2,582 research outputs found
Four payment models for the multi-mode resource constrained project scheduling problem with discounted cash flows
In this paper, the multi-mode resource constrained project scheduling problem with discounted cash flows is considered. The objective is the maximization of the net present value of all cash flows. Time value of money is taken into consideration, and cash in- and outflows are associated with activities and/or events. The resources can be of renewable, nonrenewable, and doubly constrained resource types. Four payment models are considered: Lump sum payment at the terminal event, payments at prespecified event nodes, payments at prespecified time points and progress payments. For finding solutions to problems proposed, a
genetic algorithm (GA) approach is employed, which uses a special crossover operator that can exploit the multi-component nature of the problem. The models are investigated at the hand of an example problem. Sensitivity analyses are performed over the mark up and the discount rate. A set of 93 problems from literature are solved under the four different payment models and resource type combinations with the GA approach employed resulting in satisfactory computation times. The GA approach is compared with a domain specific heuristic for the lump sum payment case with renewable resources and is shown to outperform it
A statistical method for revealing form-function relations in biological networks
Over the past decade, a number of researchers in systems biology have sought
to relate the function of biological systems to their network-level
descriptions -- lists of the most important players and the pairwise
interactions between them. Both for large networks (in which statistical
analysis is often framed in terms of the abundance of repeated small subgraphs)
and for small networks which can be analyzed in greater detail (or even
synthesized in vivo and subjected to experiment), revealing the relationship
between the topology of small subgraphs and their biological function has been
a central goal. We here seek to pose this revelation as a statistical task,
illustrated using a particular setup which has been constructed experimentally
and for which parameterized models of transcriptional regulation have been
studied extensively. The question "how does function follow form" is here
mathematized by identifying which topological attributes correlate with the
diverse possible information-processing tasks which a transcriptional
regulatory network can realize. The resulting method reveals one form-function
relationship which had earlier been predicted based on analytic results, and
reveals a second for which we can provide an analytic interpretation. Resulting
source code is distributed via http://formfunction.sourceforge.net.Comment: To appear in Proc. Natl. Acad. Sci. USA. 17 pages, 9 figures, 2
table
Deterministic Annealing and Nonlinear Assignment
For combinatorial optimization problems that can be formulated as Ising or
Potts spin systems, the Mean Field (MF) approximation yields a versatile and
simple ANN heuristic, Deterministic Annealing. For assignment problems the
situation is more complex -- the natural analog of the MF approximation lacks
the simplicity present in the Potts and Ising cases. In this article the
difficulties associated with this issue are investigated, and the options for
solving them discussed. Improvements to existing Potts-based MF-inspired
heuristics are suggested, and the possibilities for defining a proper
variational approach are scrutinized.Comment: 15 pages, 3 figure
Reparameterizing the Birkhoff Polytope for Variational Permutation Inference
Many matching, tracking, sorting, and ranking problems require probabilistic
reasoning about possible permutations, a set that grows factorially with
dimension. Combinatorial optimization algorithms may enable efficient point
estimation, but fully Bayesian inference poses a severe challenge in this
high-dimensional, discrete space. To surmount this challenge, we start with the
usual step of relaxing a discrete set (here, of permutation matrices) to its
convex hull, which here is the Birkhoff polytope: the set of all
doubly-stochastic matrices. We then introduce two novel transformations: first,
an invertible and differentiable stick-breaking procedure that maps
unconstrained space to the Birkhoff polytope; second, a map that rounds points
toward the vertices of the polytope. Both transformations include a temperature
parameter that, in the limit, concentrates the densities on permutation
matrices. We then exploit these transformations and reparameterization
gradients to introduce variational inference over permutation matrices, and we
demonstrate its utility in a series of experiments
Resource dedication problem in a multi-project environment
There can be different approaches to the management of resources within
the context of multi-project scheduling problems. In general, approaches to multiproject scheduling problems consider the resources as a pool shared by all projects. On the other hand, when projects are distributed geographically or sharing resources between projects is not preferred, then this resource sharing policy may not be feasible. In such cases, the resources must be dedicated to individual projects throughout the project durations. This multi-project problem environment is defined here as the resource dedication problem (RDP). RDP is defined as the optimal dedication of resource capacities to different projects within the overall limits of the resources and with the objective of minimizing a predetermined objective function. The projects involved are multi-mode resource constrained project scheduling problems with finish to start zero time lag and non-preemptive activities and limited renewable and nonrenewable resources. Here, the characterization of RDP, its mathematical formulation and two different solution methodologies are presented. The first solution approach is a genetic algorithm employing a new improvement move called combinatorial auction for RDP, which is based on preferences of projects for resources. Two different methods for calculating the projects’ preferences based on linear and Lagrangian relaxation are proposed. The second solution approach is a Lagrangian relaxation based heuristic employing subgradient optimization. Numerical studies demonstrate that the proposed approaches are powerful methods for solving this problem
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