In this paper, we consider a dial-a-ride problem where the objective is to maximize the passenger occupancy rate. The problem arises from an on-demand transportation system developed in a rural zone in France, where the objective
of encouraging people meeting is pursued. We address the solution of the problem with a column generation approach, applied to a Assortment Women Nike Air Presto Grey Blue Yellow set partitioning formulation where the objective function is fractional. Based on the literature on linear fractional programming, two methods are developed to deal with this fractional objective. Experiments permit to compare these two approaches and to evaluate the impact of the new objective compared to a standard min-cost Individual Women Free Run 2 Black Green ID208 Shoes
or min-time optimization.
New simultaneous iteration techniques are developed for solving the generalized eigenproblem Ax=λBx, where A and B are real symmetric matrices and B is positive definite. The approach is to minimize the generalized Rayleigh quotient in some sense over several independent vectors simultaneously. In particular, each new vector iterate is formed from a linear combination of current iterates and correction vectors that are derived from either gradient or conjugate-gradient techniques. A Ritz projection or simultaneous iteration process is used to accelerate convergence. For one of the gradient versions, convergence and asymptotic rates of convergence are established. Also, some numerical experiments are reported that demonstrate the convergence behavior of these methods.