Mobility allowance shuttle transit (MAST) services: MIP formulation and strengthening with logic constraints

We study a hybrid transportation system referred to as mobility allowance shuttle transit (MAST) where vehicles may deviate from a fixed path consisting of a few mandatory checkpoints to serve demand distributed within a proper service area. In this paper we propose a mixed integer programming (MIP) formulation for the static scheduling problem of a MAST type system. Since the problem is NP-Hard, we develop sets of logic cuts, by using reasonable assumptions on passengers’ behavior. The purpose of these constraints is to speed up the search for optimality by removing inefficient solutions from the original feasible region. Experiments show the effectiveness of the developed inequalities, achieving a reduction up to 90% of the CPU solving time for some of the instances.     

Ant colony optimization for power plant maintenance scheduling optimization—a five-station hydropower system

A number of algorithms have been developed for the optimization of power plant maintenance schedules. However, the true test of such algorithms occurs when they are applied to real systems. In this paper, the application of an Ant Colony Optimization formulation to a hydropower system is presented. The formulation is found to be effective in handling various constraints commonly encountered in practice. Overall, the results obtained using the ACO formulation are better than those given by traditional methods using engineering judgment, which indicates the potential of ACO in solving realistic power plant maintenance scheduling problems.     

Economic and economic-statistical design of a chi-square chart for CBM

In this paper, the economic and economic-statistical design of a χ² chart for a maintenance application is considered. The machine deterioration process is described by a three-state continuous time Markov chain. The machine state is unobservable, except for the failure state. To avoid costly failures, the system is monitored by a χ² chart. The observation process stochastically related to the machine condition is assumed to be multivariate, normally distributed. When the chart signals, full inspection is performed to determine the actual machine condition. The system can be preventively replaced at a sampling epoch and must be replaced upon failure; preventive replacement costs less than failure replacement. The objective is to find the optimal control chart parameters that minimize the long-run average maintenance cost per unit time. For the economic-statistical design, an additional constraint guaranteeing the occurrence of the true alarm signal on the chart before failure with given probability is considered. For both designs, the objective function is derived using renewal theory.     

Worst-case distribution analysis of stochastic programs

We show that for even quasi-concave objective functions the worst-case distribution, with respect to a family of unimodal distributions, of a stochastic programming problem is a uniform distribution. This extends the so-called ``Uniformity Principle' of Barmish and Lagoa (1997) where the objective function is the indicator function of a convex symmetric set.     

Optimality conditions for state constrained nonlinear control problems

The problem of optimal control of nonlinear control and state constrained control problems, where the state constraint may involve differential operators and the cost functionals may be nonsmooth, is studied. For this class of problems, necessary optimality conditions using techniques from infinite dimensional optimization theory adapted to the framework of control problems are derived. It is shown that the underlying structure admits a considerable relaxation of the classical constraint qualifications. The theory then is applied to examples of various nonlinear elliptic equations and state constraints.     

Mixed integer programming for a special logic constrained optimal control problem

Integrating logical constraints into optimal control problems is not an easy task. In fact, optimal control problems are usually continuous while logical constraints are naturally expressed by integer (binary) variables. In this article we are interested is a particular form of an LQR optimal control problem: the energy (control L² norm) is to be minimized, system dynamic is linear and logical constraints on the control use are to be fulfilled. Even if the starting continuous problem is not a complicated one, difficulties arise when integrating the additional logical constraints. First, we will present two different ways of modeling the problem, both of them leading us to Mixed Integer Problems. Furthermore, algorithms (Generalized Outer Approximation, Benders Decomposition and Branch and Cut) are applied on each model and results analyzed. We also present a Benders Decomposition algorithm variant that is adapted to our problem (taking into account its particular form) and we will conclude by looking at the optimal solutions obtained in an interesting physical example: the harmonic spring.     

SEQUENTIAL QUADRATIC PROGRAMMING METHODS FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS

A Kind of direct methods is presented for the solution of optimal control problems with state constraints.These methods are sequential quadratic programming methods.At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and Linear approximations to constraints is solved to get a search direction for a merit function.The merit function is formulated by augmenting the Lagrangian funetion with a penalty term.A line search is carried out along the search direction to determine a step length such that the merit function is decreased.The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadrade programming methods.     

Some properties of cliques in 0–1 mixed integer programs

Summary In this note we present new properties of cliques induced constraints straintsX(C _r ⁺ )-X(C _r ^- ) ≤ 1 - |C _r ^- | for λ εS, whereS is the set of cliques that are implied by 0–1 mixed integer programs. These properties allow to further fixing of 0–1 variables, to detect instance's infeasibility and to imply new cliques.     

Constraints and the Hellmann-Feynman theorem

It is pointed out that Hurley's condition applies even in the presence of Lagrange multipliers. Also a useful formula for E is derived which allows for the possibility that both the trial functions and the constraints may depend on .     

Elimination of bounds in optimization problems by transforming variables

The problem of minimizing a nonlinear objective function ofn variables, with continuous first and second partial derivatives, subject to nonnegativity constraints or upper and lower bounds on the variables is studied. The advisability of solving such a constrained optimization problem by making a suitable transformation of its variables in order to change the problem into one of unconstrained minimization is considered. A set of conditions which guarantees that every local minimum of the new unconstrained problem also satisfies the first-order necessary (Kuhn—Tucker) conditions for a local minimum of the original constrained problem is developed. It is shown that there are certain conditions under which the transformed objective function will maintain the convexity of the original objective function in a neighborhood of the solution. A modification of the method of transformations which moves away from extraneous stationary points is introduced and conditions under which the method generates a sequence of points which converges to the solution at a superlinear rate are given.