Bilevel optimization with a multiobjective problem in the lower level

Andreani, Roberto; Ramirez, V. A.; Santos, Sandra A.; Secchin, Leonardo D.

doi:10.1007/s11075-018-0576-1

Cited by 12 publications

(1 citation statement)

References 21 publications

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“…A commonly used approach in mathematical programming is to convert bilevel optimization problem into a single level COP with Karush-Kuhn-Tucker (KKT) conditions, however, it may not necessarily be simple to handle especially when the upperlevel's constraint functions are in an arbitrary linear form [2,22]. Another commonly used approach is the penalty function methods where constraints are transformed into penalty terms, which in turn are used for reward and/or punishment for satisfying and/or violating the constraints, respectively [32].…”

Section: Introductionmentioning

confidence: 99%

Optimistic Variants of Single-Objective Bilevel Optimization for Evolutionary Algorithms

Sharma

2020

Int. J. Comp. Intel. Appl.

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Single-objective bilevel optimization is a specialized form of constraint optimization problems where one of the constraints is an optimization problem itself. These problems are typically non-convex and strongly NP-Hard. Recently, there has been an increased interest from the evolutionary computation community to model bilevel problems due to its applicability in real-world applications for decision-making problems. In this work, a partial nested evolutionary approach with a local heuristic search has been proposed to solve the benchmark problems and have outstanding results. This approach relies on the concept of intermarriage-crossover in search of feasible regions by exploiting information from the constraints. A new variant has also been proposed to the commonly used convergence approaches, i.e., optimistic and pessimistic. It is called an extreme optimistic approach. The experimental results demonstrate the algorithm converges differently to known optimum solutions with the optimistic variants. Optimistic approach also outperforms pessimistic approach. Comparative statistical analysis of our approach with other recently published partial to complete evolutionary approaches demonstrates very competitive results.

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Section: Introductionmentioning

confidence: 99%