## 1 Introduction  
International trade is the exchange of goods or services across nations. There are different kinds of transportations for exchanging goods, including air, land, and maritime. Among these transportations, maritime transport is essential due to its having a relatively lower transport cost as a result of mass transport. Among various kinds of maritime transport, container transport is especially important, as the number of global container shipments is increasing continuously. To serve calling ships, many of the busy global ports, such as Hamburg, Rotterdam, and Antwerp in Europe, and Busan, Shanghai, and Hong Kong, employ multi-user terminals [1]. To improve productivity at this kind of terminal, a better solution for the berth allocation problem (BAP) is essential. There are many approaches available for improving the productivity of a container terminal. Basically, these approaches can be classified into the two categories: hardware and software approaches. For example, increasing the number of quays or quay cranes (QCs) is an example of a hardware approach, whereas improving the utilization of quays or QCs is an example of a software approach. In this research, the software approach is used, as it is less expensive and time-consuming. In a container terminal, the operations can mainly be classified into three areas: seaside, yard, and landslide. In the seaside area, there are three famous seaside operational problems: the berth allocation problem (BAP), the quay crane assignment problem (QCAP), and the quay crane scheduling problem (QCSP) [2; 3]. These seaside operational problems are more critical than others in the yard area and landslide due to the use of berths and QCs. In this research, we therefore focus on one of the three well-known seaside operational problems, i.e., the BAP. However, our literature review shows that the BAP can be further characterized with respect to certain factors. To deal with the BAP, it is necessary to understand the factors and variables affecting it, as further detailed in the next paragraph. The BAP is a problem of allocating berths to ships. This problem can be further characterized by two main factors: (1) the arrival times of ships; and (2) the configuration of quays. The first factor characterizes the BAP as being a _static_ or _dynamic_ version of the problem. In the _static_ BAP (SBAP), only arrived ships are considered, whereas in the _dynamic_ BAP (DBAP), incoming ships are also taken into consideration. In this research, we focus on the dynamic version (DBAP) due to the fact that ships continue to come during BAP planning. The second factor characterizes the BAP as either a _discrete_ or _continuous_ version of the problem. In the _discrete_ BAP, a quay is separated into several fixed sections, and each section can only accommodate one ship at a time, whereas in the _continuous_ BAP, a quay in its entirety is regarded as a continuous line that is able to accommodate as many ships as possible at any given time. In this research, we focus on dealing with the _dynamic_ and _continuous_ BAP (DCBAP), whereby a quay is used as a continuous line, and both arrived ships and incoming ships are considered. Different approaches are available for dealing with the BAP, including mathematical models, heuristics and metaheuristics. Mathematical models, such as the Integer Programming (IP) and Mixed Integer Programming (MIP) models, are exact approaches commonly used to find the optimal solution. However, due to NP-complete [4; 5; 6], the exponentially increasing computational times required for exact approaches prevent them from being employed in practice. As a result, heuristics and metaheuristics have become popular. Recently, evolutionary and population-based metaheuristics have increasingly been being used to deal with various container terminal operational problems. One advantage of this kind of approach is that they can iteratively drive solution(s) towards optimality. This improves the simplicity of simple heuristics.