Branch, bound and remember algorithm for U-shaped assembly line balancing problem

Abstract

This research develops a branch, bound and remember algorithm to address U-shaped assembly line balancing problem. This method proposes a cyclic best-first search strategy which uses memory to preserve searched sub-problems and eliminate redundancy. As the search space in U-shaped assembly lines is much larger than that in simple assembly lines, the search process is easily terminated due to out of memory issue when solving large-size problems. The proposed method employs several improvements, including two new dominance rules, renumbering the tasks when generating the station loads, a new criterion to select the most promising sub-problem and limiting the number of sub-problems at each depth. The proposed methodology is tested on Scholl's well-known 269 benchmark problems and a new data set published in 2013, where backtracking rule is also applied to save memory. Computational comparative study demonstrates that the proposed method outperforms the two current best exact methods (ULINO and branch, price and remember algorithm) by achieving 259 optimal solutions for Scholl's well-known 269 benchmark problems. The proposed method also outperforms the current best branch, price and remember algorithm by optimally solving over 97% of the problems in the new data set.