Stability, parametric, and postoptimality analysis of discrete optimization problems

Kozeratskaya, L. N.; Lebedeva, T. T.; Сергиенко, И. В.

doi:10.1007/bf01068340

Cited by 28 publications

(6 citation statements)

References 18 publications

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“…We refer the reader to [5,13] where the authors state the conditions under which primal feasibility, dual feasibility, and optimality still hold for * and * (optimal primal vector and subadditive dual function) after changes made to the input of (MILP).…”

Section: Definition 15mentioning

confidence: 99%

Certificates of Optimality for Mixed Integer Linear Programming Using Generalized Subadditive Generator Functions

Cheung

Moazzez²

2016

Advances in Operations Research

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We introduce generalized subadditive generator functions for mixed integer linear programs. Our results extend Klabjan’s work from pure integer programs with nonnegative entries to general MILPs. These functions suffice to achieve strong subadditive duality. Several properties of the functions are shown. We then use this class of functions to generate certificates of optimality for MILPs. We have performed a computational test study on knapsack problems to investigate the efficiency of the certificates.

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Section: Definition 15mentioning

confidence: 99%

Certificates of Optimality for Mixed Integer Linear Programming Using Generalized Subadditive Generator Functions

Cheung

Moazzez²

2016

Advances in Operations Research

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“…There are many definitions of sensitivity analysis and stability analysis in the literature and both are used to evaluate the effects of variations on the optimal solution or basis of the LP problem. 17,18 2.1. Sensitivity Analysis.…”

Section: Postoptimality Analysismentioning

confidence: 99%

Uncertainty Analysis for Refinery Production Planning

Al-Shammari

Ba-Shammakh

2011

Ind. Eng. Chem. Res.

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Nowadays, oil refineries are facing a challenging task to optimize their production levels and increase their incomes. The objective of refinery optimization is to determine the best production levels that can maximize profit and minimize operating costs with respect to operational and environmental constraints. The existence of uncertainty or variations in some parameters such as the prices of raw materials and products can seriously affect the optimization results and lead to inefficient operation. Many techniques of stochastic programming were proposed to handle the effect of variations in process parameters in order to determine a robust operation conditions; however, applications of postoptimality analysis have received less attention, especially in the refinery industry. In this work, postoptimality analysis is used to study the effect of such variations on the optimal solution of refinery process that is simplified and formulated as a LP model. We used a modified method of postoptimality analysis that jointly use sensitivity relations and stability region calculations to provide the decision maker in the refinery with valuable and easy-to-use information that helps in handling the effect of variation in process parameters. The results of this study can help the decision maker to identify sensitive parameters that need accurate estimate or intensive monitoring; and compute their stability limits, allowable variation ranges, within which the operation remains optimum. Independent and simultaneous variations in the products prices or in the capacities of process units are considered in this study; and it is shown how the refinery profit can be increased up to 4.2% by utilizing sensitivity and stability results.

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“…However, the operator faces the difficulty of choosing and tuning these weighting parameters. It is therefore interesting to characterize the robustness of an optimal tour with respect to the weights, because in discrete optimization problems small changes in the problem data may lead to significant changes in the solution [4].…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of multi-objective planning problems for unmanned aircraft

Niendorf

Kabamba

Girard

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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By performing sensitivity analysis on multiobjective mission planning problems for unmanned aircraft, this paper provides insight into properties of optimal solutions and their robustness with respect to trade-offs between objectives and also perturbations in the objective functions. We consider mission planning for unmanned aircraft in hostile environments, where a trade-off between short mission execution time and low risk must be made. This paper develops a method to compute stability regions for a set of schedules for a prototypical mission for unmanned aircraft, the weighted multiobjective symmetric traveling salesman problem. A stability region associated with an optimal solution is the set of all perturbations to the input parameters for which that solution remains optimal. In particular, this paper studies perturbations to the weights and costs in the objective functions. This work has multiple potential benefits such as providing insight into how robust a solution is with respect to modeling uncertainties, how limited intelligence resources should be allocated, and the influence of each objective on the solution. A numerical example is given to demonstrate the methods developed in this paper.

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Stability, parametric, and postoptimality analysis of discrete optimization problems

Cited by 28 publications

References 18 publications

Certificates of Optimality for Mixed Integer Linear Programming Using Generalized Subadditive Generator Functions

Certificates of Optimality for Mixed Integer Linear Programming Using Generalized Subadditive Generator Functions

Uncertainty Analysis for Refinery Production Planning

Stability analysis of multi-objective planning problems for unmanned aircraft

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