# A Novel Hybrid Metaheuristic Algorithm for Optimization of Construction Management Site Layout Planning

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## Abstract

**:**

## 1. Introduction

## 2. The Symbiotic Organisms Search Algorithm

Algorithm 1 Symbiotic Organism Search pseudo-code |

Initialization: ecosystem $Po{p}_{i},i=1,2,\dots ,pop\_size$ |

Input: population size: $pop\_size$, the maximum number of evaluation number |

Output: best solution $Po{p}_{best}$ |

1: For counter = 1 to $maxIter$ (termination condition) |

2: For each organism in $Po{p}_{i}$ (maximum number of function evaluations) |

3: Update the current best organism $Po{p}_{best}$ |

4: Modify organism by |

a. Mutualism phase |

b. Commensalism phase |

c. Parasitism phase |

5: End for |

6: End for |

## 3. Construction Site Layout Planning Problem

## 4. Application of HSOS-LO to CSLP problem

#### 4.1. Solution Representation

#### 4.2. Local Search Improvement

_{i}) is improved using the local search improvement by implementing a neighbourhood operator. The neighbourhood operator is randomly chosen, including swap, insert, and reverse.

- (1)
- SwapThis neighbourhood operator randomly selects two elements in the solution vectors, i and j, with i ≠ j, and swaps the customer located in position i with the customer at position j.
- (2)
- InsertionThis neighbourhood operator randomly selects positions i and j, where i ≠ j, and relocates the customer from position i to position j.
- (3)
- Random ReverseThis neighbourhood replaces a randomly chosen facility’s subsequence by its reversal.

Algorithm 2 Local search pseudo-code |

Input: current solution $Po{p}_{i}$, best solution $Po{p}_{best}$ |

Output: updated solution $Po{p}_{i}$ |

1: Let the initial solution X = decode ($Po{p}_{i}$) |

2: Generate r = rand (0,1) |

3: If r <= 1/3 then |

4: Apply swap operator to X |

5: Else if r <= 2/3 then |

6: Apply insert operator to X |

7: Else |

8: Apply random reverse operator to X |

9: End If |

10: $Po{p}_{i}$ = encode (X) |

11: If f($Po{p}_{i}$) < f($Po{p}_{best}$) then |

12: $Po{p}_{best}$ = $Po{p}_{i}$ |

13: End if |

#### 4.3. Parameter Used

#### 4.4. The HSOS-LO Procedure for CSLP Problem

_{i}, with a corresponding fitness value, f(Pop

_{i}). The evaluation process is then conducted by calculating the objective function for the corresponding solution vector of each solution. The decoding method for calculating the fitness value is explained in Section 4.1. Next, the population of the solution is iteratively updated through the mutualism phase, commensalism phase, and parasitism phase.

_{best}is updated if a new best solution has been found during SOS phases or local search improvement. Finally, the procedure is repeated until it meets the maximum number of function evaluations. Then the best result in that iteration, Pop

_{best}, is appointed as the final result of the optimization process.

## 5. Case Studies for Construction Site Layout Planning and Managerial Implication

#### 5.1. Parameter Setting

#### 5.2. Case Study 1

- Site office (F1)
- Falsework workshop (F2)
- Labour residence (F3)
- Storeroom 1 (F4)
- Storeroom 2 (F5)
- Carpentry workshop (F6)
- Reinforcement steel workshop (F7)
- Side gate (F8, fixed to L1)
- Electrical, water and other utilities control room (F9)
- Concrete batch workshop (F10)
- The main gate (F11, fixed to L10)

#### 5.3. Case Study 2

- The building has 30 floors and floors one to eight can be used as materials storage.
- There are 10 types of materials and each floor has five storage cells that can only be used by 1 type of material.
- There are three types of transportation costs: horizontal movement, vertical movement from the ground floor to the storage floor, and vertical movement from the storage floor to the demanding floor.
- There are fixed and predetermined physical and demand quantities.
- Only one lift used as the materials hoist.
- All storage cell areas are large enough to meet storage requirements.
- After being built, lower building floors can function as materials storages.
- There are no costs related to loading and unloading of materials in the hoist system.
- All details can be seen in Fung et al. [35].

- j = Index of Material types.
- l = Index of a building’s floor used for material storage as supply sources.
- k = Index of storage cells on building floors.
- m = Index of a building floor requesting the materials.
- J = The total number of material.
- L = The total number of floors for storage.
- K = The total number of cells on the building level’s.
- M = The total number of levels.
- ${Q}_{j,m}$ = Floor m’s demand in a building for material type j.
- ${C}_{j}^{h}$ = Cost of horizontal unit transportation of material type j.
- ${C}_{j,l}^{v}$ = Cost of vertical unit transportation of material type j to a building’s floor l from the ground.
- ${C}_{j,m}^{v}$ = Cost of vertical unit transportation of material type j to a building’s floor m from the ground.
- ${D}_{l,k}$ = Distance from the material hoist on level l to cell k.
- ${x}_{j,l,k}$ = Binary decision variable for storing material j on level l inside cell k.
- ${\delta}_{j,k,l,m}$ = Auxiliary binary-type variable where one means material j is transferred from floor l cell k to floor m, otherwise zero.

#### 5.4. Case Study 3

#### 5.5. Managerial Implication

## 6. Conclusions and Future Research

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Facility | Facility | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |

1 | 0 | 5 | 2 | 2 | 1 | 1 | 4 | 1 | 2 | 9 | 1 |

2 | 5 | 0 | 2 | 5 | 1 | 2 | 7 | 8 | 2 | 3 | 8 |

3 | 2 | 2 | 0 | 7 | 4 | 4 | 9 | 4 | 5 | 6 | 5 |

4 | 2 | 5 | 7 | 0 | 8 | 7 | 8 | 1 | 8 | 5 | 1 |

5 | 1 | 1 | 4 | 8 | 0 | 3 | 4 | 1 | 3 | 3 | 6 |

6 | 1 | 2 | 4 | 7 | 3 | 0 | 5 | 8 | 4 | 7 | 5 |

7 | 4 | 7 | 9 | 8 | 4 | 5 | 0 | 7 | 6 | 3 | 2 |

8 | 1 | 8 | 4 | 1 | 1 | 8 | 7 | 0 | 9 | 4 | 8 |

9 | 2 | 2 | 5 | 8 | 3 | 4 | 6 | 9 | 0 | 5 | 3 |

10 | 9 | 3 | 6 | 5 | 3 | 7 | 3 | 4 | 5 | 0 | 5 |

11 | 1 | 8 | 5 | 1 | 6 | 5 | 2 | 8 | 3 | 5 | 0 |

Location | Location | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |

1 | 0 | 15 | 25 | 33 | 40 | 42 | 47 | 55 | 35 | 30 | 20 |

2 | 15 | 0 | 10 | 18 | 25 | 27 | 32 | 42 | 50 | 45 | 35 |

3 | 25 | 10 | 0 | 8 | 15 | 17 | 22 | 32 | 52 | 55 | 45 |

4 | 33 | 18 | 8 | 0 | 7 | 9 | 14 | 24 | 44 | 49 | 53 |

5 | 40 | 25 | 15 | 7 | 0 | 2 | 7 | 17 | 37 | 42 | 52 |

6 | 42 | 27 | 17 | 9 | 2 | 0 | 5 | 15 | 35 | 40 | 50 |

7 | 47 | 32 | 22 | 14 | 7 | 5 | 0 | 10 | 30 | 35 | 40 |

8 | 55 | 42 | 32 | 24 | 17 | 15 | 10 | 0 | 20 | 25 | 35 |

9 | 35 | 50 | 52 | 44 | 37 | 35 | 30 | 20 | 0 | 5 | 15 |

10 | 30 | 45 | 55 | 49 | 42 | 40 | 35 | 25 | 5 | 0 | 10 |

11 | 20 | 35 | 45 | 53 | 52 | 50 | 40 | 35 | 15 | 10 | 0 |

Algorithms | Best | Average | Worst | Standard Deviation | Best–Average | Best–Worst | Average Time |
---|---|---|---|---|---|---|---|

PSO | 12,546 | 12,581.24 | 12,984 | 79.02 | 0.281% | 3.491% | 0.062 |

DE | 12,546 | 12,561.88 | 12,760 | 47.36 | 0.127% | 1.706% | 0.085 |

SOS | 12,546 | 12,560.56 | 12,792 | 42.52 | 0.116% | 1.961% | 0.075 |

HSOS-LO | 12,546 | 12,553.86 | 12,672 | 19.37 | 0.063% | 1.004% | 0.084 |

Metaheuristic | Results | Best Layout | Parameters | ||||
---|---|---|---|---|---|---|---|

Algorithms | Best | Average | Standard Deviation | F1–F11 | pop_size | maxIter | maxFE |

GA [34] | 15,090 | N/A | N/A | 11 5 8 7 2 9 3 1 6 4 10 | 100 | 90 | 9,000 |

Multi-searching TS [14] | 12,880 | N/A | N/A | 8 11 5 7 9 3 6 1 2 4 10 | N/A | N/A | N/A |

CBO [37] | 12,546 | 12,558 | 45.51 | 9 11 5 6 7 4 3 1 2 8 10 | 50 | 200 | 10,000 |

ECBO [37] | 12,546 | 12,555 | 32.11 | 9 11 5 6 7 4 3 1 2 8 10 | 50 | 200 | 10,000 |

SOS * | 12,546 | 12,560.56 | 42.52 | 9 11 5 6 7 4 3 1 2 8 10 | 50 | 30 | 3000 |

HSOS-LO * | 12,546 | 12,553.86 | 19.37 | 9 11 5 6 7 4 3 1 2 8 10 | 50 | 20 | 3000 |

Algorithms | Best | Average | Worst | Standard Deviation | Best–Average | Best–Worst | Average Time |
---|---|---|---|---|---|---|---|

PSO | 4,288,196 | 4,288,533.60 | 4,290,468 | 423.14 | 0.008% | 0.053% | 0.562 |

DE | 4,287,996 | 4,288,302.56 | 4,288,988 | 211.98 | 0.007% | 0.023% | 0.385 |

SOS | 4,288,196 | 4,288,196 | 4,288,196 | 0.00 | 0.000% | 0.000% | 0.294 |

HSOS-LO | 4,287,996 | 4,288,083.12 | 4,288,196 | 61.30 | 0.002% | 0.005% | 0.492 |

Optimized Storage Location (Floor, Cell) | |||
---|---|---|---|

Material Type | GA [35] | MIP [38] | HSOS-LO * |

1 | (5,1) | (3,1) | (1,1) |

2 | (6,1) | (4,5) | (2,1) |

3 | (2,1) | (1,5) | (1,3) |

4 | (7,1) | (3,5) | (2,2) |

5 | (1,1) | (1,1) | (1,2) |

6 | (7,5) | (2,5) | (1,4) |

7 | (6,5) | (2,1) | (1,5) |

8 | (1,5) | (4,1) | (2,3) |

9 | (4,1) | (5,1) | (2,4) |

10 | (5,5) | (5,5) | (2,5) |

Total cost ($) | 4,562,620 | 4,293,020 | 4,287,996 |

Facility | Facility | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |

1 | 0 | 10 | 8 | 9 | 3 | 9 | 0 | 0 | 0 | 0 |

2 | 10 | 0 | 8 | 12 | 8 | 9 | 11 | 5 | 0 | 1 |

3 | 8 | 8 | 0 | 4 | 3 | 8 | 0 | 0 | 0 | 0 |

4 | 9 | 12 | 4 | 0 | 6 | 15 | 10 | 10 | 8 | 5 |

5 | 3 | 8 | 3 | 6 | 0 | 9 | 5 | 3 | 2 | 1 |

6 | 9 | 9 | 8 | 15 | 9 | 0 | 0 | 0 | 0 | 0 |

7 | 0 | 11 | 0 | 10 | 5 | 0 | 0 | 7 | 7 | 10 |

8 | 0 | 5 | 0 | 10 | 3 | 0 | 7 | 0 | 25 | 27 |

9 | 0 | 0 | 0 | 8 | 2 | 0 | 7 | 25 | 0 | 16 |

10 | 0 | 1 | 0 | 5 | 1 | 0 | 10 | 27 | 16 | 0 |

Location | Location | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |

1 | 0 | 139 | 156 | 33 | 39 | 49 | 139 | 170 | 174 | 150 |

2 | 139 | 0 | 19 | 106 | 100 | 112 | 128 | 160 | 165 | 188 |

3 | 156 | 19 | 0 | 125 | 119 | 131 | 112 | 144 | 148 | 207 |

4 | 33 | 106 | 125 | 0 | 12 | 23 | 111 | 143 | 147 | 123 |

5 | 39 | 100 | 119 | 12 | 0 | 12 | 99 | 131 | 135 | 111 |

6 | 49 | 112 | 131 | 23 | 12 | 0 | 89 | 121 | 125 | 101 |

7 | 138 | 128 | 112 | 111 | 99 | 89 | 0 | 32 | 36 | 104 |

8 | 170 | 160 | 144 | 143 | 131 | 121 | 32 | 0 | 9 | 42 |

9 | 174 | 165 | 148 | 147 | 135 | 125 | 36 | 9 | 0 | 102 |

10 | 150 | 188 | 207 | 123 | 111 | 101 | 104 | 42 | 102 | 0 |

Metaheuristic | Results | Best Layout | Parameters | |||
---|---|---|---|---|---|---|

Algorithms | Best | Average | Standard Deviation | F1–F10 | pop_size | maxIter |

PSO [36] | 39184 | 39327.07 | 303.011 | 2 6 3 4 5 1 10 7 9 8 | 30 | 30 |

ABC [36] | 39184 | 41733.77 | 2013.849 | 2 6 3 4 5 1 10 7 9 8 | 30 | 30 |

SOS [36] | 39184 | 39243.40 | 274.206 | 2 6 3 4 5 1 10 7 9 8 | 30 | 30 |

HSOS-LO * | 39184 | 39184 | 0 | 2 6 3 4 5 1 10 7 9 8 | 30 | 30 |

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## Share and Cite

**MDPI and ACS Style**

Prayogo, D.; Cheng, M.-Y.; Wu, Y.-W.; Redi, A.A.N.P.; Yu, V.F.; Persada, S.F.; Nadlifatin, R.
A Novel Hybrid Metaheuristic Algorithm for Optimization of Construction Management Site Layout Planning. *Algorithms* **2020**, *13*, 117.
https://doi.org/10.3390/a13050117

**AMA Style**

Prayogo D, Cheng M-Y, Wu Y-W, Redi AANP, Yu VF, Persada SF, Nadlifatin R.
A Novel Hybrid Metaheuristic Algorithm for Optimization of Construction Management Site Layout Planning. *Algorithms*. 2020; 13(5):117.
https://doi.org/10.3390/a13050117

**Chicago/Turabian Style**

Prayogo, Doddy, Min-Yuan Cheng, Yu-Wei Wu, A. A. N. Perwira Redi, Vincent F. Yu, Satria Fadil Persada, and Reny Nadlifatin.
2020. "A Novel Hybrid Metaheuristic Algorithm for Optimization of Construction Management Site Layout Planning" *Algorithms* 13, no. 5: 117.
https://doi.org/10.3390/a13050117