## 1 Introduction  
Nowadays, it has been realized that ordinary asphalt pavements are usually unable to service the development of traffic, due to various forms of destruction including cracking, rutting etc. [1, 2, 3, 4, 5, 6, 7, 8]. Many researchers around the world tried to use different methods to enhance the service performances of asphalt pavement, and many additives like polymers, diatomic, fibres, etc. were selected to mix with asphalt materials [9, 10, 11, 12, 13]. Studies demonstrated that diatomic has been effective in improving the anti-rutting performance and water damage resistance [14]. In addition, fibres were proved to be a kind of effective material for the crack resistance of asphalt mixture [15]. Thus, asphalt mixture proportion design is a key step in asphalt pavement design and application. Conventionally, asphalt mixture proportions are optimized by laboratory tests including asphalt content, amount of aggregates, additive parameters, etc. to achieve a designed performance that meets requirements [16, 17]. When there is only one objective to be optimized, the traditional experimental-based method is generally feasible [18]. However,in most cases, proportion optimization of asphalt mixture is a complex problem, which needs to optimize multiple objectives simultaneously, such as performances, cost and environmental pollution, etc. Moreover, the proportion optimization problem with multiple objectives for asphalt mixture is usually investigated based on traditional prescriptive approaches and design of experiments (DOE), such as orthogonality design method, factorial experiments and response surface methodology (RSM), etc. [19]. This would result in an exponential increase in the number of laboratory trial specimens. These experimental optimization process would be both time- and resource-intensive. On the other hand, asphalt mixture proportions obtained by traditional prescriptive approaches and experiment-based methods are considered as practical solutions, not optimal solutions [20]. To solve the boundedness of traditional prescriptive approaches and experiment-based methods, many research studies have attempted computational design optimization, which is a mathematical approach for mixture proportions using advanced mathematical techniques and high-performance computing [21]. In this computational design optimization process, there are three steps including the problem statement, modelling and optimization algorithm [22]. The problem statement involves variables, objectives and constraints. The modelling step focuses on the mathematical relationships between variables and objectives. Nowadays, computational optimization methods based on machine learning (ML) technology are popularly used in a lot of fields of engineering for optimization and prediction [23]. In most cases, the mixture proportion optimization problem needs to be forecasted without knowing the explicit relationships between variables and objectives [24]. Therefore, the objective functions can be developed based on ML techniques. There are some ML models used for the optimization of mixture proportion, e.g., clustering, artificial neural networks, instance-based learning, regression-based methods, decision trees and support vector machines, etc. [25; 26; 27]. After that, the optimization algorithm was employed to mathematically address the problem and obtain its optimal mixture proportion [28]. Computational optimization methods based on metaheuristic algorithms are used for mixture optimization problem with the help of simplicity and efficiency. The metaheuristic algorithms known as \"guided search\" aim to find the global optimal solution for optimization problems, which is very useful for objectives and constraints without mathematical relationships. Many metaheuristic optimization algorithms were developed for dealing with optimization problems. In the field of mixture proportion design, there are multiple competing objectives, creating a rapidly growing area of optimization study [29].