Fathoming rules for biobjective mixed integer linear programs: Review and extensions

Belotti, Pietro; Soylu, Banu; Wiecek, Margaret M.

doi:10.1016/j.disopt.2016.09.003

Cited by 22 publications

(27 citation statements)

References 27 publications

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“…Later in [32], the authors propose a branch-and-bound algorithm for multiobjective integer linear programming problems extending the bounding procedure introduced in [16]: the aim in [32] is to find separating hypersurfaces in the objective space between the upper and lower bound sets in order to prune the current node in the enumeration tree. More recently, Belotti and coauthors proposed advanced branchand-bound algorithms for biobjective mixed-integer problems [2,3]. They focus on the idea of finding the complete Pareto frontier for a relaxed subproblem, using this information to derive practical fathoming rules.…”

Section: Introductionmentioning

confidence: 99%

Branching with hyperplanes in the criterion space: The frontier partitioner algorithm for biobjective integer programming

Santis

Grani

Palagi

2020

European Journal of Operational Research

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We present an algorithm for finding the complete Pareto frontier of biobjective integer programming problems. The method is based on the solution of a finite number of integer programs. The feasible sets of the integer programs are built from the original feasible set, by adding cuts that separate efficient solutions. Providing the existence of an oracle to solve suitably defined single objective integer subproblems, the algorithm can handle biobjective nonlinear integer problems, in particular biobjective convex quadratic integer optimization problems. Our numerical experience on a benchmark of biobjective integer linear programming instances shows the efficiency of the approach in comparison with existing state-of-the-art methods. Further experiments on biobjective integer quadratic programming instances are reported.

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Section: Introductionmentioning

confidence: 99%

Branching with hyperplanes in the criterion space: The frontier partitioner algorithm for biobjective integer programming

Santis

Grani

Palagi

2020

European Journal of Operational Research

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“…One major difficulty in previous bi-objective branch-and-bound approaches lies in the evaluation of the dominance of a given LB set by a given UB set. Multiple fathoming rules have been developed over the years (see Belotti et al 2016, for the current state of the art). We now introduce the fathoming rule used in BIOBAB.…”

Section: Bound Set Filtering and Node Fathomingmentioning

confidence: 99%

Branch-and-Bound for Bi-objective Integer Programming

Parragh

Tricoire

2019

INFORMS Journal on Computing

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In bi-objective integer optimization the optimal result corresponds to a set of non-dominated solutions. We propose a generic bi-objective branch-and-bound algorithm that uses a problem-independent branching rule exploiting available integer solutions and takes advantage of integer objective coefficients. The developed algorithm is applied to bi-objective facility location problems, to the bi-objective set covering problem, as well as to the bi-objective team orienteering problem with time windows. In the latter case, lower bound sets are computed by means of column generation. Comparison to state-of-the-art exact algorithms shows the effectiveness of the proposed branch-and-bound algorithm.

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“…(a) Inserting (5,11). (8, 7), (14,3). π.l and placing π := (S , ∅, π.r) as the right child of π ensures that the same holds for π.r.…”

Section: Correctnessmentioning

confidence: 99%

“…These results suggest that an efficient data structure will be essential when faster and more stable BB solvers, for instance using quicker fathoming rules [3], become available: as the time for each BB node decreases and the number of inserted solutions increases, the data structure must be efficient enough that the insertion function only takes a small percentage of the total CPU time.…”

Section: Using a Bot In Branch-and-bound Algorithmsmentioning

confidence: 99%

“…Exact procedures for solving BOMILP with general integers have been recently the subject of intense research. Exact methods have been presented by Belotti et al [2,3], Boland et al [4], and more recently by Soylu and Yıldız [18].Özpeynirci and Köksalan [14] give an exact method for finding supported solutions of BOMILP. Most other techniques in the literature tackle specific cases.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Storage of Pareto Points in Biobjective Mixed Integer Programming

Adelgren

Belotti²,

Gupte

2018

INFORMS Journal on Computing

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In biobjective mixed integer linear programs (BOMILPs), two linear objectives are minimized over a polyhedron while restricting some of the variables to be integer. Since many of the techniques for finding or approximating the Pareto set of a BOMILP use and update a subset of nondominated solutions, it is highly desirable to efficiently store this subset. We present a new data structure, a variant of a binary tree that takes as input points and line segments in R 2 and stores the nondominated subset of this input. When used within an exact solution procedure, such as branch-and-bound (BB), at termination this structure contains the set of Pareto optimal solutions.We compare the efficiency of our structure in storing solutions to that of a dynamic list which updates via pairwise comparison. Then we use our data structure in two biobjective BB techniques available in the literature and solve three classes of instances of BOMILP, one of which is generated by us. The first experiment shows that our data structure handles up to 10 7 points or segments much more efficiently than a dynamic list. The second experiment shows that our data structure handles points and segments much more efficiently than a list when used in a BB.

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Fathoming rules for biobjective mixed integer linear programs: Review and extensions

Cited by 22 publications

References 27 publications

Branching with hyperplanes in the criterion space: The frontier partitioner algorithm for biobjective integer programming

Branching with hyperplanes in the criterion space: The frontier partitioner algorithm for biobjective integer programming

Branch-and-Bound for Bi-objective Integer Programming

Efficient Storage of Pareto Points in Biobjective Mixed Integer Programming

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