A scalable parallel implementation of the Cluster Benders Decomposition algorithm

Benders Decomposition (BD) is a method used to solve stochastic linear problems via scenario analysis. Cluster BD (CBD) is one of its smart improvements that speed up the execution time, taking advantage of tighter feasible cuts found by grouping scenarios into clusters. In this paper, we propose a new design for CBD, one which takes into account the role played by optimal cuts in the solution. Besides, we propose a new parallel scheme for CBD to deal with large-scale two-stage stochastic linear problems. Moreover, we characterise the problems for which our proposal performs best. The results obtained show computational gains from our proposal compared with the plain use of CPLEX, serial BD, parallel BD, serial CBD and parallel CBD.