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Global supply chains of high value low volume products
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On Robust Tie-line Scheduling in Multi-Area Power Systems
The tie-line scheduling problem in a multi-area power system seeks to
optimize tie-line power flows across areas that are independently operated by
different system operators (SOs). In this paper, we leverage the theory of
multi-parametric linear programming to propose algorithms for optimal tie-line
scheduling within a deterministic and a robust optimization framework. Through
a coordinator, the proposed algorithms are proved to converge to the optimal
schedule within a finite number of iterations. A key feature of the proposed
algorithms, besides their finite step convergence, is the privacy of the
information exchanges; the SO in an area does not need to reveal its dispatch
cost structure, network constraints, or the nature of the uncertainty set to
the coordinator. The performance of the algorithms is evaluated using several
power system examples
Random Neural Networks and Optimisation
In this thesis we introduce new models and learning algorithms for the Random
Neural Network (RNN), and we develop RNN-based and other approaches for the
solution of emergency management optimisation problems.
With respect to RNN developments, two novel supervised learning algorithms are
proposed. The first, is a gradient descent algorithm for an RNN extension model
that we have introduced, the RNN with synchronised interactions (RNNSI), which
was inspired from the synchronised firing activity observed in brain neural circuits.
The second algorithm is based on modelling the signal-flow equations in RNN as a
nonnegative least squares (NNLS) problem. NNLS is solved using a limited-memory
quasi-Newton algorithm specifically designed for the RNN case.
Regarding the investigation of emergency management optimisation problems,
we examine combinatorial assignment problems that require fast, distributed and
close to optimal solution, under information uncertainty. We consider three different
problems with the above characteristics associated with the assignment of
emergency units to incidents with injured civilians (AEUI), the assignment of assets
to tasks under execution uncertainty (ATAU), and the deployment of a robotic
network to establish communication with trapped civilians (DRNCTC).
AEUI is solved by training an RNN tool with instances of the optimisation problem
and then using the trained RNN for decision making; training is achieved using
the developed learning algorithms. For the solution of ATAU problem, we introduce
two different approaches. The first is based on mapping parameters of the
optimisation problem to RNN parameters, and the second on solving a sequence of
minimum cost flow problems on appropriately constructed networks with estimated
arc costs. For the exact solution of DRNCTC problem, we develop a mixed-integer
linear programming formulation, which is based on network flows. Finally, we design
and implement distributed heuristic algorithms for the deployment of robots
when the civilian locations are known or uncertain
Network recovery from massive failures under uncertain knowledge of damages
This paper addresses progressive network recovery under uncertain knowledge of damages. We formulate the problem as a mixed integer linear programming (MILP), and show that it is NP-Hard. We propose an iterative stochastic recovery algorithm (ISR) to recover the network in a progressive manner to satisfy the critical services. At each optimization step, we make a decision to repair a part of the network and gather more information iteratively, until critical services are completely restored. Three different algorithms are used to find a feasible set and determine which node to repair, namely, 1) an iterative shortest path algorithm (ISR-SRT), 2) an approximate branch and bound (ISR-BB) and 3) an iterative multi-commodity LP relaxation (ISR-MULT). Further, we have modified the state-of-the-Art iterative split and prune (ISP) algorithm to incorporate the uncertain failures. Our results show that ISR-BB and ISR- MULT outperform the state-of-the-Art 'progressive ISP' algorithm while we can configure our choice of trade-off between the execution time, number of repairs (cost) and the demand loss. We show that our recovery algorithm, on average, can reduce the total number of repairs by a factor of about 3 with respect to ISP, while satisfying all critical deman
Robust optimization with incremental recourse
In this paper, we consider an adaptive approach to address optimization
problems with uncertain cost parameters. Here, the decision maker selects an
initial decision, observes the realization of the uncertain cost parameters,
and then is permitted to modify the initial decision. We treat the uncertainty
using the framework of robust optimization in which uncertain parameters lie
within a given set. The decision maker optimizes so as to develop the best cost
guarantee in terms of the worst-case analysis. The recourse decision is
``incremental"; that is, the decision maker is permitted to change the initial
solution by a small fixed amount. We refer to the resulting problem as the
robust incremental problem. We study robust incremental variants of several
optimization problems. We show that the robust incremental counterpart of a
linear program is itself a linear program if the uncertainty set is polyhedral.
Hence, it is solvable in polynomial time. We establish the NP-hardness for
robust incremental linear programming for the case of a discrete uncertainty
set. We show that the robust incremental shortest path problem is NP-complete
when costs are chosen from a polyhedral uncertainty set, even in the case that
only one new arc may be added to the initial path. We also address the
complexity of several special cases of the robust incremental shortest path
problem and the robust incremental minimum spanning tree problem
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