Solving Parallel Machine Scheduling Problems with Variable Depth Local Search

We present new local search heuristic for the parallel machine total weighted completion time scheduling problem. Our algorithm is a local search method based on combining a variable number of insertion moves. We develop an efficient heuristic for finding a sequence of profitable insertion moves. In a computational study we compare the performance of new and old neighborhoods and various search frameworks including steepest descent, multistart tabu search, and iterated local search. Experimental results show that a version of the new variable depth sequential insertions neighborhood implemented within an iterated local search framework is the most effective heuristic among the ones we implemented.

[1]  Wayne E. Smith.  Various optimizers for single‐stage production , 1956 .

[2]  William L. Maxwell,et al.  Theory of scheduling , 1967 .

[3]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[4]  Edward G. Coffman,et al.  Scheduling independent tasks to reduce mean finishing time , 1974, CACM.

[5]  Jan Karel Lenstra,et al.  Complexity of machine scheduling problems , 1975 .

[6]  J. J. Brennan,et al.  An Improved Algorithm for Scheduling Jobs on Identical Machines , 1977 .

[7]  John Baxter,et al.  Local Optima Avoidance in Depot Location , 1981 .

[8]  Seiki Kyan,et al.  Worst Case Bound of an LRF Schedule for the Mean Weighted Flow-Time Problem , 1986, SIAM J. Comput..

[9]  Fred W. Glover,et al.  Future paths for integer programming and links to artificial intelligence , 1986, Comput. Oper. Res..

[10]  James B. Orlin,et al.  Theory of cyclic transfers , 1989 .

[11]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[12]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[13]  Edward W. Felten,et al.  Large-Step Markov Chains for the Traveling Salesman Problem , 1991, Complex Syst..

[14]  Edward W. Felten,et al.  Large-step markov chains for the TSP incorporating local search heuristics , 1992, Oper. Res. Lett..

[15]  M. Laguna,et al.  SOLVING THE MULTIPLE-MACHINE WEIGHTED FLOW TIME PROBLEM USING TABU SEARCH , 1993 .

[16]  Chris N. Potts,et al.  Scheduling Identical Parallel Machines to Minimize Total Weighted Completion Time , 1994, Discret. Appl. Math..

[17]  Helena Ramalhinho Dias Lourenço,et al.  Job-shop scheduling: Computational study of local search and large-step optimization methods , 1995 .

[18]  Scott Webster,et al.  Weighted flow time bounds for scheduling identical processors , 1995 .

[19]  Yves Crama,et al.  Local Search in Combinatorial Optimization , 2018, Artificial Neural Networks.

[20]  Helena Ramalhinho Dias Lourenço,et al.  Combining the Large-Step Optimization with Tabu-Search: Application to The Job-Shop Scheduling Problem , 1996 .

[21]  Peter Brucker,et al.  Improving Local Search Heuristics for Some Scheduling Problems-I , 1996, Discret. Appl. Math..

[22]  Peter Brucker,et al.  Improving Local Search Heuristics for some Scheduling Problems. Part II , 1996, Discret. Appl. Math..

[23]  Warren B. Powell,et al.  Solving Parallel Machine Scheduling Problems by Column Generation , 1999, INFORMS J. Comput..

[24]  Han Hoogeveen,et al.  Parallel Machine Scheduling by Column Generation , 1999, Oper. Res..

[25]  Gerhard J. Woeginger,et al.  A study of exponential neighborhoods for the Travelling Salesman Problem and for the Quadratic Assignment Problem , 2000, Math. Program..

[26]  Waleed Meleis,et al.  An Experimental Study of Algorithms for Weighted Completion Time Scheduling , 2002, Algorithmica.

[27]  Abraham P. Punnen,et al.  A survey of very large-scale neighborhood search techniques , 2002, Discret. Appl. Math..

[28]  Chris N. Potts,et al.  An Iterated Dynasearch Algorithm for the Single-Machine Total Weighted Tardiness Scheduling Problem , 2002, INFORMS J. Comput..

[29]  James B. Orlin,et al.  Creating very large scale neighborhoods out of smaller ones by compounding moves , 2006, J. Heuristics.