Evaluating Typical Algorithms of Combinatorial Optimization to Solve Continuous-Time Based Scheduling Problem

Lazarev, Alexander A.; Nekrasov, Ivan; Pravdivets, Nikolay

doi:10.3390/a11040050

Cited by 4 publications

(2 citation statements)

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“…The paper [4] is devoted to a formalization of the resource-constrained project scheduling problem (RCPSP) in terms of combinatorial optimization theory. The transformation of the original RCPSP into a combinatorial setting is based on interpreting each operation as an atomic entity that has a defined duration and has to reside on the continuous time axis meeting additional restrictions.…”

Section: Special Issuementioning

confidence: 99%

Special Issue on Algorithms for Scheduling Problems

2018

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This special issue of Algorithms is devoted to the development of scheduling algorithms based on innovative approaches for solving hard scheduling problems either exactly or approximately. Submissions were welcome both for traditional scheduling problems as well as for new practical applications. The main topics include sequencing and scheduling with additional constraints (setup times or costs, precedence constraints, resource constraints, and batch production environment) and production planning and scheduling problems arising in real-world applications.

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Section: Special Issuementioning

confidence: 99%

Special Issue on Algorithms for Scheduling Problems

2018

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“…Scheduling theory is a branch of discrete optimization devoted to planning operations over time. The problems of scheduling theory are diverse, including, but not limited to, production scheduling, including human-robot collaborations [1], classical Resource-Constrained Project Scheduling Problem (RCPSP) [2], creating smart planning eco-systems [3], distributed scheduling problems [4], and dynamic systems [5]. However, classical problems for a single machine remain relevant, still capture the attention of the scientific community [6] and are also used in modern approaches of Industry 4.0 [7].…”

Section: Introductionmentioning

confidence: 99%

Approximation of the Objective Function of Single-Machine Scheduling Problem

Lazarev,

Pravdivets,

Barashov

2024

Mathematics

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The problem of the approximation of the coefficients of the objective function of a scheduling problem for a single machine is considered. It is necessary to minimize the total weighted completion times of jobs with unknown weight coefficients when a set of problem instances with known optimal schedules is given. It is shown that the approximation problem can be reduced to finding a solution to a system of linear inequalities for weight coefficients. For the case of simultaneous job release times, a method for solving the corresponding system of inequalities has been developed. Based on it, a polynomial algorithm for finding values of weight coefficients that satisfy the given optimal schedules was constructed. The complexity of the algorithm is O(n2(N+n)) operations, where n is the number of jobs and N is the number of given instances with known optimal schedules. The accuracy of the algorithm is estimated by experimentally measuring the function ε(N,n)=1n∑j=1n∣wj−wj0∣wj0, which is an indicator of the average modulus of the relative deviation of the found values wj from the true values wj0. An analysis of the results shows a high correlation between the dependence ε(N,n) and a function of the form α(n)/N, where α(n) is a decreasing function of n.

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