729 research outputs found
Modeling and optimization of production and distribution of drinking water at VMW
We develop and discuss an operational planning model aiming at minimizing production and distribution costs in large drinking water networks containing buffers with free inflow. Modeling drinking water networks is very challenging due of the presence of complex hydraulic constraints, such as friction losses and pump curves. Non-linear, non-convex constraints result from the relationships between pressure and flow in power terms. Also, binary variables are needed to model the possibility of free inflow or re-injection of water at reservoirs. The resulting model is thus a non-convex Mixed-Integer Non-Linear Program (MINLP). A discrete-time setting is proposed to solve the problem over a finite horizon made of several intervals. A commercial solver, BONMIN, suited for convex MINLP models is used to heuristically solve the problem. We are able to find a good solution for a small part of an existing network operated by the Vlaamse Maatschappij voor Watervoorziening (VMW), a major drinking water company in Flanders
Avoiding unnecessary demerging and remerging of multiâcommodity integer flows
Resource flows may merge and demerge at a network node. Sometimes several demerged flows may be immediately merged again, but in different combinations compared to before they were demerged. However, the demerging is unnecessary in the first place if the total resources at each of the network nodes involved remains unchanged. We describe this situation as âunnecessary demerging and remerging (UDR)â of flows, which would incur unnecessary operations and costs in practice. Multiâcommodity integer flows in particular will be considered in this paper. This deficiency could be theoretically overcome by means of fixedâcharge variables, but the practicality of this approach is restricted by the difficulty in solving the corresponding integer linear program (ILP). Moreover, in a problem where the objective function has many cost elements, it would be helpful if such operational costs are optimized implicitly. This paper presents a heuristic branching method within an ILP solver for removing UDR without the use of fixedâcharge variables. We use the concept of âflow potentialsâ (different from âflow residuesâ for maxâflows) guided by which underutilized arcs are heuristically banned, thus reducing occurrences of UDR. Flow connection bigraphs and flow connection groups (FCGs) are introduced. We prove that if certain conditions are met, fully utilizing an arc will guarantee an improvement within an FCG. Moreover, a location subâmodel is given when the former cannot guarantee an improvement. More importantly, the heuristic approach can significantly enhance the full fixedâcharge model by warmâstarting. Computational experiments based on realâworld instances have shown the usefulness of the proposed methods
Singleâcommodity stochastic network design under demand and topological uncertainties with insufficient data
Stochastic network design is fundamental to transportation and logistic problems in practice, yet faces new modeling and computational challenges resulted from heterogeneous sources of uncertainties and their unknown distributions given limited data. In this article, we design arcs in a network to optimize the cost of singleâcommodity flows under random demand and arc disruptions. We minimize the network design cost plus cost associated with network performance under uncertainty evaluated by two schemes. The first scheme restricts demand and arc capacities in budgeted uncertainty sets and minimizes the worstâcase cost of supply generation and network flows for any possible realizations. The second scheme generates a finite set of samples from statistical information (e.g., moments) of data and minimizes the expected cost of supplies and flows, for which we bound the worstâcase cost using budgeted uncertainty sets. We develop cuttingâplane algorithms for solving the mixedâinteger nonlinear programming reformulations of the problem under the two schemes. We compare the computational efficacy of different approaches and analyze the results by testing diverse instances of random and realâworld networks. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 154â173, 2017Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137236/1/nav21739_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137236/2/nav21739.pd
On Approximating Restricted Cycle Covers
A cycle cover of a graph is a set of cycles such that every vertex is part of
exactly one cycle. An L-cycle cover is a cycle cover in which the length of
every cycle is in the set L. The weight of a cycle cover of an edge-weighted
graph is the sum of the weights of its edges.
We come close to settling the complexity and approximability of computing
L-cycle covers. On the one hand, we show that for almost all L, computing
L-cycle covers of maximum weight in directed and undirected graphs is APX-hard
and NP-hard. Most of our hardness results hold even if the edge weights are
restricted to zero and one.
On the other hand, we show that the problem of computing L-cycle covers of
maximum weight can be approximated within a factor of 2 for undirected graphs
and within a factor of 8/3 in the case of directed graphs. This holds for
arbitrary sets L.Comment: To appear in SIAM Journal on Computing. Minor change
Topology of Cell-Aggregated Planar Graphs
We present new algorithm for growth of non-clustered planar graphs by
aggregation of cells with given distribution of size and constraint of
connectivity k=3 per node. The emergent graph structures are controlled by two
parameters--chemical potential of the cell aggregation and the width of the
cell size distribution. We compute several statistical properties of these
graphs--fractal dimension of the perimeter, distribution of shortest paths
between pairs of nodes and topological betweenness of nodes and links. We show
how these topological properties depend on the control parameters of the
aggregation process and discuss their relevance for the conduction of current
in self-assembled nanopatterns.Comment: 8 pages, 5 figure
Deciding Feasibility of a Booking in the European Gas Market on a Cycle is in P for the Case of Passive Networks
We show that the feasibility of a booking in the European entry-exit gas market can be decided in polynomial time on single-cycle networks that are passive, i.e., do not contain controllable elements. The feasibility of a booking can be characterized by solving polynomially many nonlinear potential-based flow models for computing so-called potential-difference maximizing load flow scenarios. We thus analyze the structure of these models and exploit both the cyclic graph structure as well as specific properties of potential-based flows. This enables us to solve the decision variant of the nonlinear potential-difference maximization by reducing it to a system of polynomials of constant dimension that is independent of the cycle's size. This system of fixed dimension can be handled with tools from real algebraic geometry to derive a polynomial-time algorithm. The characterization in terms of potential-difference maximizing load flow scenarios then leads to a polynomial-time algorithm for deciding the feasibility of a booking. Our theoretical results extend the existing knowledge about the complexity of deciding the feasibility of bookings from trees to single-cycle networks
A polynomial oracle-time algorithm for convex integer minimization
In this paper we consider the solution of certain convex integer minimization
problems via greedy augmentation procedures. We show that a greedy augmentation
procedure that employs only directions from certain Graver bases needs only
polynomially many augmentation steps to solve the given problem. We extend
these results to convex -fold integer minimization problems and to convex
2-stage stochastic integer minimization problems. Finally, we present some
applications of convex -fold integer minimization problems for which our
approach provides polynomial time solution algorithms.Comment: 19 pages, 1 figur
Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times â A polymatroid optimization approach
We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective
is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem.
We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can
be solved in O(Tfeas(n) log n) time by using our divide-and-conquer technique, where n is the number of jobs and Tfeas(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper
Generalized Multi-Camera Scene Reconstruction Using Graph Cuts
Reconstructing a 3-D scene from more than one camera is a classical problem in computer vision. One of the major sources of difficulty is the fact that not all scene elements are visible from all cameras. In the last few years, two promising approaches have been developed [. . .] that formulate the scene reconstruction problem in terms of energy minimization, and minimize the energy using graph cuts. These energy minimization approaches treat the input images symmetrically, handle visibility constraints correctly, and allow spatial smoothness to be enforced. However, these algorithm propose different problem formulations, and handle a limited class of smoothness terms. One algorithm [. . .] uses a problem formulation that is restricted to two-camera stereo, and imposes smoothness between a pair of cameras. The other algorithm [. . .] can handle an arbitrary number of cameras, but imposes smoothness only with respect to a single camera. In this paper we give a more general energy minimization formulation for the problem, which allows a larger class of spatial smoothness constraints. We show that our formulation includes both of the previous approaches as special cases, as well as permitting new energy functions. Experimental results on real data with ground truth are also included.Engineering and Applied Science
- âŠ