Linear programming problem is widely applied in engineering group. And artificial neural network is an effective and practical method and approach for solving linear programming problem of nonlinear convex set constraints in engineering field. Most models of artificial neural network are nonlinear dynamic system. If the objective function of optimization calculation problem is corresponding to ...

Bilevel scheduling problems constitute a hardly studied area of scheduling theory. In this paper we summarise the basic concepts of bilevel optimisation, and discuss two problem classes for which we establish various complexity and algorithmic results. The first one is the bilevel total weighted completion time problem in which the leader assigns the jobs to parallel machines and the follower s...

We consider a bilevel programming (or leader’s) problem with linear lower-level (or follower’s) problem. Under a regularity condition based on the stability regions for the follower’s problem, some simple optimality conditions are derived for the leader’s problem. Furthermore, we apply this model to the formulation of a traffic control problem designed to solve problems including accidents and/...

Bilevel programming problems are hierarchical optimization problems where an objective function is to be minimized over the graph of the solution set mapping of a second parametric optimization problem. It is the aim of the paper to give a survey for this living research area indicating main recent approaches to solve such problems and to describe optimality conditions as well as to touch main ...

A special class of bilevel programming problems with discrete para-metric lower level problems is considered. First, necessary and suucient conditions for the existence of optimal solutions are given. Then, a pseu-dopolynomial exact and a polynomial approximate algorithms for solving the bilevel problem are proposed.

Bilevel programming is a branch of optimization where a subset of variables is constrained to lie in the optimal set of an auxiliary mathematical program. This chapter presents an overview of two specific classes of bilevel programs, and in particular their relationship to well-known combinatorial problems.

The paper studies and designs an genetic algorithm (GA) of the bilevel linear programming problem (BLPP) by constructing the fitness function of the upper-level programming problem based on the definition of the feasible degree. This GA avoids the use of penalty function to deal with the constraints, by changing the randomly generated initial population into an initial population satisfying the...