Informatica

One of the most known applications of Discrete Optimization is on scheduling. In contrast, one of the most known applications of Continuous Nonlinear Optimization is on the control of dynamic systems. In this paper, we combine both views, solving scheduling problems as dynamic systems, modeled as discrete-time nonlinear optimal control problems with state and control continuous variables subjected to upper and lower bounds. Complementarity constraints are used to represent scheduling decisions. One example we discuss in detail is the crude oil scheduling in ports, with numerical results presented.

This paper deals with the study of the optimal control problem for the objective F(x,u,v)=∫^T0f(x(t),x(t−h),ζ(t),u(t),v(t),t)dt, with x∈X,u∈U,v∈V;X,U and V being vector spaces, and ζ(t)=∫^h0R(t,τ)x(t−τ)dτ subject to the differential equation $\frac{d}{dt}x(t)=m(x(t),x(t-h),\zeta(t),u(t),v(t),t)(0\leq t\leq T)$, and the constraints g1(u(t),t)∈S1,g2(v(t),t)∈S2;n1(x(t),t)∈V1,n2(x(t−h),t)∈V2;n3(ζ(t),t)∈V3(0≤t≤T), where x(t)∈Rⁿ;ζ(t)∈Rⁿ;u(t)∈R^k;f,m,gi(i=1,2),ni(1≤i≤3) and the entries to r(t,τ):R+×R+→L(X,X) are continuously differentiable functions. It is assumed that boundary conditions x(0)=x(T)=0 are imposed. Si(i=1;2) and Vi(1≤i≤3) are convex cones. The existence of a time-optimal control in analytic linear systems is also investigated via an extension of the bang-bang principle.