An Exact Algorithm for Finding Extreme Supported Nondominated Points of Multiobjective Mixed Integer Programs

Özpeynirci, Özgür; Köksalan, Murat

doi:10.1287/mnsc.1100.1248

Cited by 82 publications

(62 citation statements)

References 8 publications

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“…Example 1. Let s 1 = (5, 1, 4, 2, 3) and s 2 = (1, 4, 5, 2, 3), and let P 1 = OIP 5 s1 (2, (13,15,18)) and let P 2 = OIP 5 s2 (2, (8,15,14)). Note that (5, 1, 4, 2, 3) = 2 (1,4,5,2,3).…”

Section: Theoretical Resultsmentioning

confidence: 99%

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Multiobjective Integer Programming: Synergistic Parallel Approaches

Pettersson

Özlen

2019

INFORMS Journal on Computing

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Exactly solving multi-objective integer programming (MOIP) problems is often a very time consuming process, especially for large and complex problems. Parallel computing has the potential to significantly reduce the time taken to solve such problems, but only if suitable algorithms are used. The first of our new algorithms follows a simple technique that demonstrates impressive performance for its design. We then go on to introduce new theory for developing more efficient parallel algorithms. The theory utilises elements of the symmetric group to apply a permutation to the objective functions to assign different workloads, and applies to algorithms that order the objective functions lexicographically. As a result, information and updated bounds can be shared in real time, creating a synergy between threads. We design and implement two algorithms that take advantage of such theory. To properly analyse the running time of our three algorithms, we compare them against two existing algorithms from the literature, and against using multiple threads within our chosen IP solver, CPLEX. This survey of six different parallel algorithms, the first of its kind, demonstrates the advantages of parallel computing. Across all problem types tested, our new algorithms are on par with existing algorithms on smaller cases and massively outperform the competition on larger cases. These new algorithms, and freely available implementations, allows the investigation of complex MOIP problems with four or more objectives.

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“…Example 1. Let s 1 = (5, 1, 4, 2, 3) and s 2 = (1, 4, 5, 2, 3), and let P 1 = OIP 5 s1 (2, (13,15,18)) and let P 2 = OIP 5 s2 (2, (8,15,14)). Note that (5, 1, 4, 2, 3) = 2 (1,4,5,2,3).…”

Section: Theoretical Resultsmentioning

confidence: 99%

“…We therefore generate our own set of benchmark instances, using similar techniques to those of [9] (for knapsack problems), [22] (for assignment problems), and [14] (for traveling salesman problems). A knapsack instance is generated by randomly assigned an integer weight (uniformly at random in the range {60, .…”

Section: Instance Generationmentioning

confidence: 99%

Multiobjective Integer Programming: Synergistic Parallel Approaches

Pettersson

Özlen

2019

INFORMS Journal on Computing

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“…Recently, in [54] a new branch and bound method is presented for solving a class of MOMILP problems, where only two objectives are allowed, the integer variables are binary, and one of the two objectives has only integer variables. An exact algorithm is proposed byÖzpeynirci and Köksalan [50] to find all extreme supported efficient points (see Ehrgott [16]) of MOMILP problems. This algorithm uses a composite linear objective function and finds all the desired points in a finite number of steps by changing the weights of the objective functions in a systematic way.…”

Section: Multi-objective Approaches For General Milp Problemsmentioning

confidence: 99%

A heuristic framework for the bi-objective enhanced index tracking problem

Filippi

Guastaroba

Speranza

2016

Omega

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The index tracking problem is the problem of determining a portfolio of assets whose performance replicates, as closely as possible, that of a financial market index chosen as benchmark. In the enhanced index tracking problem the portfolio is expected to outperform the benchmark with minimal additional risk. In this paper, we study the bi-objective enhanced index tracking problem where two competing objectives, i.e., the expected excess return of the portfolio over the benchmark and the tracking error, are taken into consideration. A bi-objective Mixed Integer Linear Programming formulation for the problem is proposed. Computational results on a set of benchmark instances are given, along with a detailed out-of-sample analysis of the performance of the optimal portfolios selected by the proposed model. Then, a heuristic procedure is designed to build an approximation of the set of Pareto optimal solutions. We test the proposed procedure on a reference set of Pareto optimal solutions. Computational results show that the procedure is significantly faster than the exact computation and provides an extremely accurate approximation.

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“…Aneja and Nair and Özpeynirci and K€ oksalan propose weight changing methods for biobjective and multiobjective problems, respectively. 25,26 When one tries to identify nondominated points using a weighted sum objective function, two important issues arise. Firstly, it is not possible to¯nd unsupported nondominated points using this approach.…”

Section: Multiobjective Order Picking Problemmentioning

confidence: 99%

A Pseudo-Polynomial Time Algorithm for a Special Multiobjective Order Picking Problem

Özpeynirci

Kandemir

2015

Int. J. Info. Tech. Dec. Mak.

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In this study, we work on the order picking problem (OPP) in a specially designed warehouse with a single picker. Ratli® and Rosenthal [Operations Research 31(3) (1983) 507-521] show that the special design of the warehouse and use of one picker lead to a polynomially solvable case. We address the multiobjective version of this special case and investigate the properties of the nondominated points. We develop an exact algorithm that¯nds any nondominated point and present an illustrative example. Finally we conduct a computational test and report the results.

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An Exact Algorithm for Finding Extreme Supported Nondominated Points of Multiobjective Mixed Integer Programs

Cited by 82 publications

References 8 publications

Multiobjective Integer Programming: Synergistic Parallel Approaches

Multiobjective Integer Programming: Synergistic Parallel Approaches

A heuristic framework for the bi-objective enhanced index tracking problem

A Pseudo-Polynomial Time Algorithm for a Special Multiobjective Order Picking Problem

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