1. Development of Methods for Solving Bilevel Optimization Problems
- Author
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Ray, Tapabrata, Engineering & Information Technology, UNSW Canberra, UNSW, Singh, Hemant Kumar, Engineering & Information Technology, UNSW Canberra, UNSW, Islam, Md Monjurul, Engineering & Information Technology, UNSW Canberra, UNSW, Ray, Tapabrata, Engineering & Information Technology, UNSW Canberra, UNSW, Singh, Hemant Kumar, Engineering & Information Technology, UNSW Canberra, UNSW, and Islam, Md Monjurul, Engineering & Information Technology, UNSW Canberra, UNSW
- Abstract
Bilevel optimization, also referred to as bilevel programming, involves solving an upper level problem subject to the optimality of a corresponding lower level problem. The upper and lower level problems are also referred to as the leader and follower problems, respectively. Both levels have their associated objective(s), variable(s) and constraint(s). Such problems model real-life scenarios of cases where the performance of an upper level authority is realizable/sustainable only if the corresponding lower level objective is optimum. A number of practical applications in the field of engineering, logistics, economics and transportation have inherent nested structure that are suited to this type of modelling. The range of applications as well as a rapid increase in the size and complexity of such problems has prompted active interest in the design of efficient algorithms for bilevel optimization. Bilevel optimization problems present a number of unique and interesting challenges to algorithm design. The nested nature of the problem requires optimization of a lower level problem to evaluate each upper level solution, which makes it computationally exorbitant. Theoretically, an upper level solution is considered valid/feasible only if the corresponding lower level variables are the true global optimum of the lower level problem. Global optimality can be reliably asserted in very limited cases, for example convex and linear problems. In deceptive cases, an inaccurate lower level optimum may result in an objective value better than true optimum at the upper level, which poses a severe challenge for ranking/selection strategies used within any optimization technique. In turn, this also makes the performance evaluation very difficult since the performance cannot be judged based on the objective values alone.While the area of bilevel (or more generally, multilevel) programming itself is not very new, most reports in this direction up until about a decade ago considered solv
- Published
- 2018