scholarly journals Efficiency conditions for multiobjective bilevel programming problems via convexificators

2020 ◽  
Vol 4 (3) ◽  
Keyword(s):  
Bilevel Programming ◽  
Bilevel Programming Problems ◽  
Efficiency Conditions

An Objective Penalty Method for Optimistic Bilevel Programming Problems

2018 ◽  
Vol 8 (1) ◽  
pp. 177-187 ◽  
Author(s):  
June Liu ◽  
Tao Zhang ◽  
Yu-Xin Fan ◽  
Bing Han ◽  
Yue Zheng
Keyword(s):  
Bilevel Programming ◽  
Penalty Method ◽  
Bilevel Programming Problems

An Efficient and Accurate Solution Methodology for Bilevel Multi-Objective Programming Problems Using a Hybrid Evolutionary-Local-Search Algorithm

2010 ◽  
Vol 18 (3) ◽  
pp. 403-449 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Ankur Sinha
Keyword(s):  
Problem Solving ◽  
Local Search ◽  
Bilevel Programming ◽  
Optimization Problem ◽  
Practical Importance ◽  
Test Problems ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Bilevel Programming Problems ◽  
Solution Methodology

Bilevel optimization problems involve two optimization tasks (upper and lower level), in which every feasible upper level solution must correspond to an optimal solution to a lower level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy developments, transportation problems, and others. However, they are commonly converted into a single level optimization problem by using an approximate solution procedure to replace the lower level optimization task. Although there exist a number of theoretical, numerical, and evolutionary optimization studies involving single-objective bilevel programming problems, not many studies look at the context of multiple conflicting objectives in each level of a bilevel programming problem. In this paper, we address certain intricate issues related to solving multi-objective bilevel programming problems, present challenging test problems, and propose a viable and hybrid evolutionary-cum-local-search based algorithm as a solution methodology. The hybrid approach performs better than a number of existing methodologies and scales well up to 40-variable difficult test problems used in this study. The population sizing and termination criteria are made self-adaptive, so that no additional parameters need to be supplied by the user. The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure. The study opens up many issues related to multi-objective bilevel programming and hopefully this study will motivate EMO and other researchers to pay more attention to this important and difficult problem solving activity.

An interior point technique for solving bilevel programming problems

2012 ◽  
Vol 14 (3) ◽  
pp. 381-394 ◽  
Author(s):  
José Herskovits ◽  
Mario Tanaka Filho ◽  
Anatoli Leontiev
Keyword(s):  
Interior Point ◽  
Bilevel Programming ◽  
Bilevel Programming Problems ◽  
Interior Point Technique
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