Exact solution approaches for integer linear generalized maximum multiplicative programs through the lens of multi-objective optimization

Saghand, Payman Ghasemi; Charkhgard, Hadi

doi:10.1016/j.cor.2021.105549

Cited by 8 publications

(5 citation statements)

References 46 publications

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“…To the best of our knowledge, those approaches are shown to be competitive with (and even better than) all the approaches mentioned above when is represented by only linear constraints involving continuous and/or integer decision variables. Interested readers may refer to the papers by Charkhgard et al [4], Saghand and Charkhgard [16, 17], Saghand et al [18] and Vazirani [21] to learn more about those approaches. Specifically, a detailed computational study comparing different solution approaches was given by Saghand and Charkhgard [17].…”

Section: Solution Methods For the Nash Social Welfare Programmentioning

confidence: 99%

“…Interested readers may refer to the papers by Charkhgard et al [4], Saghand and Charkhgard [16, 17], Saghand et al [18] and Vazirani [21] to learn more about those approaches. Specifically, a detailed computational study comparing different solution approaches was given by Saghand and Charkhgard [17].…”

Section: Solution Methods For the Nash Social Welfare Programmentioning

confidence: 99%

See 1 more Smart Citation

The Magic of Nash Social Welfare in Optimization: Do Not Sum, Just Multiply!

Charkhgard

Keshanian²,

Esmaeilbeigi³

et al. 2022

ANZIAM J.

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We explain some key challenges when dealing with a single- or multi-objective optimization problem in practice. To overcome these challenges, we present a mathematical program that optimizes the Nash social welfare function. We refer to this mathematical program as the Nash social welfare program (NSWP). An interesting property of the NSWP is that it can be constructed for any single- or multi-objective optimization problem. We show that solving the NSWP could result in more desirable solutions in practice than its single- or multi-objective counterpart. We also discuss several promising approaches that could be employed to solve the NSWP in practice.

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Section: Solution Methods For the Nash Social Welfare Programmentioning

confidence: 99%

Section: Solution Methods For the Nash Social Welfare Programmentioning

confidence: 99%

The Magic of Nash Social Welfare in Optimization: Do Not Sum, Just Multiply!

Charkhgard

Keshanian²,

Esmaeilbeigi³

et al. 2022

ANZIAM J.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Given the complexity of the exact model, this research aims to propose an efficient solution methodology to locate and size FACTS in medium-voltage distribution networks by reformulating the MINLP model as a mixedinteger convex approximation [18]. The main advantage of convex optimization is that it allows representing optimization problems in engineering and science while ensuring a global optimal solution [19]. This research aims to provide the literature and the industry with an efficient and reliable solution methodology to address the studied problem, with superior performance compared to MINLP solvers in commercial software or metaheuristic algorithms [18].…”

Section: Motivationmentioning

confidence: 99%

“…The equations for the active and reactive power flows, as presented in ( 20)-( 23), depend on the auxiliary variables in (18) and (19). These equations are non-convex, so it is necessary to relax them via a hyperbolic shape, as shown below:…”

Section: Convex Representation Of the Active And Reactive Power Flow ...mentioning

confidence: 99%

Optimal Integration of Flexible Alternating Current Transmission Systems in Electrical Distribution Grids Using a Mixed-Integer Convex Model

Gil-González,

Montoya,

Trujillo-Rodríguez

2023

Algorithms

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This research addresses the efficient integration and sizing of flexible alternating current transmission systems (FACTS) in electrical distribution networks via a convex optimization approach. The exact mixed-integer nonlinear programming (MINLP) model associated with FACTS siting and sizing aims for the minimization of the expected annual operating costs of the network (i.e., energy losses and FACTS purchasing costs). The constraints of this problem include power equilibrium equalities, voltage regulation bounds, and device capacities, among others. Due to the power equilibrium constraints per node and period, the MINLP model is a non-convex optimization problem. To transform the exact MINLP model into a mixed-integer convex one, the approximation of the product between two variables in the complex domain is relaxed through its hyperbolic equivalent, which generates a set of convex cones. The main advantage of the proposed mixed-integer convex model is that it ensures the global optimum of the problem, even when considering objective multiplexes. Numerical simulations in the IEEE 33-, 69-, and 85-bus grids demonstrate the effectiveness and robustness of FACTS integration via the proposed convex approach in comparison with the exact solution of the MINLP model in the GAMS software as well as with combinatorial optimization algorithms (i.e., the black widow optimizer and the vortex search algorithm). All simulations were carried out in MATLAB with Yalmip optimization and the Gurobi and Mosek solvers. The simulation results show that, for a fixed operation of the FACTS devices (i.e., a VAR compensator) during the day, the annual operating costs are reduced by 12.63%, 13.97%, and 26.53% for the IEEE 33-, 69-, and 85-bus test systems, respectively, while for the operation variable, the reductions are by 14.24%, 15.79%, and 30.31%, respectively.

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“…In [3] the so-called Integer Linear Generalized Maximum Multiplicative Programs (IL-GMMP) is studied with the development of three new multi-objective optimization based algorithms. With 57600 experiments, the performance of Gurobi, CPLEX and FICO Xpress is compared when used for solving single-objective integer linear programs.…”

Section: Related Workmentioning

confidence: 99%

Evaluation and Comparison of Integer Programming Solvers for Hard Real-Time Scheduling

Guasque

Balbastre

2022

IEICE Trans. Inf. & Syst.

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In order to obtain a feasible schedule of a hard real-time system, heuristic based techniques are the solution of choice. In the last few years, optimization solvers have gained attention from research communities due to their capability of handling large number of constraints. Recently, some works have used integer linear programming (ILP) for solving mono processor scheduling of real-time systems. In fact, ILP is commonly used for static scheduling of multiprocessor systems. However, two main solvers are used to solve the problem indistinctly. But, which one is the best for obtaining a schedulable system for hard real-time systems? This paper makes a comparison of two well-known optimization software packages (CPLEX and GUROBI) for the problem of finding a feasible schedule on monoprocessor hard real-time systems.

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Exact solution approaches for integer linear generalized maximum multiplicative programs through the lens of multi-objective optimization

Cited by 8 publications

References 46 publications

The Magic of Nash Social Welfare in Optimization: Do Not Sum, Just Multiply!

The Magic of Nash Social Welfare in Optimization: Do Not Sum, Just Multiply!

Optimal Integration of Flexible Alternating Current Transmission Systems in Electrical Distribution Grids Using a Mixed-Integer Convex Model

Evaluation and Comparison of Integer Programming Solvers for Hard Real-Time Scheduling

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