Refine
Document Type
- ZIB-Report (4)
Language
- English (4)
Has Fulltext
- yes (4)
Is part of the Bibliography
- no (4)
Keywords
- online optimization (4) (remove)
Institute
The Dynamic Multi-Period Routing Problem DMPRP introduced by Angelelli et al. gives a model for a two-stage online-offline routing problem. At the beginning of each time period a set of customers becomes known. The customers need to be served either in the current time period or in the following. Postponed customers have to be served in the next time period. The decision whether to postpone a customer has to be done online. At the end of each time period, an optimal tour for the customers assigned to this period has to be computed and this computation can be done offline. The objective of the problem is to minimize the distance traveled over all planning periods assuming optimal routes for the customers selected in each period. We provide the first randomized online algorithms for the DMPRP which beat the known lower bounds for deterministic algorithms. For the special case of two planning periods we provide lower bounds on the competitive ratio of any randomized online algorithm against the oblivious adversary. We identify a randomized algorithm that achieves the optimal competitive ratio of $\frac{1+\sqrt{2}}{2}$ for two time periods on the real line. For three time periods, we give a randomized algorithm that is strictly better than any deterministic algorithm.
In \emph{classical optimization} it is assumed that full information about the problem to be solved is given. This, in particular, includes that all data are at hand. The real world may not be so nice'' to optimizers. Some problem constraints may not be known, the data may be corrupted, or some data may not be available at the moments when decisions have to be made. The last issue is the subject of \emph{online optimization} which will be addressed here. We explain some theory that has been developed to cope with such situations and provide examples from practice where unavailable information is not the result of bad data handling but an inevitable phenomenon.
Algorithmic control of elevator systems has been studied for a long time. More recently, a new paradigm for elevator control has emerged. In destination call systems, the passenger specifies not only the direction of his ride, but the destination floor. Such a destination call system is very interesting from an optimization point of view, since more information is available earlier, which should allow improved planning. However, the real-world destination call system envisioned by our industry partner requires that each destination call (i.e. passenger) is assigned to a serving elevator immediately. This early assignment restricts the potential gained from the destination information. Another aspect is that there is no way to specify the destination floor in the cabin. Therefore, the elevator has to stop on every destination floor of an assigned call, although the passenger may not have boarded the cabin, e.g. due to insufficient capacity. In this paper we introduce a new destination call control algorithm suited to this setting. Since the control algorithm for an entire elevator group has to run on embedded microprocessors, computing resources are very scarce. Since exact optimization is not feasible on such hardware, the algorithm is an insertion heuristic using a non-trivial data structure to maintain a set of tours. To assess the performance of our algorithm, we compare it to similar and more powerful algorithms by simulation. We also compare to algorithms for a conventional system and with a more idealized destination call system. This gives an indication of the relative potentials of these systems. In particular, we assess how the above real-world restrictions influence performance. The algorithm introduced has been implemented by our industry partner for real-world use.
This extended abstract is about algorithms for controlling elevator systems employing destination hall calls, i.e. the passenger provides his destination floor when calling an elevator. We present the first exact algorithm for controlling a group of elevators and report on simulation results indicating that destination hall call systems outperform conventional systems.