19,559 research outputs found
A computational analysis of lower bounds for big bucket production planning problems
In this paper, we analyze a variety of approaches to obtain lower bounds for multi-level production planning problems with big bucket capacities, i.e., problems in which multiple items compete for the same resources. We give an extensive survey of both known and new methods, and also establish relationships between some of these methods that, to our knowledge, have not been presented before. As will be highlighted, understanding the substructures of difficult problems provide crucial insights on why these problems are hard to solve, and this is addressed by a thorough analysis in the paper. We conclude with computational results on a variety of widely used test sets, and a discussion of future research
Transmit Signal and Bandwidth Optimization in Multiple-Antenna Relay Channels
Transmit signal and bandwidth optimization is considered in multiple-antenna
relay channels. Assuming all terminals have channel state information, the
cut-set capacity upper bound and decode-and-forward rate under full-duplex
relaying are evaluated by formulating them as convex optimization problems. For
half-duplex relays, bandwidth allocation and transmit signals are optimized
jointly. Moreover, achievable rates based on the compress-and-forward
transmission strategy are presented using rate-distortion and Wyner-Ziv
compression schemes. It is observed that when the relay is close to the source,
decode-and-forward is almost optimal, whereas compress-and-forward achieves
good performance when the relay is close to the destination.Comment: 16 pages, 10 figure
Convex Relaxations for Gas Expansion Planning
Expansion of natural gas networks is a critical process involving substantial
capital expenditures with complex decision-support requirements. Given the
non-convex nature of gas transmission constraints, global optimality and
infeasibility guarantees can only be offered by global optimisation approaches.
Unfortunately, state-of-the-art global optimisation solvers are unable to scale
up to real-world size instances. In this study, we present a convex
mixed-integer second-order cone relaxation for the gas expansion planning
problem under steady-state conditions. The underlying model offers tight lower
bounds with high computational efficiency. In addition, the optimal solution of
the relaxation can often be used to derive high-quality solutions to the
original problem, leading to provably tight optimality gaps and, in some cases,
global optimal soluutions. The convex relaxation is based on a few key ideas,
including the introduction of flux direction variables, exact McCormick
relaxations, on/off constraints, and integer cuts. Numerical experiments are
conducted on the traditional Belgian gas network, as well as other real larger
networks. The results demonstrate both the accuracy and computational speed of
the relaxation and its ability to produce high-quality solutions
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