# Integrated Simulation-Based Optimization of Operational Decisions at Container Terminals

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## Abstract

**:**

## 1. Introduction

#### 1.1. Literature Review on Integrated Decision Problems

#### 1.2. Optimizing Objective Functions without Mathematical Optimization

#### 1.3. Relationship between Hyper-Parameter Optimization and Simulation-Based Optimization

## 2. Materials and Methods

#### 2.1. Simulation Model

#### 2.2. Employed Meta-Heuristics

#### 2.2.1. Tree-Structured Parzen Estimator

#### 2.2.2. Simulated Annealing

#### 2.2.3. Bayesian Optimization

#### 2.2.4. Random Search

#### 2.3. Optimization Procedure

#### 2.3.1. Parameter Configuration Space

#### 2.3.2. Objective Function

#### 2.3.3. Structure of Optimization Study

## 3. Results and Discussion

#### 3.1. Preparatory Study

#### 3.2. Observations from All Experiments

#### 3.3. Approximated Optima

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

BO | Bayesian Optimization |

NFLT | No Free Lunch Theorem |

QC | Quay Crane |

RS | Random Search |

RTG | Rubber-tired Gantry Crane |

SA | Simulated Annealing |

TPE | Tree-structured Parzen Estimator |

TEU | Twenty-foot Equivalent Unit |

YB | Yard Block |

YT | Yard Truck |

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**Figure 4.**The Tree-structured Parzen Estimation (TPE) uses the ratio of better- and worse-performing parameters to guide the search. In the example on the left, the categorical variable takes one of the three values “a”, “b”, and “c”. For the continuous variable, in the example on the right the values range from 0 to 20.

**Figure 9.**The number of YBs in the set of approximated optima. The parameter value that leads to the best objective function value over all optimization runs is marked with an asterisk.

**Figure 10.**The number of YTs in the set of approximated optima. The parameter value that leads to the best objective function value over all optimization runs is marked with an asterisk.

Number of QCs | Makespan (in Hours, Rounded) | ||
---|---|---|---|

Median | Minimum | Maximum | |

3 | 61 | 51 | 158 |

4 | 49 | 39 | 161 |

5 | 47 | 38 | 160 |

6 | 35 | 29 | 161 |

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**MDPI and ACS Style**

Kastner, M.; Nellen, N.; Schwientek, A.; Jahn, C.
Integrated Simulation-Based Optimization of Operational Decisions at Container Terminals. *Algorithms* **2021**, *14*, 42.
https://doi.org/10.3390/a14020042

**AMA Style**

Kastner M, Nellen N, Schwientek A, Jahn C.
Integrated Simulation-Based Optimization of Operational Decisions at Container Terminals. *Algorithms*. 2021; 14(2):42.
https://doi.org/10.3390/a14020042

**Chicago/Turabian Style**

Kastner, Marvin, Nicole Nellen, Anne Schwientek, and Carlos Jahn.
2021. "Integrated Simulation-Based Optimization of Operational Decisions at Container Terminals" *Algorithms* 14, no. 2: 42.
https://doi.org/10.3390/a14020042