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Branch-and-bound for biobjective mixed-integer linear programming [article]

Nathan Adelgren, Akshay Gupte
2020 arXiv   pre-print
We present a generic branch-and-bound algorithm for finding all the Pareto solutions of a biobjective mixed-integer linear program.  ...  The main contributions are new algorithms for obtaining dual bounds at a node, for checking node fathoming, presolve and duality gap measurement.  ...  The first one [5] works in the x-space in R n+p by modifying the classical branch-and-bound method BB [33] devised for mixed-integer linear programs (MILPs), and solves linear programs (LPs) at each  ... 
arXiv:1709.03668v2 fatcat:my7tzwxbxvh7hfxem4esnpaagq

A review of interactive methods for multiobjective integer and mixed-integer programming

Maria João Alves, João Clímaco
2007 European Journal of Operational Research  
This paper makes a review of interactive methods devoted to multiobjective integer and mixed-integer programming (MOIP/MOMIP) problems.  ...  We try to draw out some contrasts and similarities of the different types of methods.  ...  to biobjective mixed-integer linear programs, is an adaptation of the non-inferior set estimation (NISE) method developed by Cohon for biobjective linear programs.  ... 
doi:10.1016/j.ejor.2006.02.033 fatcat:fie6e65injb6lnrszswlzlo5sa

A hybrid approach for biobjective optimization

Thomas Stidsen, Kim Allan Andersen
2018 Discrete Optimization  
The approach enables massive efficient parallelisation and can be used to a wide variety of biobjective Mixed Integer Programming models.  ...  The reason for converting, i.e. simplifying, multiobjective problems to singleobjective problems is that no standard multiobjective solvers exist and specialized algorithms need to be programmed from scratch  ...  Acknowledgement In memory of Professor Jens Clausen, 1951-2011, supervisor, mentor and friend.  ... 
doi:10.1016/j.disopt.2018.02.001 fatcat:6gzglnczz5d4vdkrzdayfaimzu

An improved algorithm for solving biobjective integer programs

Ted K. Ralphs, Matthew J. Saltzman, Margaret M. Wiecek
2006 Annals of Operations Research  
A parametric algorithm for identifying the Pareto set of a biobjective integer program is proposed.  ...  Extensive computational tests on instances of the biobjective knapsack problem and a capacitated network routing problem are presented.  ...  Authors Saltzman and Wiecek were partially supported by ONR Grant N00014-97-1-0784.  ... 
doi:10.1007/s10479-006-0058-z fatcat:sr4nfslznnf4zelkzyzy3zmz54

Solving biobjective network flow problem associated with minimum cost-time loading

Omid Baghani, Saideh Ghafoori
2020 Iranian journal of numerical analysis and optimization  
This problem is a mixed-integer programming, which the decision variables are directly dependent together.  ...  We apply a primal-dual simplex algorithm for solving the biobjective min imum cost-time network flow problem such that the total shipping cost and the total shipping fixed time are considered as the first  ...  Acknowledgements The authors would like to thank the referees (especially the second reviewer) for constructive comments and suggestions, which improved the quality of the first version of this paper.  ... 
doi:10.22067/ijnao.v10i2.84890 doaj:6b94abdf919e4d90af92fb62d99f5805 fatcat:q7lzn4c7kvfrboqxfsotiyqxwu

Multi-group support vector machines with measurement costs: A biobjective approach

Emilio Carrizosa, Belen Martin-Barragan, Dolores Romero Morales
2008 Discrete Applied Mathematics  
We introduce a biobjective mixed integer problem, for which Pareto optimal solutions are obtained.  ...  In this paper we propose, for multi-group classification, a biobjective optimization model in which we consider not only the generalization ability (modelled through the margin maximization), but also  ...  We will show in Sections 5 and 6, that this modelling technique allows formulations as Biobjective Mixed Integer Programs.  ... 
doi:10.1016/j.dam.2007.05.060 fatcat:orr3sjovqvejniewku67jo3fga

Credibility-Based Biobjective Fuzzy Optimization for Supplier Selection Problem with Disruption

Xuejie Bai
2015 Mathematical Problems in Engineering  
The problem is formulated as a new credibility-based biobjective fuzzy optimization model.  ...  Taking advantage of the structural characteristics of the equivalent model, the goal programming method is employed to solve the supplier selection model, which can be solved by conventional optimization  ...  mixed-integer programming with the expectation objective and credibility constraints.  ... 
doi:10.1155/2015/256428 fatcat:dvfcjyl2irgg7e5plggm4a4hqe

Optimal Coordination of Last Trains for Maximum Transfer Accessibility with Heterogeneous Walking Time

Yao Chen, Baohua Mao, Yun Bai, Tin Kin Ho, Zhujun Li
2019 Journal of Advanced Transportation  
A biobjective function is proposed to seek the trade-off between the maximal transfer accessibility and the minimal extension of dwell time.  ...  The first model fine-tunes the last train timetable under the given bound of the dwell time.  ...  Model (A) fine-tunes the running and dwell time of last trains with the given lower and upper bounds, which is formulated as a mixed integer linear programming.  ... 
doi:10.1155/2019/9692024 fatcat:23jolbtvqrd2tn5kwc56akjzna

An Improved CPU Time in Triangle Splitting Method for Solving a Biobjective Mixed Integer Program

Ali Al-Hasani, Al-Rabeeah Al-Rabeeah, Santosh Kumar, Andrew Eberhard
2018 International journal of mathematical, engineering and management sciences  
In this paper, an existing algorithm known as Triangle Splitting Method (TSM) for the Bi-Objective Mixed Integer Program (BOMIP) has been modified, which has been named "An Improved Triangle Splitting  ...  The TSM solves many unnecessary single objectives Mixed Integer Programs (MIP) to split each triangle with two rectangles, and second, it doesn't find the all efficient frontiers.  ...  when = 0 and ≥ 1 the problem turns into a Bi-objective linear program.  ... 
doi:10.33889/ijmems.2018.3.4-025 fatcat:2nt63f37sjgxnaaowjec7vb4ju

Efficient Storage of Pareto Points in Biobjective Mixed Integer Programming

Nathan Adelgren, Pietro Belotti, Akshay Gupte
2018 INFORMS journal on computing  
In biobjective mixed integer linear programs (BOMILPs), two linear objectives are minimized over a polyhedron while restricting some of the variables to be integer.  ...  When used within an exact solution procedure, such as branch-and-bound (BB), at termination this structure contains the set of Pareto optimal solutions.  ...  (x, y) ∈ P I := {(x, y) ∈ R m × Z n : Ax + By ≤ b} (1) where P I is a bounded set. Thus BOMILP encompasses both biobjective linear programs (BOLP) and biobjective integer programs (BOIP).  ... 
doi:10.1287/ijoc.2017.0783 fatcat:wlxs3ko2lnhgjbyuwldsgnlqti

Hybridizing exact methods and metaheuristics: A taxonomy

L. Jourdan, M. Basseur, E.-G. Talbi
2009 European Journal of Operational Research  
First, we propose some natural approaches for the different schemes of cooperation encountered, and we analyse, for each model, some examples taken from the literature.  ...  The interest about hybrid optimization methods has grown for the last few years. Indeed, more and more papers about cooperation between heuristics and exact techniques are published.  ...  In [49] , Kostikas and Fragakis present the application of Genetic Programming (GP) in B&B based on Mixed Integer linear Programming (MIP).  ... 
doi:10.1016/j.ejor.2007.07.035 fatcat:uq3aphcfqbgujf5idpcdqxd66i

The biobjective travelling purchaser problem

Jorge Riera-Ledesma, Juan José Salazar-González
2005 European Journal of Operational Research  
It is here formulated as a Biobjective Mixed Integer Linear Programming model with an exponential number of valid inequalities, and this model is used within a cutting plane algorithm to generate the set  ...  The general procedure can be extended to address other biobjective combinatorial optimization problems whenever a branch-and-cut algorithm is available to solve a single-objective linear combination of  ...  Thanks to the anonymous referees and the associated editor for their very helpful comments on the preliminary version of this article.  ... 
doi:10.1016/j.ejor.2003.10.003 fatcat:37wzinwvjzd25er2ekqxpn4na4

Computing the Pareto frontier of a bi-objective bi-level linear problem using a multiobjective mixed-integer programming algorithm

Maria João Alves, Stephan Dempe, Joaquim J. Júdice
2012 Optimization  
The basic idea consists in applying a reference point algorithm that has been originally developed as an interactive procedure for multiobjective mixed-integer programming.  ...  We examine some properties of this problem and propose a methodological approach based on the reformulation of the problem as a multiobjective mixed 0-1 linear programming problem.  ...  Regarding the parametric mixed-integer program SP( , ), the linear sub-problem associated with a node p of the branch-and-bound tree can be generically formulated as follows.  ... 
doi:10.1080/02331934.2010.511674 fatcat:cxjs3bepefaqvp4ige55slxcxm

Diversity Maximization Approach for Multiobjective Optimization

Michael Masin, Yossi Bukchin
2008 Operations Research  
This approach is capable of solving mixed-integer and combinatorial problems.  ...  We can use the DMA by solving directly a modified version of the mixed-integer programming (MIP) formulation of the multiobjective problem.  ...  Acknowledgments The authors thank Mordechai Henig and the two anonymous referees for their valuable comments and suggestions, which led to considerable improvement of the paper.  ... 
doi:10.1287/opre.1070.0413 fatcat:sgno2mm3jfdmnodmfaqertgfcq

A Stochastic Programming Approach for Scheduling Extra Metro Trains to Serve Passengers from Uncertain Delayed High-Speed Railway Trains

Sihui Long, Lingyun Meng, Xiaojie Luan, Alessio Trivella, Jianrui Miao, Francesco Corman, Jing Dong
2020 Journal of Advanced Transportation  
In other words, the problem we consider is stochastic and biobjective.  ...  Moreover, we show that our solutions are nearly optimal by computing a perfect information dual bound and obtaining average optimality gaps below 1%.  ...  Since all objective functions and constraints are linear, this mathematical program is classified as a biobjective mixed-integer program.  ... 
doi:10.1155/2020/8894174 fatcat:ncb2mpzmmndshaou5dlphtoo4i
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