In this chapter, we present a survey of constraint-handling techniques based on evolutionary multiobjective optimization concepts. We present some basic definitions required to make this chapter self-contained, and then we introduce the way in which a global (single-objective) nonlinear optimization problem is transformed into an unconstrained multiobjective optimization problem. A taxonomy of ...

The Quadratic Convex Reformulation (QCR) method is used to solve quadratic unconstrained binary optimization problems. In this method, the semidefinite relaxation is used to reformulate it to a convex binary quadratic program which is solved using mixed integer quadratic programming solvers. We extend this method to random quadratic unconstrained binary optimization problems. We develop a Penal...

Given a set of objects with profits (any, even negative, numbers) assigned not only to separate objects but also to pairs of them, the unconstrained binary quadratic optimization problem consists in finding a subset of objects for which the overall profit is maximized. In this paper, an iterated tabu search algorithm for solving this problem is proposed. Computational results for problem instan...

We consider a class of generalized Nash equilibrium problems (GNEPs) where both the objective functions and the constraints are allowed to depend on the decision variables of the other players. It is well-known that this problem can be reformulated as a constrained optimization problem via the (regularized) Nikaido-Isoda-function, but this reformulation is usually nonsmooth. Here we observe tha...

The generalized Nash equilibrium problem is a Nash game which, in contrast to the standard Nash equilibrium problem, allows the strategy sets of each player to depend on the decision variables of all other players. It was recently shown by the authors that this generalized Nash equilibrium problem can be reformulated as both an unconstrained and a constrained optimization problem with continuou...

The minimization problem of an L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints is formulated for a class of two-dimensional (2-D) state-space digital filters. First, the problem is converted into an unconstrained optimization problem by using linear-algebraic techniques. Next, the unconstrained optimization problem is solved by applying an efficient quasi-Newton algo...

Control forces in semi-active control systems are constrained by the dynamics of actuators that regulate energy transmission through variable damping and/or stiffness mechanisms. The potential benefit of developing and implementing new semi-active control devices and applications can be determined by optimizing the controlled performance subject to the constraints of the dynamics of the system ...