MakespanMinimizing Heterogeneous Task Allocation under Temporal Constraints
Abstract
:1. Introduction
2. Problem Statement
2.1. Heterogeneous MultiUAV System and Temporal Constraints
2.2. Problem Formulation
3. Loitering Time and Penalty Value Calculation
3.1. Temporal Constraints
3.2. Loitering Time Calculation Method
3.3. Penalty Value Calculation
4. Modification of Existing Heuristic Algorithms for the Constrained Task Allocation
4.1. The Sequential Greedy Algorithm
Algorithm 1 Sequential Greedy Algorithm 

4.2. The Genetic Algorithm
4.3. Simulated Annealing
5. The Rebalancing Algorithm
5.1. Algorithm Structure
5.2. The Initial Allocation Step
Algorithm 2 Initial Allocation 

5.3. The Rebalancing Step
Algorithm 3 Rebalancing 

6. Numerical Simulation
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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UAV  Camera  Thermal  LIDAR  

Task  
Search  0  1  0  
Fixed surv.  1  1  0  
Moving surv.  1  1  0  
Mapping  0  0  1 
#  Temporal Constraint  Algebraic Representation 

1  Task A Before Time T  ${A}^{+}<T$ 
2  Task A After Time T  ${A}^{}>T$ 
3  Task A Before Task B  ${A}^{+}<{B}^{}$ 
4  Task A After Task B  ${A}^{}>{B}^{+}$ 
5  Task A Simultaneous Task B  ${A}^{}={B}^{}$ 
6  During Task A Start Task B  ${A}^{}<{B}^{}\cap {B}^{}<{A}^{+}$ 
7  During Task A End Task B  ${A}^{}<{B}^{+}\cap {B}^{+}<{A}^{+}$ 
8  Task A Envelop Task B  ${A}^{}<{B}^{}\cap {B}^{+}<{A}^{+}$ 
Constraint 1  Constraint 2  Action 

${A}^{0}<{T}_{1}$  ${A}^{0}<{T}_{2}$  Remove “${A}^{0}<{T}_{1}$” (if ${T}_{1}<{T}_{2}$) Remove “${A}^{0}<{T}_{2}$” (if ${T}_{1}>{T}_{2}$) 
${A}^{0}>{T}_{2}$  Infeasible (if ${T}_{1}\le {T}_{2}$) No action (if ${T}_{1}>{T}_{2}$)  
${A}^{0}>{B}^{0}$  Add “${B}^{0}<{T}_{1}$”  
${A}^{0}<{B}^{0}$  No action  
${A}^{0}={B}^{0}$  Add “${B}^{0}<{T}_{1}$”  
${A}^{0}>{T}_{1}$  ${A}^{0}>{T}_{2}$  Remove “${A}^{0}>{T}_{2}$” (if ${T}_{1}<{T}_{2}$) Remove “${A}^{0}>{T}_{1}$” (if ${T}_{1}>{T}_{2}$) 
${A}^{0}>{B}^{0}$  No action  
${A}^{0}<{B}^{0}$  Add “${B}^{0}>{T}_{1}$”  
${A}^{0}={B}^{0}$  Add “${B}^{0}>{T}_{1}$”  
${A}^{0}>{B}^{0}$  ${A}^{0}<{C}^{0}$  Add “${B}^{0}<{C}^{0}$” 
${C}^{0}<{A}^{0}$  No action  
${A}^{0}={B}^{0}$  Infeasible  
${A}^{0}={C}^{0}$  Add “${B}^{0}<{C}^{0}$”  
${A}^{0}={B}^{0}$  ${A}^{0}={C}^{0}$  Add “${B}^{0}={C}^{0}$” 
${\mathit{k}}^{\mathit{th}}$ Constraint  ${\mathit{V}}_{\mathit{k}}(\mathit{P},\mathit{W})$ 

${A}^{0}<{T}_{1}$  big number (if violated) 0 (if not) 
${A}^{0}>{T}_{1}$  max(${T}_{1}{T}_{{A}^{0}},0$) 
${A}^{0}<{B}^{0}$  max(${T}_{{A}^{0}}{T}_{{B}^{0}},0$) 
${A}^{0}={B}^{0}$  $abs({T}_{{A}^{0}}{T}_{{B}^{0}})$ 
$UA{V}_{A}\ne UA{V}_{B}$  big number (if violated) 0 (if not) 
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Jeong, B.M.; Oh, Y.S.; Jang, D.S.; Hwang, N.E.; Kim, J.W.; Choi, H.L. MakespanMinimizing Heterogeneous Task Allocation under Temporal Constraints. Aerospace 2023, 10, 1032. https://doi.org/10.3390/aerospace10121032
Jeong BM, Oh YS, Jang DS, Hwang NE, Kim JW, Choi HL. MakespanMinimizing Heterogeneous Task Allocation under Temporal Constraints. Aerospace. 2023; 10(12):1032. https://doi.org/10.3390/aerospace10121032
Chicago/Turabian StyleJeong, ByeongMin, YunSeo Oh, DaeSung Jang, NamEung Hwang, JoonWon Kim, and HanLim Choi. 2023. "MakespanMinimizing Heterogeneous Task Allocation under Temporal Constraints" Aerospace 10, no. 12: 1032. https://doi.org/10.3390/aerospace10121032