential evolution algorithms with their respective variation techniques represented.in which represents the scaling factor and represent random integers in and are not equal. The variation of has good global search ability and can effectively maintain the diversity of the population, the variation of takes the better individuals in the current population as the base vector and has good convergence ability, the variation of has good balance for the maintenance of population diversity, and the current-to-best variation has a good balance between the maintenance of population diversity and the enhancement of population convergence.
It is proposed that, in order to improve upon the shortcomings of the standard comparison criterion, the revised standard comparison criterion 10 published in the literature 10 and the adaptive adjustment method be used. The judgment criterion is as follows:(1)Lower goal function value is selected when both individuals are practicable.(2)The option can be separated into two categories when one person is a feasible individual and the other is an infeasible individual. It is preferable to choose the infeasible individual whose constraint violation degree is less than; alternatively it is preferable to choose the feasible individual whose objective function value is less than.(3)The individual whose objective function value is the smallest chosen in cases when both individuals are infeasible individuals and if both individuals have a constraint violation degree less than s.
The adaptive equation is as follows:where represents the truncated evolutionary algebra, which can be used to adjust the size of , where , and represents the proportion of viable individuals in the population. is generally set to 1000 when the evolutionary algebra is 1000, and this value will also be used in this paper.
3. Experiment Result
In conjunction with the resources index system, a multiobjective function is used, in which each particle represents a configuration scheme, the individual optimal solution y represents the optimal configuration scheme sought by each particle, and the population optimal solution represents the optimal configuration scheme sought by all particles.
A machine with the following hardware configuration is used to conduct all of the experiments in this paper. Matlab2018 was used to construct the majority of the software, which was run on an Inter Core processor with an i9-10850K, 64 GB of RAM, and a 3.4 GHz main clock.
On the simulation software, the simulation operation is carried out by integrating the multiobjective optimization objective function and the restrictions of the resource configuration. Iteration diagrams of algorithms are represented in Figure 2 following implementation of the algorithm as shown in the previous section.
As can be seen from Figure 2, the optimization method proposed in this paper is more in line with the actual situation. It can be seen from the experimental results that the model improves the efficiency of resource utilization. Figure 3 shows a graph of how efficiently each university used its resources before and after the experiment.
In Figure 3, it is clear that this is the case. The resource utilization efficiency of all colleges and universities has improved, with an average gain of 16.37 percent between before and after the experiment, and the resource utilization efficiency of all colleges and universities is trending toward a more balanced state. Compared with their respective baselines, the resource utilization efficiency of colleges C1, C3, and C11 with lower resource utilization efficiency improved significantly, rising from 0.705, 0.985, and 0.755 before optimization to 1.055, 1.025, and 1.078 after optimization.
According to Figure 4, the original data of each university, as well as the optimized allocation scheme, are substituted into (3) to calculate the overall resource allocation efficiency of each university before and after optimization, respectively. This is done to determine whether the model improves the resource allocation efficiency.
Figure 4 shows that the difference in resource allocation efficiency between universities prior to the experiment is significant, with a minimum value of 0.127 and a maximum value of 0.32 for the minimum and maximum values, respectively. Following the optimization, the allocation efficiency is 0.188, with an average increase of 42.99 percent, indicating that the optimization of education resource allocation may be achieved by altering the amount and structure of education resources, as demonstrated by the results.
It can be seen from Figure 4 that the optimized educational resource allocation is more reasonable, and its application effect is closer to the actual demand.
4. Conclusion
The optimal allocation of educational resources in colleges and universities is not only related to the development of colleges and universities and the cultivation of regional talents but also related to the improvement of the overall level of national higher education and the scientific utilization of national higher education resources. In order to maximize the allocation of educational resources in colleges and universities, a multiobjective allocation method of high-quality higher education resources based on cytogenetic algorithm is proposed. Schools and universities vary greatly in the allocation of various resources, and there is no clear standard. After optimization, the utilization efficiency and allocation efficiency of educational resources in colleges and universities increased by an average of 21.33% and 18.92%, respectively. In the future research, how to optimize the allocation of educational resources in real time according to the dynamic changes of the external environment has become one of the focuses of the research, which is also a problem that needs to be paid attention to in the future research of this paper.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The author declares that he has no conflicts of interest.