Exact algorithms for multiobjective linear optimization problems with integer variables: A state of the art survey

P Halffmann, LE Schäfer, K Dächert… - Journal of Multi …, 2022 - Wiley Online Library
We provide a comprehensive overview of the literature of algorithmic approaches for
multiobjective mixed‐integer and integer linear optimization problems. More precisely, we …

Algorithms for generating pareto fronts of multi-objective integer and mixed-integer programming problems

RS Burachik, CY Kaya, MM Rizvi - Engineering Optimization, 2022 - Taylor & Francis
Multi-objective integer or mixed-integer programming problems typically have disconnected
feasible domains, making the task of constructing an approximation of the Pareto front …

A criterion space search algorithm for biobjective integer programming: The balanced box method

N Boland, H Charkhgard… - INFORMS Journal on …, 2015 - pubsonline.informs.org
We present a new criterion space search algorithm, the balanced box method, for finding all
nondominated points of a biobjective integer program. The method extends the box …

[HTML][HTML] Branch-and-bound and objective branching with three or more objectives

N Forget, SL Gadegaard, K Klamroth… - Computers & Operations …, 2022 - Elsevier
The recent success of bi-objective Branch-and-Bound (B&B) algorithms heavily relies on the
efficient computation of upper and lower bound sets. These bound sets are used as a …

A simple augmented∊-constraint method for multi-objective mathematical integer programming problems

W Zhang, M Reimann - European Journal of Operational Research, 2014 - Elsevier
A simple augmented∊-constraint (SAUGMECON) method is put forward to generate all non-
dominated solutions of multi-objective integer programming (MOIP) problems. The …

[HTML][HTML] New ϵ− constraint methods for multi-objective integer linear programming: A Pareto front representation approach

M Mesquita-Cunha, JR Figueira… - European Journal of …, 2023 - Elsevier
Dealing with multi-objective problems by using generation methods has some interesting
advantages since it provides the decision-maker with the complete information about the set …

A linear bound on the number of scalarizations needed to solve discrete tricriteria optimization problems

K Dächert, K Klamroth - Journal of Global Optimization, 2015 - Springer
Multi-objective optimization problems are often solved by a sequence of parametric single-
objective problems, so-called scalarizations. If the set of nondominated points is finite, the …

Efficient computation of the search region in multi-objective optimization

K Dächert, K Klamroth, R Lacour… - European Journal of …, 2017 - Elsevier
Multi-objective optimization procedures usually proceed by iteratively producing new
solutions. For this purpose, a key issue is to determine and efficiently update the search …

The quadrant shrinking method: A simple and efficient algorithm for solving tri-objective integer programs

N Boland, H Charkhgard, M Savelsbergh - European Journal of …, 2017 - Elsevier
We present a new variant of the full 2-split algorithm, the Quadrant Shrinking Method (QSM),
for finding all nondominated points of a tri-objective integer program. The algorithm is easy …

A new method for optimizing a linear function over the efficient set of a multiobjective integer program

N Boland, H Charkhgard, M Savelsbergh - European journal of operational …, 2017 - Elsevier
We present a new algorithm for optimizing a linear function over the set of efficient solutions
of a multiobjective integer program (MOIP). The algorithm's success relies on the efficiency …