• Vol 11, No 2 (2020)
  • Civil Engineering

A Comparative Study on Swarm-based Algorithms to Solve the Stochastic Optimization Problem in Container Terminal Design

Febri Zukhruf, Russ Bona Frazila, Wijang Widhiarso

Corresponding email: febri.zukhruf@ftsl.itb.ac.id

Cite this article as:
Zukhruf, F., Frazila, R.B., Widhiarso, W., 2020. A Comparative Study on Swarm-based Algorithms to Solve the Stochastic Optimization Problem in Container Terminal Design. International Journal of Technology. Volume 11(2), pp. 374-387
Febri Zukhruf Faculty of Civil and Environmental Engineering, Institut Teknologi Bandung, Jl. Ganesha No. 10, Bandung 40132, Indonesia
Russ Bona Frazila Faculty of Civil and Environmental Engineering, Institut Teknologi Bandung, Jl. Ganesha No. 10, Bandung 40132, Indonesia
Wijang Widhiarso Faculty of Information Technology, Multi Data Palembang Bachelor Program, Palembang 30113, Indonesia
Email to Corresponding Author


This study compared swarm-based algorithms in terms of their effectiveness in improving the design of facilities in container terminals (CTs). The design was conducted within the framework of stochastic discrete optimization and involved determining the number of equipment needed in CTs by considering variations in demand and the productivity of facilities—issues that are rarely elaborated in CT design. Variations were identified via Monte Carlo simulation characterized by a particular distribution. The conflicting issue due to increments in equipment investment that possibly cause the distribution delays was also modeled, specifically in relation to the increasing number of trucks used in terminals. Given that the optimization problem is typified by numerous combinations of actions, the swarm-based algorithms were deployed to develop a feasible solution. A new variant of glowworm swarm optimization (GSO) was then proposed and compared with particle swarm optimization (PSO) algorithms. The numerical results showed that the performance of the proposed GSO is superior to that of PSO algorithms. 

Design of container terminal facilities; Glowworm swarm optimization; Particle swarm optimization; Stochastic optimization.


As an essential part of annually expanding global trade, the container shipping industry has been compelled to extensively develop container terminals (CTs) by investing in large-scale equipment and advanced hardware for tackling container flows (Mishra et al., 2017). This development has correspondingly increased the complexity of CT operations, which encompass interactions among resources, entities, and activities. Such interactions begin at the seaside, where a vessel requires assistance from a tugboat for berthing. After berthing, quay cranes (QCs) simultaneously handle containers and transport them to a loading dock or transport vehicles. Multiple transport vehicles then convey the containers to a stacking yard, where smooth distribution is considerably facilitated by the existence of an internal road network. Cumulatively, these interactions reflect seaport performance, which is manifested in different forms that range from operational performance (Cartenì 2012 Luca, 2012) to environmental performance (Budiyanto et al., 2019).

The above-mentioned interactions equally contribute to the complexity of CT operations, which is hardly represented in analytical models (Dragovi? et al., 2017)This deficiency prompted researchers to pay increasing attention to the use of simulation models in depicting how CTs are run. In line with this trend, the current research constructed a simulation model on the basis of the Monte Carlo (MC) framework. As part of a stochastic-based procedure, the MC framework can uncover the expected values of components through randomization processes. These processes generate a random number iteratively, thereby creating various event scenarios that illustrate the stochasticity that characterizes CT operations.

The complexity of CT operations can likewise be viewed as an optimization problem, whose resolution lies in selecting the action that best enhances the performance of CTs. Given that CTs operate under uncertainties (i.e., variations at the demand and supply sides), this study also established a stochastic optimization model that directly incorporates uncertainty into the decision-making process. In this model, variations in vessel size are the uncertainties manifested in the demand side, whereas fluctuations in equipment productivity represent the uncertainties in the supply side. The stochastic modeling also considered the QCs, container truck-trailer units (TTUs), and container yard equipment [i.e., rubber tyred gantry crane (RTGC)] employed in CT operations. Because an increment in TTUs used potentially causes delays at land-side area, this research integrated estimations of delays in travel time by applying the Bureau of Public Roads (BPR) function.

Optimization in CTs may be embodied by an enormous number of problem combinations, so the issue was resolved in this research through a metaheuristic approach, which comes in several types, such as genetic algorithms, tabu search, simulated annealing, and swarm-based algorithms. Swarm-based algorithms are grounded in the natural behaviors of swarm entities, such as a flock of birds [i.e., particle swarm optimization (PSO)] and a colony of glowworms [i.e., glowworm swarm optimization (GSO)]. Because of the excellent performance of these algorithms, they have been widely used in solving various optimization problems. However, to the best of our knowledge, little research has been devoted to the performance comparison of swarm-based algorithms intended to address the CT optimization problem, specifically the stochastic type. To fill this void, the present study evaluated the effectiveness of these algorithms in enhancing the design of CT facilities. The comparison revolved specifically around the latest variants of PSO and a version of GSO within the framework of a binary optimization problem.

The rest of the paper is organized as follows. Section 2 describes CT operations and discusses the optimization modeling framework. Section 3 elaborates on swarm-based algorithms and presents the case study on the performance of these approaches. Section 4 concludes the paper with a summary.


        This research investigated the performance of swarm-based algorithms in the design of CT facilities. To this end, a new variant of binary GSO and the latest types of binary PSOs (i.e., PBPSO and MPBPSO) were incorporated into the framework of stochastic discrete optimization. Taking into account uncertainty issues and possible additional delays due to increments in the number of facilities, the swarm-based algorithms were used to determine the number of additional facilities required for CT operations. The results revealed that an increase in the number of trucks and gantry cranes improves CT performance. The numerical experiment showed that the binary version of GSO realizes better optimization results and computational times than those achieved by the comparison algorithms. However, its stability needs to be carefully considered in future works. Another essential issue of stochastic optimization is computational time because MC simulation requires massive repetitions, albeit the proposed algorithm can reduce this requirement significantly. Further efforts may be needed to inquire into the development of a more efficient algorithm.


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