• Dr. Anuradha Sharma

This paper presents a quadratic/Linear Bilevel Programming Problem (QLBPP) having single decision maker at both levels i.e. upper level (first level) and lower level(second level).The objective function of first level being quadratic and lower level objective being a linear function over a convex polyhedral set as the constraint set.The solution approach follows a hierarchical strategy i.e. the objective function at upper level is optimized first and then for a given set of variables under the control of first level, the objective function at second level is optimized. In the decision making situation, decision deadlock occurs very often. This algorithm deals by changing the randomly generated initial population into an initial population satisfying the constraints to improve the efficiency of the algorithm to deal with the constraint which utilizes N number of D-dimensional parameter vectors as a population for each generation G. The main advantage of the proposed algorithm is that it avoids the introduction of penalty function in order to deal with the given constraint set. The algorithm presented in this paper aims at global optimization and lesser computations to solve decentralized systems . The algorithm presented in this article incorporates a parallel direct search method which utilizes N number of D-dimensional parameter vectors as a population for each generation G. The algorithm proposed in this paper bears good convergence properties and controls only few variables which are fixed. The(QLBPP) under consideration is at first reduced to a single level program using KKT conditions and then decomposed into two separate problems which is plausible because the decomposed problems don’t carry common variables thereby highlighting the advantages of the proposed method. Despite of the fact that feasible region of (QLBPP) is a convex polyhedron(irrespective of linear/nonlinear nature of objective functions),the BLPs are neither continuous everywhere nor convex because the objective function value of the first level problem is implicitly determined by the follower’s objective function which is neither linear nor differentiable. The proposed approach is demonstrated numerically.

Bilevel Programming; Quadratic programming; Differential Evolution; Separable Problems; Hierarchical optimization; NP-Hard.

"A New Approach For Quadratic/Linear Bilevel Programs Using Differential Evolution ", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.2, Issue 12, page no.871-877, December-2015, Available :http://www.jetir.org/papers/JETIR1701539.pdf

"A New Approach For Quadratic/Linear Bilevel Programs Using Differential Evolution ", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.2, Issue 12, page no. pp871-877, December-2015, Available at : http://www.jetir.org/papers/JETIR1701539.pdf