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***: a julia package for optimizing a linear function over the set of efficient solutions for biobjective mixed integer linear programming

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2020年第2期27卷 945-957页

作者： Sierra-Altamiranda, Alvaro Charkhgard, Hadi Univ S Florida Dept Ind & Management Syst Engn Tampa FL 33620 USA

We present ***, a package for optimizing a linear function over the efficient set of biobjective mixed integer linear programs. The proposed package extends our recent study (see Sierra-Altamiranda and Charkhgard [INFORMS Journal on Computing, https://***/10.1287/ijoc.2018.0851]) by adding two main features: (a) in addition to CPLEX, the package allows employing any single-objective solver supported by ***, for example, GLPK, CPLEX, and SCIP;(b) the package supports execution on multiple processors and is compatible with the JuMP modeling language. An extensive computational study shows the efficacy of the package and its features.

关键词： biobjective mixed integer linear programming optimization over efficient set parallelization commercial and noncommercial solvers

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Nondominated Nash points: application of biobjective mixed integer programming

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4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH 2018年第2期16卷 151-171页

作者： Charkhgard, Hadi Savelsbergh, Martin Talebian, Masoud Univ S Florida Dept Ind & Management Syst Engn Tampa FL 33620 USA Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA Sharif Univ Technol Grad Sch Management & Econ Tehran Iran

We study the connection between biobjective mixed integer linear programming and normal form games with two players. We first investigate computing Nash equilibria of normal form games with two players using single-objective mixed integer linear programming. Then, we define the concept of efficient (Pareto optimal) Nash equilibria. This concept is precisely equivalent to the concept of efficient solutions in multi-objective optimization, where the solutions are Nash equilibria. We prove that the set of all points in the payoff (or objective) space of a normal form game with two players corresponding to the utilities of players in an efficient Nash equilibrium, the so-called nondominated Nash points, is finite. We demonstrate that biobjective mixed integer linear programming, where the utility of each player is an objective function, can be used to compute the set of nondominated Nash points. Finally, we illustrate how the nondominated Nash points can be used to determine the disagreement point of a bargaining problem.

关键词： biobjective mixed integer linear programming Normal form game Efficient Nash equilibria Disagreement point

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A New Exact Algorithm to Optimize a linear Function over the Set of Efficient Solutions for biobjective mixed integer linear Programs

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INFORMS JOURNAL ON COMPUTING 2019年第4期31卷 823-840页

作者： Altamiranda, Alvaro Sierra Charkhgard, Hadi Univ S Florida Dept Ind & Management Syst Engn Tampa FL 33620 USA

We present the first (criterion space search) algorithm for optimizing a linear function over the set of efficient solutions of biobjective mixed integer linear programs. The proposed algorithm is developed based on the triangle splitting method [Boland N, Charkhgard H, Savelsbergh M (2015) A criterion space search algorithm for biobjective mixed integer programming: The triangle splitting method. INFORMS J. Comput. 27(4): 597-618.], which can find a full representation of the nondominated frontier of any biobjective mixed integer linear program. The proposed algorithm is easy to implement and converges quickly to an optimal solution. An extensive computational study shows the efficacy of the algorithm. We numerically show that the proposed algorithm can be used to quickly generate a provably high-quality approximate solution because it maintains a lower and an upper bound on the optimal value of the linear function at any point in time.

关键词： biobjective mixed integer linear programming criterion space search algorithm optimization over efficient frontier triangle splitting method

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A robust biobjective optimization approach for operating a shared energy storage under price uncertainty

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2022年第3期29卷 1627-1658页

作者： Dai, Rui Charkhgard, Hadi Rigterink, Fabian Univ S Florida Dept Ind & Management Syst Engn Tampa FL 33620 USA Aurubis AG Hovestr 50 D-20539 Hamburg Germany

Energy storage (ES) is acknowledged to play an important role in modern energy technologies due to its potential to reduce operational costs, enhance the resilience, and level energy load for energy systems. Efficient ES management can achieve cost savings, also known as energy arbitrage, by charging at off-peak prices and discharging at peak prices. This arbitrage can be further boosted by allowing the ES to be shared by multiple users/buildings. However, since energy arbitrage relies on the variation of energy prices, it is hard to achieve this arbitrage if the prices are uncertain. To address this challenge, we present a robust optimization approach to fairly and efficiently operate an ES shared between two users under price uncertainty. This sharing strategy is formulated as a biobjective mixed integer bilinear programming model. To facilitate solution efficiency, we propose a binary formulation for piecewise McCormick relaxations to approximate the bilinear model by a tractable linear model. A computational study demonstrates the effectiveness of our robust sharing strategy for managing ES sharing under price uncertainty. Also, it shows that the proposed binary formulation for piecewise McCormick relaxations reduces the runtime by around 80% compared to the traditional unary formulation.

关键词： energy storage sharing robust optimization piecewise McCormick relaxation Nash bargaining solution biobjective mixed integer linear programming

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