Dominance rules in combinatorial optimization problems

Jouglet, Antoine; Carlier, Jacques

doi:10.1016/j.ejor.2010.11.008

Cited by 40 publications

(19 citation statements)

References 47 publications

(81 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Dominance conditions proved to be especially useful in the reduction in the size of problems when scheduling jobs on a single machine for the minimization of the weighted total tardiness [29]. A dominance rule has been informally defined by Kanet [30] as identifying a subset of solutions, which contain at least one optimal solution for a problem. According to Kanet's scheduling context [29], a dominance condition is described as a rule, which specifies that one job will precede another if certain conditions hold.…”

Section: Neural Comput and Applicmentioning

confidence: 99%

A new neuro-dominance rule for single-machine tardiness problem with double due date

Çakar

Köker

Canay

2015

Neural Comput & Applic

View full text Add to dashboard Cite

show abstract

Section: Neural Comput and Applicmentioning

confidence: 99%

A new neuro-dominance rule for single-machine tardiness problem with double due date

Çakar

Köker

Canay

2015

Neural Comput & Applic

View full text Add to dashboard Cite

show abstract

“…Dominance rules are widely applied in solution procedures for a variety of COPs [19]. Suppose that a node u = (π 1 , π 2 , .…”

Section: Dominance Rulesmentioning

confidence: 99%

Enhanced Branch-and-Bound Framework for a Class of Sequencing Problems

Zhang

Teng

Zhou

et al. 2021

IEEE Trans. Syst. Man Cybern, Syst.

View full text Add to dashboard Cite

In this paper, we propose an enhanced branch-andbound (B&B) framework for a class of sequencing problems, which aim to find a permutation of all involved elements to minimize a given objective function. We require that the sequencing problems satisfy three conditions: 1) incrementally computable; 2) monotonic; and 3) overlapping subproblems. Our enhanced B&B framework is built on the classical B&B process by introducing two techniques, i.e., dominance rules and caching search states. Following the enhanced B&B framework, we conduct empirical studies on three typical and challenging sequencing problems, i.e., quadratic traveling salesman problem, traveling repairman problem, and talent scheduling problem. The computational results demonstrate the effectiveness of our enhanced B&B framework when compared to classical B&B and some exact approaches, such as dynamic programming and constraint programming. Additional experiments are carried out to analyze different configurations of the algorithm. Index Terms-Branch-and-bound (B&B), caching states, dominance rules, dynamic programming (DP), talent scheduling problem, traveling salesman/repairman problem. I. INTRODUCTION T HE SEARCH techniques for solving combinatorial optimization problems (COPs) have been widely studied in the communities of artificial intelligence, industrial engineering, and operations research during the last century. The simplest and standard framework for solving COPs is to use branch-and-bound (B&B) algorithms [3], [8], [14]. Its basic idea is to systematically and implicitly enumerate all possible candidate solutions, where large subsets of fruitless candidates Manuscript

show abstract

“…Dominance rules have been extensively used in the past in combinatorial optimization problems and specially in scheduling problems [18]. A dominance rule is established in order to reduce the solution space either by adding new constraints to the problem, or by writing a procedure that attempts to reduce the domain of the variables, or by building interesting solutions directly.…”

Section: Dominance Rulesmentioning

confidence: 99%

Solution algorithms for minimizing the total tardiness with budgeted processing time uncertainty

Silva

Poss

Maculan

2020

European Journal of Operational Research

View full text Add to dashboard Cite

We investigate algorithms that solve exactly the robust single machine scheduling problem that minimizes the total tardiness. We model the processing times as uncertain and let them take any value in a budgeted uncertainty set. Therefore, the objective seeks to minimize the worst-case tardiness over all possible values. We compare, through computational experiments, two types of solution algorithms. The first combines classical MILP formulations with row-andcolumn generation algorithms. The second generalizes the classical branch-andbound algorithms to the robust context, extending state-of-the-art concepts used for the deterministic version of the problem. By generalizing the classical branch-and-bound algorithm we are able to assemble and discuss good algorithmic decisions steps that once put together make our robust branch-andbound case attractive. For example, we extend and adapt dominance rules to our uncertain problem, making them an important component of our robust algorithms. We assess our algorithms on instances inspired by the scientific literature and identify under what conditions an algorithm has better performance than others. We introduce a new classifying parameter to group our instances, also extending existing methods for the deterministic problem case.

show abstract

Dominance rules in combinatorial optimization problems

Cited by 40 publications

References 47 publications

A new neuro-dominance rule for single-machine tardiness problem with double due date

A new neuro-dominance rule for single-machine tardiness problem with double due date

Enhanced Branch-and-Bound Framework for a Class of Sequencing Problems

Solution algorithms for minimizing the total tardiness with budgeted processing time uncertainty

Contact Info

Product

Resources

About