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We consider the problem to evacuate several regions due to river flooding, where sufficient time is given to plan ahead. To ensure a smooth evacuation procedure, our model includes the decision which regions to assign to which shelter, and when evacuation orders should be issued, such that roads do not become congested.
Due to uncertainty in weather forecast, several possible scenarios are simultaneously considered in a robust optimization framework. To solve the resulting integer program, we apply a Tabu search algorithm based on decomposing the problem into better tractable subproblems. Computational experiments on random instances and an instance based on Kulmbach, Germany, data show considerable improvement compared to an MIP solver provided with a strong starting solution.

Due to the increasing number of natural or man-made disasters, the application of operations research methods in evacuation planning has seen a rising interest in the research community. From the beginning, evacuation planning has been highly focused on car-based evacuation. Recently, also the evacuation of transit depended evacuees with the help of buses has been considered.
In this case study, we apply two such models and solution algorithms to evacuate a core part of the metropolitan capital city Kathmandu of Nepal as a hypothetical endangered region, where a large part of population is transit dependent. We discuss the computational results for evacuation time under a broad range of possible scenarios, and derive planning suggestions for practitioners.

By natural or man-made disasters, the evacuation of a whole region or city may become necessary. Apart from private traffic, the evacuation from collection points to secure shelters outside the endangered region will be realized by a bus fleet made available by emergency relief. The arising Bus Evacuation Problem (BEP) is a vehicle scheduling problem, in which a given number of evacuees needs to be transported from a set of collection points to a set of capacitated shelters, minimizing the total evacuation time, i.e., the time needed until the last person is brought to safety.
In this paper we consider an extended version of the BEP, the Robust Bus Evacuation Problem (RBEP), in which the exact numbers of evacuees are not known, but may stem from a set of probable scenarios. However, after a given reckoning time, this uncertainty is eliminated and planners are given exact figures. The problem is to decide for each bus, if it is better to send it right away -- using uncertain numbers of evacuees -- or to wait until the numbers become known.
We present a mixed-integer linear programming formulation for the RBEP and discuss solution approaches; in particular, we present a tabu search framework for finding heuristic solutions of acceptable quality within short computation time. In computational experiments using both randomly generated instances and the real-world scenario of evacuating the city of Kaiserslautern, we compare our solution approaches.

We consider storage loading problems where items with uncertain weights have
to be loaded into a storage area, taking into account stacking and
payload constraints. Following the robust optimization paradigm, we propose
strict and adjustable optimization models for finite and interval-based
uncertainties. To solve these problems, exact decomposition and heuristic
solution algorithms are developed.
For strict robustness, we also present a compact formulation based
on a characterization of worst-case scenarios.
Computational results show that computation times and algorithm
gaps are reasonable for practical applications.
Furthermore, we find that the robustness concepts show different
potential depending on the type of data being used.

Geometric Programming is a useful tool with a wide range of applications in engineering. As in real-world problems input data is likely to be affected by uncertainty, Hsiung, Kim, and Boyd introduced robust geometric programming to include the uncertainty in the optimization process. They also developed a tractable approximation method to tackle this problem. Further, they pose the question whether there exists a tractable reformulation of their robust geometric programming model instead of only an approximation method. We give a negative answer to this question by showing that robust geometric programming is co-NP hard in its natural posynomial form.

We consider a network flow problem, where the outgoing flow is reduced by a certain percentage in each node. Given a maximum amount of flow that can leave the source node, the aim is to find a solution that maximizes the amount of flow which arrives at the sink.
Starting from this basic model, we include two new, additional aspects: On the one hand, we are able to reduce the loss at some of the nodes; on the other hand, the exact loss values are not known, but may come from a discrete uncertainty set of exponential size.
Applications for problems of this type can be found in evacuation planning, where one would like to improve the safety of nodes such that the number of evacuees reaching safety is maximized.
We formulate the resulting robust flow problem with losses and improvability as a mixed-integer program for finitely many scenarios, and present an iterative scenario-generation procedure that avoids the inclusion of all scenarios from the beginning. In a computational study using both randomly generated instance and realistic data based on the city of Nice, France, we compare our solution algorithms.

We present a new approach to handle uncertain combinatorial optimization problems that uses solution ranking procedures to determine the degree of robustness of a solution. Unlike classic concepts for robust optimization, our approach is not purely based on absolute quantitative performance, but also includes qualitative aspects that are of major importance for the decision maker.
We discuss the two variants, solution ranking and objective ranking robustness, in more detail, presenting problem complexities and solution approaches. Using an uncertain shortest path problem as a computational example, the potential of our approach is demonstrated in the context of evacuation planning due to river flooding.

We discuss the problem of evaluating a robust solution.
To this end, we first give a short primer on how to apply robustification approaches to uncertain optimization problems using the assignment problem and the knapsack problem as illustrative examples.
As it is not immediately clear in practice which such robustness approach is suitable for the problem at hand,
we present current approaches for evaluating and comparing robustness from the literature, and introduce the new concept of a scenario curve. Using the methods presented in this paper, an easy guide is given to the decision maker to find, solve and compare the best robust optimization method for his purposes.

We argue that the concepts of resilience in engineering science and robustness in mathematical optimization are strongly related. Using evacuation planning as an example application, we demonstrate optimization techniques to improve solution resilience. These include a direct modelling of the uncertainty for stochastic or robust optimization, as well as taking multiple objective functions into account.

We consider an uncertain traveling salesman problem, where distances between nodes are not known exactly, but may stem from an uncertainty set of possible scenarios. This uncertainty set is given as intervals with an additional bound on the number of distances that may deviate from their expected, nominal value.
A recoverable robust model is proposed, that allows a tour to change a bounded number of edges once a scenario becomes known. As the model contains an exponential number of constraints and variables, an iterative algorithm is proposed, in which tours and scenarios are computed alternately.
While this approach is able to find a provably optimal solution to the robust model, it also needs to solve increasingly complex subproblems. Therefore, we also consider heuristic solution procedures based on local search moves using a heuristic estimate of the actual objective function. In computational experiments, these approaches are compared.
Finally, an alternative recovery model is discussed, where a second-stage recovery tour is not required to visit all nodes of the graph. We show that the previously NP-hard evaluation of a fixed solution now becomes solvable in polynomial time.