Multi-Objective Optimization for Selecting and Scheduling - PowerPoint PPT Presentation

Multi-Objective Optimization for Selecting and Scheduling Observations by Agile Earth Observing Satellites Panwadee Tangpattanakul, Nicolas Jozefowiez, Pierre Lopez 13 e Congrès de la Société Française de Recherche Opérationnelle et d’Aide à la Décision (ROADEF 2012) Angers, France 11-13 Avril 2012

2 Contents • Introduction • Multi-objective photograph scheduling problem of agile Earth observing satellites • Biased random-key genetic algorithm for the multi-user photograph scheduling • Computational results • Conclusions and future works

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 3 Introduction Agile Earth observing satellites (agile EOS) • Mission: • Acquire photographs of the Earth surface, in response to observation requests from several users • Management problem: • Select and schedule a subset of photographs from a set of candidates • Properties: • Single camera • 3 degrees of freedom (roll, pitch, yaw) • Non-fixed starting time of photograph acquisition

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 4 Multi-objective photograph scheduling problem • Multi-objective • Maximize profit • Minimize the maximum profit difference between users • ensure fairness • Constraints P(x) • Time windows 1 • No overlapping images • Sufficient transition times • Each strip is acquired in only 1 direction • Stereoscopic constraint 0.4 • Profit calculation • gains 0.1 • partial acquisition 0 0.4 0.7 1 x • piecewise linear function Ref: Lemaître et al. (2002)

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 5 Multi-objective photograph scheduling problem • Selecting and scheduling of multi-user requests Requests from User 2 P4 = 8 P5 = 4 User 1 P1 = 12 P2 = 3 P3 = 6 Time • Considered objective values • Total profit • Maximum profit difference between users

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 6 Multi-objective photograph scheduling problem • Selecting and scheduling of multi-user requests Requests from User 2 P4 = 8 P5 = 4 User 1 P1 = 12 P2 = 3 P3 = 6 Time Fairness Solution 1 : (P1,P2,P3) Total profit = 21 Max difference = 21 Total profit

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 7 Multi-objective photograph scheduling problem • Selecting and scheduling of multi-user requests Requests from User 2 P4 = 8 P5 = 4 User 1 P1 = 12 P2 = 3 P3 = 6 Time Fairness Solution 1 : (P1,P2,P3) Total profit = 21 Max difference = 21 Solution 2 : (P4,P2,P3) Total profit = 17 Max difference = 1 Total profit

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 8 Multi-objective photograph scheduling problem • Selecting and scheduling of multi-user requests Requests from User 2 P4 = 8 P5 = 4 User 1 P1 = 12 P2 = 3 P3 = 6 Time Fairness Solution 1 : (P1,P2,P3) Total profit = 21 Max difference = 21 Solution 2 : (P4,P2,P3) Total profit = 17 Max difference = 1 Solution 3 : (P1,P2,P5) Total profit = 19 Max difference = 11 Total profit

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 9 Multi-objective photograph scheduling problem • Selecting and scheduling of multi-user requests Requests from User 2 P4 = 8 P5 = 4 User 1 P1 = 12 P2 = 3 P3 = 6 Time Max difference Solution 1 : (P1,P2,P3) Total profit = 21 Max difference = 21 Solution 2 : (P4,P2,P3) Total profit = 17 Max difference = 1 Solution 3 : (P1,P2,P5) Total profit = 19 Max difference = 11 Total profit Solution 4 : (P4,P2,P5) Total profit = 15 Max difference = 9

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 10 Multi-objective photograph scheduling problem • Multi-objective optimization problem

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 11 Multi-objective photograph scheduling problem Pareto dominance (maximize , minimize ) A solution dominates (denoted ) a solution if E D B C A : total profit : maximum profit difference between users

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 12 BRKGA for the multi-user photograph scheduling • Genetic algorithm Initialisation Pareto front Evaluation Parents Selection Stop? Replacement Genitors Generations Crossover Evaluation Offspring Mutation Ref: http://eodev.sourceforge.net/eo/tutorial/html/eoTutorial.html

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 13 BRKGA for the multi-user photograph scheduling • Biased random-key genetic algorithm (BRKGA) ELITE ELITE X POPULATION CROSSOVER OFFSPRING NON-ELITE MUTANT Generation i Generation i+1 Ref: Gonçalves et al. (2011)

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 14 BRKGA for the multi-user photograph scheduling • Encoding • One chromosome for one solution • Number of genes is two times the number of strips • Each gene represents one strip acquisition • By real values randomly generated in the interval (0,1] • Example: 2 strips (strip 0 and strip 1) • Each chromosome in population Stp0 Dir0 Stp0 Dir1 Stp1 Dir0 Stp1 Dir1 Index 0 Index 1 Index 2 Index3 0.6984 0.9939 0.6885 0.2509

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 15 BRKGA for the multi-user photograph scheduling • Decoding

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 16 BRKGA for the multi-user photograph scheduling • Two methods for choosing preference chromosomes • Dominance-based (Fast nondominated sorting and crowding distance assignment) • Fast nondominated sorting (find the solution in rank zero) • Crowding distance assignment (limit the size of elite set) • Indicator-based (Indicator based on the hypervolume concept) • Assign fitness values to the population members • Select some solutions to become elite set by repeat • removing the worst solution • updating the fitness values of remaining solutions until the remaining solution satisfies the elite set size Ref: Deb et al. (2002) and Zitzler et al. (2004)

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 17 Computational results • Instances: 4-users modified ROADEF 2003 challenge instances (Subset A) • Stopping criterion: Number of iterations of the last archive set improvement • Parameters setting: • Language: C++ • Number of runs/instances: 10

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 18 Computational results

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 19 Computational results

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 20 Computational results • Compare the results from population size n and 2n: • Compare the results from dominance-based and indicator based:

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 21 Conclusions and future works • Conclusions • The multi-objective optimization is applied to solve the problem of selecting and scheduling the observations of agile Earth observing satellites. • The instances of ROADEF 2003 challenge are modified to 4 user requirements. • Two objective functions are considered: • Maximize the total profit • Minimize the maximum profit difference between users (fairness of resource sharing) • A biased random-key genetic algorithm (BRKGA) is applied to solve this problem. • Two methods are used for selecting the elite set: • Dominance-based • Indicator-based • The approximate solutions are obtained, but the computation time for large instances are quite high.

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions 22 Conclusions and future works • Future works • Use the other random-key decoding methods (in order to reduce the computation times) • Use an indicator-based multi-objective local search (IBMOLS) • Compare the results between BRKGA and IBMOLS

23 Thank you for your attention. Questions and suggestions?