# Berth Allocation Considering Multiple Quays: A Practical Approach Using Cuckoo Search Optimization

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## Abstract

**:**

## 1. Introduction

- Develop a mixed-integer linear programming (MILP) model for a realistic port environment that considers multiple quays and several practical constraints with the objective of minimizing the total service cost.
- Propose the cuckoo search algorithm (CSA), a recently developed computational intelligence (CI)-based approach, to solve the problem in affordable computation time, since MQ-BAP is NP-hard and cannot be solved efficiently by exact methods.
- Validate the performance of the developed method against the exact MILP method and three widely adopted approaches (genetic algorithm, particle swarm optimization, and first come first serve) using both random data as well as real data from the Port of Limassol, Cyprus.

## 2. Literature Review

## 3. Problem Definition and Formulations

#### 3.1. Problem Explanation

#### 3.2. Assumptions of This Study

- The number of incoming ships in the planning period is known;
- When a vessel starts operations at any quay, it cannot be interrupted until loading/unloading is completed;
- Berths from any quay become available immediately after a ship completes its tasks;
- The length of a continuous quay and the number of berths available at a discrete quay are known;
- The ETA and ETD for each vessel are known;
- The estimated turnaround time for each vessel is known;
- Each vessel has a PBQ, a PBP, and ABQs that are known in advance;
- All berths are assumed to be free at the beginning of the time horizon (t = 0);
- The processing speed is the same for all QCs and it is known;
- Handling and waiting costs per hour for all vessels are known;
- Penalty costs for late departure, non-optimal berth allocation, and non-optimal quay allocation are known and assumed to be the same for all arriving vessels;
- This study ignores any meteorological or other uncertainty conditions.

#### 3.3. Mathematical Formulation

General constraints | |
---|---|

$${x}_{sqbt}\in \{0,\phantom{\rule{0.277778em}{0ex}}1\},\forall \phantom{\rule{0.277778em}{0ex}}s\in S,\phantom{\rule{0.277778em}{0ex}}q\in Q,\phantom{\rule{0.277778em}{0ex}}b\in {B}_{q},\phantom{\rule{0.277778em}{0ex}}t\in T$$
| The variable ${x}_{sqbt}$ is 1 if the ship s is scheduled at position b of quay q at time t, and 0 otherwise. |

$$\sum _{q\phantom{\rule{0.277778em}{0ex}}\in \phantom{\rule{0.277778em}{0ex}}Q}\phantom{\rule{0.277778em}{0ex}}\sum _{b\phantom{\rule{0.277778em}{0ex}}\in \phantom{\rule{0.277778em}{0ex}}{B}_{q}}\phantom{\rule{0.277778em}{0ex}}\sum _{t\phantom{\rule{0.277778em}{0ex}}\in \phantom{\rule{0.277778em}{0ex}}T}{x}_{sqbt}=1,\phantom{\rule{0.277778em}{0ex}}\forall \phantom{\rule{0.277778em}{0ex}}s\in S$$
| This constraint ensures that each ship may moor only once during the time t at the mooring position b of the quay q. |

$${T}_{s}^{b}\ge {T}_{s}^{ea},\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\forall \phantom{\rule{0.277778em}{0ex}}s\in S.$$
| The constraint specifies that the proposed berthing time ${T}_{s}^{b}$ for a given ship s must always be equal to or later than its expected time of arrival ${T}_{s}^{ea}$. |

$${T}_{s}^{b}-{T}_{j}^{b}\ge SE\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\forall \phantom{\rule{0.277778em}{0ex}}s\ne j\in S$$
| This condition guarantees a minimum safety entrance time $SE$ between any two consecutive berthing operations. |

Constraints for continuous berthing layout | |

$$\begin{array}{c}\hfill \sum _{j\ne s\phantom{\rule{0.277778em}{0ex}}\in \phantom{\rule{0.277778em}{0ex}}S}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\sum _{b=B{P}_{s}-{L}_{j}-SD+1}^{B{P}_{s}+{L}_{s}+SD}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\sum _{t={T}_{s}^{b}-{T}_{j}^{h}-ST+1}^{{T}_{s}^{b}+{T}_{s}^{h}+ST}{x}_{jqbt}=0,\\ \hfill \forall \phantom{\rule{0.277778em}{0ex}}s,j\in S,q={Q}_{s}\end{array}$$
| This is an overlap avoidance constraint that does not allow two vessels to share (part of) the same berth positions during their handling times. Visually, this constraint ensures that two rectangles (denoting the time intervals and the berths assigned to the ships) shown in Figure 4 can never overlap. In addition, this constraint is also responsible for maintaining the safety distance $SD$ and safety time $ST$ between two ships to avoid any danger during berthing. |

$$B{P}_{s}+{L}_{s}\le {L}_{q},\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\forall \phantom{\rule{0.277778em}{0ex}}s\in S,\phantom{\rule{0.277778em}{0ex}}$$
| This constraint ensures that the length ${L}_{s}$ of any ship s plus its berthing position $B{P}_{s}$ must be less than or equal to the length ${L}_{q}$ of the quay q, where s is planned to be berthed. |

Constraints for discrete berthing layout | |

$$\sum _{j\ne s\phantom{\rule{0.277778em}{0ex}}\in \phantom{\rule{0.277778em}{0ex}}S}\phantom{\rule{0.277778em}{0ex}}\sum _{t={T}_{s}^{b}-{T}_{j}^{h}-ST+1}^{{T}_{s}^{b}+{T}_{s}^{h}+ST}{x}_{jqbt}=0,\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\forall \phantom{\rule{0.277778em}{0ex}}s,j\in S,q={Q}_{s},b=B{P}_{s}$$
| This is a restriction to avoid overlap in the case of a discrete berthing layout that does not allow two vessels to use the same berth at the same time. Furthermore, this constraint is responsible to ensure safety time $ST$ between any two ships s and j. |

$${L}_{s}\le {L}_{b},\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\forall \phantom{\rule{0.277778em}{0ex}}s\in S,\phantom{\rule{0.277778em}{0ex}}b=B{P}_{s}$$
| This constraint ensures that a berth b assigned to any vessel s must be at least as long as the vessel itself. |

## 4. Developed Methodologies

#### 4.1. Cuckoo Search Algorithm

- Each cuckoo bird dumps only one egg at a time in a random nest;
- The best nests having high-quality eggs are kept and used for the next generation;
- The number of host nests is fixed and the egg laid by a cuckoo is detected by a host bird with probability ${p}_{\alpha}\phantom{\rule{0.277778em}{0ex}}\in \phantom{\rule{0.277778em}{0ex}}(0,1)$.

Algorithm 1 CSA for MQ-BAP |

1: $X[1..k]=$ Generate initial population of host nests |

2: (each nest contains 3N possible solutions) |

3: for $t=1$ to max number of iterations do |

4: for $i=1$ to k do |

5: ${x}_{new}=X\left[i\right]+\alpha \phantom{\rule{3.33333pt}{0ex}}\oplus \phantom{\rule{3.33333pt}{0ex}}Levy\left(\lambda \right)$ |

6: if (cost(${x}_{new}$) < cost($X\left[i\right]$)) then |

7: $X\left[i\right]={x}_{new}$ |

8: for $i=1$ to k do |

9: if ($rand(0,1)<{p}_{a}$) then |

10: $X\left[i\right]=$ Destroy old nest |

11: $X\left[i\right]=$ Generate new host nest with |

12: new possible solutions |

13: ${x}_{best}=$ Find nest with lowest fitness value in X |

#### 4.2. Genetic Algorithm

#### 4.3. Particle Swarm Optimization

#### 4.4. First Come First Serve (FCFS)

## 5. Computational Experiments

#### 5.1. Real Data Instances from Port of Limassol

#### 5.2. Randomly Generated Data Instances

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ABQ | Alternative berthing quay |

BAP | Berth allocation problem |

CSA | Cuckoo search algorithm |

ETA | Expected time of arrival |

ETD | Expected time of departure |

GA | Genetic algorithm |

HT | Handling time |

LoS | Length of ship |

MCT | Maritime container terminal |

MQ-BAP | Multi-quay BAP |

NOB | Non-optimal berthing |

PBP | Preferred berthing position |

PBQ | Preferred berthing quay |

PSO | Particle swarm optimization |

QCs | Quay cranes |

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**Figure 1.**A satellite view of the Port of Limassol, Cyprus, illustrating its seven berthing quays (taken from [15]). Note: Only the quays marked with a ∗ are used for commercial purposes.

**Figure 2.**BAP solution with two berthing quays (Quay 1: continuous and Quay 2: discrete) and 10 arriving ships. Each rectangle denotes a ship, whose height (y-dimension) shows the ship’s length and whose width (x-dimension) represents the handling time (in hours) of the ship.

**Figure 3.**An illustration of the berthing timeline (showing waiting, handling, and late departure times).

**Figure 4.**An illustration of overlapping constraint (12) with three arriving ships (ship s, j, and k) with different berthing times, berthing positions, and lengths. This figure shows the restricted areas for ships j and k (using dotted boxed) to avoid overlap with ship s, the already scheduled ship.

**Figure 8.**Berth allocation solutions by the four compared approaches for ships arriving over one week planning horizon. (

**a**) solution by CSA; (

**b**) solution by GA; (

**c**) solution by PSO; and (

**d**) solution by MILP.

**Figure 9.**Mean difference between optimal and proposed berthing time for all vessels per method. MILP obtains zero difference for one week and is not able to run for two weeks and four weeks.

**Figure 10.**Non-optimal berthing (NOB) cost for all vessels per method. MILP is not able to run for two weeks and four weeks.

**Figure 11.**Total service cost for arriving vessels in one, two, and four weeks, for each approach. MILP is not able to run for two weeks and four weeks.

Notation | Explanation |
---|---|

Cost-related variables | |

${C}_{s}^{d}$ | Penalty cost for late departure (per hour) of ship s |

${C}_{s}^{h}$ | Handling cost per time unit (hour) of ship s |

${C}_{s}^{nob}$ | Penalty cost for NOB position per m of ship s |

${C}_{s}^{noq}$ | Penalty cost for NOB quay of ship s |

${C}_{s}^{w}$ | Waiting cost per time unit (hour) of ship s |

Time-related variables | |

$SE$ | Safety entrance time between two ships |

$ST$ | Safety time between two ships during berthing |

${T}_{s}^{ad}$ | Actual departure time of ship s |

${T}_{s}^{d}$ | Late departure time of ship s |

${T}_{s}^{ea}$ | Expected arrival time of ship s |

${T}_{s}^{ed}$ | Expected departure time of ship s |

${T}_{s}^{h}$ | Handling time of ship s |

${T}_{s}^{w}$ | Waiting time of ship s |

Other variables | |

${H\phantom{\rule{-0.166667em}{0ex}}P}_{s}^{qc}$ | Handling productivity of QCs assigned to ship s |

$Loa{d}_{s}$ | Total load (in TEUs) on ships s |

${L}_{b}$ | Length of a berth segment b (in a discrete quay) |

${L}_{q}$ | Length of a (continuous) quay q |

${L}_{s}$ | Length of ship s |

${N}_{s}^{qc}$ | Number of quay cranes assigned to ship s |

$SD$ | Safety distance (in meters) between two ships |

Decision variables | |

${Q}_{s}$ | Berthing quay of ship s |

$B{P}_{s}$ | Berthing position of ship s on ${Q}_{s}$ |

${T}_{s}^{b}$ | Berthing time of ship s |

${x}_{sqbt}$ | 1 if ship s is scheduled at position b of quay q at time t; 0 otherwise |

Indices | |

$s\in S$ | A ship s from a set of arriving ships S |

$q\in Q$ | A quay q from a set of continuous and discrete quays Q |

$b\in {B}_{q}$ | A berth position or segment b from a set of available berth positions/segments ${B}_{q}$ in a continuous or discrete quay q, respectively |

$t\in T$ | A time interval t from a set of time intervals T |

**Table 3.**Example data for 28 ships that arrived during the first week of March 2018 at the Port of Limassol, Cyprus.

Ship # | ETA (Date\Time) | HT (min.) | ETD (Date\Time) | PBQ | ABQ | PBP | LoS (m) |
---|---|---|---|---|---|---|---|

1 | 1\04:00 | 919 | 1\22:30 | Container/Ro-Ro Quay | Container Quay | 240 | 194 |

2 | 1\05:30 | 1490 | 2\06:50 | East Quay | - | 276 | 139 |

3 | 1\14:00 | 1285 | 2\12:50 | West Quay | North Quay | 84 | 84 |

4 | 1\15:00 | 5700 | 5\14:03 | East Quay | - | 51 | 89 |

5 | 1\17:00 | 5970 | 5\21:00 | West Quay | North Quay | 314 | 190 |

6 | 2\04:30 | 470 | 2\13:50 | Container/Ro-Ro Quay | Container Quay | 138 | 159 |

7 | 2\05:00 | 168 | 2\09:30 | Container Quay | Container/Ro-Ro Quay | 571 | 196 |

8 | 2\08:00 | 440 | 2\15:55 | North Quay | West Quay | 53 | 155 |

9 | 3\04:00 | 905 | 3\20:50 | Container/Ro-Ro Quay | Container Quay | 31 | 175 |

10 | 3\03:30 | 1331 | 4\06:15 | Container Quay | Container/Ro-Ro Quay | 389 | 277 |

11 | 3\07:30 | 1870 | 4\14:55 | East Quay | - | 358 | 162 |

12 | 3\12:30 | 640 | 3\22:40 | West Quay | North Quay | 34 | 88 |

13 | 3\23:00 | 295 | 4\05:00 | Container/Ro-Ro Quay | Container Quay | 162 | 133 |

14 | 5\05:00 | 825 | 5\19:00 | West Quay | North Quay | 208 | 90 |

15 | 5\05:30 | 635 | 5\16:30 | North Quay | West Quay | 190 | 121 |

16 | 5\08:30 | 315 | 5\13:15 | East Quay | - | 267 | 178 |

17 | 5\17:30 | 1290 | 6\20:50 | Container/Ro-Ro Quay | Container Quay | 96 | 129 |

18 | 5\16:00 | 455 | 6\00:25 | North Quay | West Quay | 112 | 84 |

19 | 5\20:00 | 614 | 6\09:35 | Container Quay | Container/Ro-Ro Quay | 125 | 294 |

20 | 6\03:30 | 937 | 6\21:25 | Container/Ro-Ro Quay | Container Quay | 269 | 122 |

21 | 6\04:30 | 425 | 6\12:00 | West Quay | North Quay | 35 | 102 |

22 | 6\05:30 | 635 | 6\16:30 | North Quay | West Quay | 128 | 87 |

23 | 6\06:30 | 705 | 6\18:05 | West Quay | North Quay | 113 | 84 |

24 | 6\07:30 | 1750 | 7\12:50 | East Quay | - | 207 | 130 |

25 | 6\12:00 | 1070 | 7\10:15 | Container Quay | Container/Ro-Ro Quay | 260 | 217 |

26 | 6\14:00 | 705 | 7\02:05 | West Quay | North Quay | 219 | 88 |

27 | 7\05:30 | 455 | 7\13:05 | West Quay | North Quay | 364 | 121 |

28 | 7\09:30 | 335 | 7\15:25 | North Quay | West Quay | 7 | 155 |

**Table 4.**Comparative analysis of all methods when using data for 1–4 weeks (March 2018). Note that all costs are in Euros. % Deviation used the total service cost of the CSA approach as baseline.

Scenarios: | One Week (28 Ships) | Two Weeks (68 Ships) | Four Weeks (168 Ships) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Algorithms: | CSA | GA | PSO | FCFS | MILP | CSA | GA | PSO | FCFS | MILP | CSA | GA | PSO | FCFS | MILP |

Waiting cost | 450 | 550 | 450 | 700 | 0 | 1850 | 4700 | 3200 | 6700 | - | 4800 | 11,100 | 11,650 | 45,900 | - |

NOB cost | 280 | 560 | 980 | 255 | 235 | 485 | 1450 | 2880 | 200 | - | 2580 | 11,125 | 8210 | 2205 | - |

Late departure cost | 0 | 0 | 0 | 1000 | 0 | 0 | 0 | 200 | 3600 | - | 400 | 200 | 1600 | 41,000 | - |

Normal handling cost | 10,770 | 10,770 | 10,770 | 10,770 | 10,770 | 19,620 | 19,620 | 19,620 | 19,620 | - | 51,170 | 51,170 | 51,170 | 51,170 | - |

Total service cost | 11,500 | 11,880 | 12,200 | 12,725 | 11,005 | 21,955 | 25,770 | 25,900 | 30,120 | - | 58,950 | 73,595 | 72,630 | 140,275 | - |

% Deviation | 3.30 | 6.08 | 10.65 | −4.30 | 17.37 | 17.96 | 37.18 | - | 24.84 | 23.20 | 137.95 | - | |||

Computation time (s) | 21.91 | 18.95 | 73.59 | 6.68 | 775.77 | 70.60 | 332.96 | 223.33 | 74.32 | - | 133.27 | 768.81 | 642.95 | 110.24 | - |

**Table 5.**Comparative analysis of all methods using uniform random data (10–150 vessels, 1–30 days, and 1–5 quays).

No. of Ships | Days | No. of Quays | Service Cost (Euro) | Computation Time (s) | ||||||
---|---|---|---|---|---|---|---|---|---|---|

CSA | GA | PSO | MILP | CSA | GA | PSO | MILP | |||

10 | 1 | 1 | 2986 | 2794 | 4884 | 2790 | 15.03 | 18.37 | 14.23 | 26.43 |

2 | 1542 | 1494 | 12,384 | 1494 | 23.52 | 13.52 | 10.69 | 14.07 | ||

3 | 1994 | 1782 | 2478 | 1780 | 21.59 | 10.38 | 12.49 | 11.92 | ||

4 | 1734 | 1576 | 2620 | 1570 | 14.19 | 9.90 | 11.73 | 11.92 | ||

5 | 1510 | 1364 | 2312 | 1342 | 16.75 | 9.04 | 11.97 | 12.27 | ||

Avg | 1953 | 1802 | 4936 | 1795 | 18.22 | 12.24 | 12.22 | 15.32 | ||

15 | 1 | 1 | 6160 | 13,956 | 15,046 | 4508 | 19.30 | 65.66 | 65.79 | 146.8 |

2 | 3152 | 3870 | 5244 | 2622 | 29.53 | 25.25 | 17.62 | 81.35 | ||

3 | 3360 | 2938 | 14,836 | 2922 | 19.74 | 69.51 | 29.44 | 103.46 | ||

4 | 3128 | 2500 | 6144 | 2494 | 18.15 | 16.93 | 20.00 | 111.71 | ||

5 | 3754 | 2500 | 4382 | 2332 | 24.06 | 16.15 | 23.71 | 17.05 | ||

Avg | 3911 | 5153 | 9130 | 2976 | 22.16 | 38.70 | 31.31 | 92.07 | ||

20 | 2 | 1 | 7504 | 7486 | 7338 | 4738 | 31.69 | 72.95 | 75.21 | 520.84 |

2 | 3136 | 2396 | 5874 | 2178 | 25.65 | 30.70 | 34.70 | 292.22 | ||

3 | 4308 | 3782 | 5468 | 3782 | 23.51 | 17.37 | 35.65 | 106.07 | ||

4 | 3588 | 3418 | 15,644 | 3170 | 21.03 | 20.18 | 38.12 | 93.03 | ||

5 | 3386 | 2716 | 5290 | 2628 | 30.41 | 13.05 | 39.76 | 98.56 | ||

Avg | 4384 | 3960 | 7923 | 3299 | 26.46 | 30.85 | 44.69 | 222.14 | ||

30 | 2 | 1 | 8312 | 10,640 | 13,784 | 7328 | 39.63 | 125.51 | 189.62 | 918.95 |

2 | 9156 | 8328 | 6378 | 6022 | 36.08 | 25.60 | 16.46 | 486.59 | ||

3 | 9370 | 7308 | 6304 | 6108 | 37.97 | 29.78 | 18.32 | 354.32 | ||

4 | 7934 | 7368 | 5656 | 5486 | 32.21 | 27.35 | 16.78 | 364.67 | ||

5 | 9150 | 6712 | 5214 | 5078 | 41.66 | 29.82 | 15.40 | 586.76 | ||

Avg | 8784 | 8071 | 7467 | 6004 | 37.51 | 47.61 | 51.32 | 542.26 | ||

60 | 7 | 1 | 30,016 | 18,672 | 37,674 | - | 107.49 | 741.91 | 43.54 | - |

2 | 21,208 | 14,744 | 11,890 | - | 75.24 | 117.47 | 33.92 | - | ||

3 | 27,576 | 17,658 | 32,574 | - | 69.39 | 97.79 | 32.88 | - | ||

4 | 19,142 | 24,366 | 12,620 | - | 89.85 | 348.56 | 33.76 | - | ||

5 | 15,342 | 21,726 | 10,686 | - | 41.83 | 236.94 | 32.17 | - | ||

Avg | 22,657 | 19,433 | 21,089 | - | 76.76 | 308.53 | 35.25 | - | ||

90 | 15 | 1 | 40,520 | 28,236 | 44,860 | - | 121.59 | 1350.63 | 92.00 | - |

2 | 24,148 | 23,122 | 29,348 | - | 251.66 | 641.48 | 45.72 | - | ||

3 | 23,584 | 32,312 | 19,026 | - | 187.22 | 644.33 | 40.86 | - | ||

4 | 28,728 | 20,872 | 29,732 | - | 129.65 | 264.31 | 49.49 | - | ||

5 | 24,290 | 40,332 | 26,570 | - | 185.92 | 240.29 | 67.04 | - | ||

Avg | 28,254 | 28,975 | 29,907 | - | 175.21 | 628.21 | 59.02 | - | ||

120 | 15 | 1 | 52,094 | 26,464 | 51,358 | - | 191.28 | 2632.96 | 66.33 | - |

2 | 40,910 | 36,152 | 53,424 | - | 174.12 | 968.62 | 63.42 | - | ||

3 | 40,794 | 57,690 | 63,590 | - | 265.19 | 1137.96 | 103.85 | - | ||

4 | 33,498 | 72,372 | 27,586 | - | 278.94 | 956.92 | 58.65 | - | ||

5 | 32,664 | 120,844 | 49,656 | - | 239.85 | 580.59 | 57.73 | - | ||

Avg | 39,992 | 62,704 | 49,123 | - | 229.88 | 1255.41 | 70.00 | - | ||

150 | 30 | 1 | 53,202 | 40,140 | 56,168 | - | 349.23 | 1921.07 | 104.58 | - |

2 | 45,828 | 40,412 | 45,148 | - | 377.76 | 1569.21 | 101.52 | - | ||

3 | 42,312 | 99,874 | 47,600 | - | 277.66 | 1633.41 | 95.71 | - | ||

4 | 45,336 | 59,142 | 35,012 | - | 361.27 | 1639.65 | 90.30 | - | ||

5 | 45,534 | 108,100 | 45,398 | - | 265.91 | 1426.03 | 109.54 | - | ||

Avg | 46,442 | 69,534 | 45,865 | - | 326.37 | 1637.87 | 100.33 | - | ||

Total | 789,890 | 998,158 | 877,200 | - | 4562.75 | 19,797.15 | 2020.70 | - |

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## Share and Cite

**MDPI and ACS Style**

Aslam, S.; Michaelides, M.P.; Herodotou, H.
Berth Allocation Considering Multiple Quays: A Practical Approach Using Cuckoo Search Optimization. *J. Mar. Sci. Eng.* **2023**, *11*, 1280.
https://doi.org/10.3390/jmse11071280

**AMA Style**

Aslam S, Michaelides MP, Herodotou H.
Berth Allocation Considering Multiple Quays: A Practical Approach Using Cuckoo Search Optimization. *Journal of Marine Science and Engineering*. 2023; 11(7):1280.
https://doi.org/10.3390/jmse11071280

**Chicago/Turabian Style**

Aslam, Sheraz, Michalis P. Michaelides, and Herodotos Herodotou.
2023. "Berth Allocation Considering Multiple Quays: A Practical Approach Using Cuckoo Search Optimization" *Journal of Marine Science and Engineering* 11, no. 7: 1280.
https://doi.org/10.3390/jmse11071280