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Dual Variable Stabilization (DVS)Dynamic Constraint Aggregation (DCA)Stabilized Dynamic Constraint Aggregation (SDCA)SDCA: Dual variable disaggregation19/27Define β s l,i :=i∑πl,j s ,j=1∀l ∈ L, i ∈ {1, . . . , |T l|}.The system of difference inequalities takes into account, for eachconstraint t ∈ T , the trust region carried out by the δ-parameters.β s l,|T l | = πs Q,l ,∀l ∈ Lβ s l,i − βs l,i−1 ≥ δs −,t, ∀t = (l, i) ∈ T such that y s −,t = 0βl,i s − βs l,i−1 = δs −,t, ∀t = (l, i) ∈ T such that 0 < y−,t s < ε s −,tβl,i s − βs l,i−1 ≤ δs −,t, ∀t = (l, i) ∈ T such that y−,t s = ε s −,tβl,i s − βs l,i−1 ≤ δs +,t, ∀t = (l, i) ∈ T such that y+,t s = 0β s l,i − βs l,i−1 = δs +,t,β s l,i − βs l,i−1 ≥ δs +,t,∀t = (l, i) ∈ T such that 0 < y+,t s < ε s +,t∀t = (l, i) ∈ T such that y+,t s = ε s +,t.Still solvable as a shortest path problem.
Dual Variable Stabilization (DVS)Dynamic Constraint Aggregation (DCA)Stabilized Dynamic Constraint Aggregation (SDCA)Results-3: DVS vs. SDCA20/27SDCA2500major iterations1 10 20 30 40420002cpu (sec.)150010000-2-4-6distance to optimal value500-800 50 100 150 200 250 300 350minor iterations-10cpu RMPcpu SPobjectiveFigure: SDCA for a 2500-task, 5-day scenario
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