List scheduling algorithms to minimize the makespan on identical parallel machines

Mokotoff, Ethel; Jimeno, José L.; Gutiérrez, Ana Isabel

doi:10.1007/bf02579085

Cited by 17 publications

(12 citation statements)

References 19 publications

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“…There is a significant amount of literature on approximation algorithms for the multi-way partition problem. See, for example, Mokotoff and Gutiérrez (2001), , Chen (2004), andDell'Amico et al (2008). Nonetheless, we found the following two simple approximation algorithms to be sufficient for our purposes.…”

Section: Polynomial-time Approximation Algorithms (Upper Bounds)mentioning

confidence: 86%

Optimal Multi-Way Number Partitioning

Schreiber

Korf

Moffitt

2018

J. ACM

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The NP-hard number-partitioning problem is to separate a multiset S of n positive integers into k subsets such that the largest sum of the integers assigned to any subset is minimized. The classic application is scheduling a set of n jobs with different runtimes on k identical machines such that the makespan, the elapsed time to complete the schedule, is minimized. The two-way number-partitioning decision problem is one of the original 21 problems that Richard Karp proved NP-complete. It is also one of Garey and Johnson's six fundamental NP-complete problems and the only one based on numbers. This article explores algorithms for solving multi-way number-partitioning problems optimally. We explore previous algorithms as well as our own algorithms, which fall into three categories: sequential number partitioning (SNP), a branch-and-bound algorithm; binary-search improved bin completion (BSIBC), a bin-packing algorithm; and cached iterative weakening (CIW), an iterative weakening algorithm. We show experimentally that, for large random numbers, SNP and CIW are state-of-the-art algorithms depending on the values of n and k. Both algorithms outperform the previous state of the art by up to seven orders of magnitude in terms of runtime.

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Section: Polynomial-time Approximation Algorithms (Upper Bounds)mentioning

confidence: 86%

Optimal Multi-Way Number Partitioning

Schreiber

Korf

Moffitt

2018

J. ACM

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“… P ≤ S . Allocating the data to the processors can find its solution from a well-studied list scheduling problem ( 27 , 28 ), the heuristic solution to which is to iteratively assign an unassigned job to the processor that currently owns the least load until all jobs have been allocated.…”

Section: Computational Cost Analysis and Parallelizationmentioning

confidence: 99%

Dijkstra’s-DBSCAN: Fast, Accurate, and Routable Density Based Clustering of Traffic Incidents on Large Road Network

Zhang

Lee

Kim

2018

Transportation Research Record

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Incident hotspots are used as a direct indicator of the needs for road maintenance and infrastructure upgrade, and an important reference for investment location decisions. Previous incident hotspot identification methods are all region based, ignoring the underlying road network constraints. We first demonstrate how region based hotspot detection may be inaccurate. We then present Dijkstra’s-DBSCAN, a new network based density clustering algorithm specifically for traffic incidents which combines a modified Dijkstra’s shortest path algorithm with DBSCAN (density based spatial clustering of applications with noise). The modified Dijkstra’s algorithm, instead of returning the shortest path from a source to a target as the original algorithm does, returns a set of nodes (incidents) that are within a requested distance when traveling from the source. By retrieving the directly reachable neighbors using this modified Dijkstra’s algorithm, DBSCAN gains its awareness of network connections and measures distance more practically. It avoids clustering incidents that are close but not connected. The new approach extracts hazardous lanes instead of regions, and so is a much more precise approach for incident management purposes; it reduces the [Formula: see text] computational cost to [Formula: see text], and can process the entire U.S. network in seconds; it has routing flexibility and can extract clusters of any shape and connections; it is parallellable and can utilize distributed computing resources. Our experiments verified the new methodology’s capability of supporting safety management on a complicated surface street configuration. It also works for customized lane configuration, such as freeways, freeway junctions, interchanges, roundabouts, and other complex combinations.

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“…The proposed approach shows a comparable result to GRASP in terms of solution quality and computation time. Mokotoff [21] shows that minimizing makespan for identical parallel BPM can be done with a new approximation algorithm based on Linear Programming (LP). The MSKP heuristic in [39] was extended by Damodaran et al [40] to identical parallel BPM and named it as Progressive Successive Knapsack Problem (PSKP).…”

Section: Single Batch Processing Machine Environmentmentioning

confidence: 99%

Lagrangian approach to minimize makespan of non-identical parallel batch processing machines

Suhaimi

Nguyen

Damodaran

2016

Computers & Industrial Engineering

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Batch Processing Machines (BPMs) are commonly used in electronics manufacturing, semi-conductor manufacturing, and metal-working -to name a few. Scheduling these machines are not an easy task; practical considerations and the exponential number of decision variables involved impede schedulers (or decision makers) from making good decisions. This research focuses on minimizing the makespan of a set of non-identical parallel batch processing machines. In order to schedule jobs on these machines, two decisions are to be made. The first decision is to group jobs to form batches such that the machine capacity is not exceeded. The second decision is to sequence the batches formed on the machines such that the makespan is minimized. Both the decisions are intertwined as the processing time of the batch is determined by the composition of the jobs in the batch. The problem under study is shown to be NP-hard. A mathematical model from the literature is adopted to develop a solution approach which would help the decision maker to make meaningful decisions.Lagrangian Relaxation approach has been shown to be very effective in solving scheduling problems. Using this decomposition approach, the mathematical model is decomposed and a sub-gradient approach was used to update the multipliers. Two sets of constraints were relaxed to consider two Lagrangian Relaxation models. Experiments were conducted with data sets from the literature. The solution quality of the proposed approach was compared with meta-heuristic (i.e. Particle Swarm Optimization (PSO) and Random Key Genetic Algorithm (RKGA)) published in the literature and a commercial solver (i.e. IBM ILOG CPLEX). On smaller instances (i.e. 10 and 20 jobs), the proposed approach outperformed PSO and RKGA. However, the proposed approach and CPLEX report the same results. On larger instances (i.e. 50, 100 and 200 job instances) with two and four-machines, the proposed approach was better than PSO whenever the variability in the processing times were smaller. The proposed approach generally outperformed RKGA and CPLEX on larger problem instances. Out of 200 experiments conducted, the proposed approach helped to find new improved solution on 34 instances and comparable on 105 instances when compared to PSO. The PSO approach was much faster than all other approaches on larger problem instances. The experimental study clearly identifies the problem instances on which the proposed approach can find a better solution. The proposed Lagrangian Relaxation solution approach helps the schedulers to make more informed decisions. Minor modifications can be made to use the proposed solution approach for other practical considerations (e.g. job ready times, tardiness objective, etc.) The main contribution of this research is the proposed solution approach which is effective in solving a class of non-identical batch processing machine problems with better solution quality when compared to existing meta-heuristic. NORTHERN

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List scheduling algorithms to minimize the makespan on identical parallel machines

Abstract: Approximate algorithms, scheduling, list scheduling, 90B35,

Cited by 17 publications

References 19 publications

Optimal Multi-Way Number Partitioning

Optimal Multi-Way Number Partitioning

Dijkstra’s-DBSCAN: Fast, Accurate, and Routable Density Based Clustering of Traffic Incidents on Large Road Network

Lagrangian approach to minimize makespan of non-identical parallel batch processing machines

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