Resource Management in Machine Scheduling Problems: A Survey

Abstract

Abstract. The paper is a survey devoted to job scheduling problems with resource allocation. We present the results available in the scientific literature for commonly used models of job processing times and job release dates, i.e., the models in which the job processing time or the job release date is given as a linear or convex function dependent on the amount of the additional resource allotted to the job. The scheduling models with resource dependent processing times or resource dependent release dates extend the classical scheduling models to reflect more precisely scheduling problems that appear in real life. Thus, in this paper we present the computational complexity results and solution algorithms that have been developed for this kind of problems.

GPU computing in discrete optimization. Part II: Survey focused on routing problems

“…This mapping can either be an explicit formula (Luong et al [62], Burke and Riise [12], Coelho et al [20], Rocki and Suda [77], Schulz [82]) or an algorithm (Luong et al [62]). Alternatively, it can be a pre-generated explicit mapping that lies in the GPU memory as investigated by Janiak et al [40], and Schulz [82]. The advantage of the mapping approach is that there is no need for copying any information to the GPU on each iteration.…”

“…The paper by Janiak et al [40] applies Tabu search also to the Permutation Flowshop Scheduling Problem (PFSP) with the Makespan criterion. Their work on the PFSP was continued by Czapinski & Barnes in [24].…”

“…Coelho et al [20] Geforce GTX 560 Ti 17 own Rocki and Suda [77] a.o. Geforce GTX 680 27 32 cores Schulz [82] GeForce GTX 480 [40] i x Luong et al [62] -/i x -/x O'Neil et al [70] i x x x Burke and Riise [12] i x Coelho et al [20] i x x Schulz [82] i x x x Table 5: Tasks performed on the GPU during one iteration. Legend: Nbh -neighborhood; gen. -generation; eval.…”

“…Table 4 provides an overview of the routing related GPU papers using some kind of local search. The earliest by Janiak et al [40] utilizes the graphics pipeline for tabu search by providing a fragment shader that evaluates the whole neighborhood in a one fragment per move fashion. The remaining steps of the search were performed on the CPU.…”

“…Year Problem Algorithm Neighborhood Janiak et al [40] 2008 TSP TS 2-exchange (swap) Luong et al [62] 2011 TSP LS 2-exchange (swap) O'Neil et al [70] 2011 TSP MS-LS 2-opt Burke and Riise [12] 2012 TSP ILS VND: 2-opt + relocate Coelho et al [20] 2012 SVRPDSP VNS swap + relocate Rocki and Suda [77] 2012 TSP (LS) 2-opt, 3-opt Schulz [82] 2013 DCVRP LS 2-opt, 3-opt Author Approach Janiak et al [40] Graphics pipeline: move evaluation by fragment shader Luong et al [62] CUDA O'Neil et al [70] CUDA: multiple-ls-per-thread, load balancing Burke and Riise [12] CUDA: one-move-per-thread, applies several independent moves at once Coelho et al [20] CUDA: one-move-per-thread Rocki and Suda [77] CUDA: several-moves-per-thread Schulz [82] CUDA: one-move-per-thread, asynchronous execution, very large nbhs Author GPU(s) Max. Speedup CPU code Janiak et al [40] GeForce 8600 GT 1.12 C# Luong et al [62] a.o.…”