New dominance rules and exploration strategies for the 1|r i |∑U i scheduling problem

Abstract

The paper proposes a new exact approach, based on a Branch, Bound, and Remember (BB&R) algorithm that uses the Cyclic Best First Search (CBFS) strategy, for the 1|r i | U i scheduling problem, a single machine scheduling problem, where the objective is to find a schedule with the minimum number of tardy jobs. The search space is reduced using new and improved dominance properties and tighter upper bounds, based on a new dynamic programming algorithm. Computational results establish the effectiveness of the BB&R algorithm with CBFS for a broad spectrum of problem instances. In particular, this algorithm was able to solve all problems instances, up to 300 jobs, while existing best known algorithms only solve problems instances up to 200 jobs. Furthermore, the BB&R algorithm with CBFS runs one to two orders of magnitude faster than the current best known algorithm on comparable instances.

A Branch, Bound, and Remember Algorithm for the Simple Assembly Line Balancing Problem

“…Kao et al (2009Kao et al ( , 2011 and Sewell et al (2009) demonstrate its effectiveness on a variety of single-machine scheduling problems. Hall et al (2008) also use branch, bound, and remember on a vaccine formulary design problem.…”

“…The cyclic best-first search (CBFS) is a new search strategy (Kao et al , 2011Sewell et al 2009) that is a hybrid between DFS and BFS (note that CBFS was formerly called distributed best-first search in Kao et al 2009). CBFS begins by choosing the best subproblem at depth 1.…”

“…This heuristic was able to find the optimal solution for 223 of the 269 benchmark problems (without proving optimality) while requiring far less time than the Beam-ACO algorithm or Bautista and Pereira's dynamic programming heuristic. Second, in the second phase it uses a cyclic best-first search (CBFS) exploration strategy , Kao et al 2011) that finds the optimal solution of the remaining 46 problems very quickly. Third, it uses a BB&R algorithm to efficiently compute a bin packing lower bound.…”