A Branch and Bound Algorithm for Transmission Network Expansion Planning Using Nonconvex Mixed-Integer Nonlinear Programming Models

The branch and bound (BB) algorithm is widely used to obtain the global solution of mixed-integer linear programming (MILP) problems. On the other hand, when the traditional BB structure is directly used to solve nonconvex mixed-integer nonlinear programming (MINLP) problems, it becomes ineffective,...

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Vydáno v:IEEE access Ročník 10; s. 39875 - 39888
Hlavní autoři: Zoppei, Reinaldo T., Delgado, Marcos A. J., Macedo, Leonardo H., Rider, Marcos J., Romero, Ruben
Médium: Journal Article
Jazyk:angličtina
Vydáno: Piscataway IEEE 2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Biological system modeling
Branch and bound algorithm
Integer programming
Linear programming
Metaheuristics
Mixed integer
mixed-integer nonlinear programming
Nonlinear programming
Nonlinearity
Optimization
Planning
Programming profession
Propagation losses
Search problems
Solvers
transmission network expansion planning
ISSN:2169-3536, 2169-3536
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Shrnutí:The branch and bound (BB) algorithm is widely used to obtain the global solution of mixed-integer linear programming (MILP) problems. On the other hand, when the traditional BB structure is directly used to solve nonconvex mixed-integer nonlinear programming (MINLP) problems, it becomes ineffective, mainly due to the nonlinearity and nonconvexity of the feasible region of the problem. This article presents the difficulties and ineffectiveness of the direct use of the traditional BB algorithm for solving nonconvex MINLP problems and proposes the formulation of an efficient BB algorithm for solving this category of problems. The algorithm is formulated taking into account particular aspects of nonconvex MINLP problems, including (i) how to deal with the nonlinear programming (NLP) subproblems, (ii) how to detect the infeasibility of an NLP subproblem, (iii) how to treat the nonconvexity of the problem, and (iv) how to define the fathoming rules. The proposed BB algorithm is used to solve the transmission network expansion planning (TNEP) problem, a classical problem in power systems optimization, and its performance is compared with the performances of off-the-shelf optimization solvers for MINLP problems. The results obtained for four test systems, with different degrees of complexity, indicate that the proposed BB algorithm is effective for solving the TNEP problem with and without considering losses, showing equal or better performance than off-the-shelf optimization solvers.
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ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2022.3166153