While most methods for solving mixed-integer optimization problems seek a single optimal solution, finding a diverse set of near-optimal solutions can often be more useful. State of the art methods for generating diverse near-optimal solutions usually take a two-phase approach, first finding a set of near-optimal solutions and then finding a diverse subset. In contrast, we present a method of finding a set of diverse solutions by emphasizing diversity within the search for near-optimal solutions. Specifically, within a branch-and-bound framework, we investigate parameterized node selection rules that explicitly consider diversity. Our results indicate that our approach significantly increases diversity of the final solution set. When compared with existing methods for finding diverse near-optimal sets, our method runs with similar run-time as regular node selection methods and gives a diversity improvement of up to 140%. In contrast, popular node selection rules such as best-first search gives an improvement of no more than 40%. Further, we find that our method is most effective when diversity is emphasized more in node selection when deeper in the tree and when the solution set has grown large enough.
Disaster recovery efforts are enhanced through the collection and dissemination of satellite data, which is downloaded from satellites to ground stations. The optimal ground station locations vary depending on the location of the disaster, but ground station construction occurs before the realization of a disaster. Thus, a stochastic optimization problem arises: decide the location of ground stations before disasters with uncertain locations. We use a stochastic programming approach to select the location of ground stations given a set of potential disaster scenarios. The objective is to maximize the expected amount of data downloaded. The problem formulation consists of a two-stage stochastic program where the first-stage determines the locations of the ground stations and the second-stage schedules the uploading and downloading of data. We solve the problem using the L-shaped method; we find that it significantly outperforms solving the deterministic equivalent problem directly. We also find that an alternate second-stage formulation significantly improves solution time. The optimized set of ground stations found by our algorithm is compared to the set of ground stations operated by the National Oceanic and Atmospheric Administration’s; results confirm that the current placement is effective and demonstrate the benefit in adding additional ground stations.
The ubiquitous nature of wireless networks makes them increasingly prone to jamming attacks as such attacks become more sophisticated. In this paper, we seek to gain understanding about a particular type of jamming attack: the flow-jamming attack. Toward this end, we provide a mixed-integer programming model for optimizing the location of jamming devices for flow-jamming attacks. An accelerated Benders decomposition approach was used to solve the model. We solved the problem for two realistic networks and 12 randomly generated networks and found that the Benders approach was computationally faster than CPLEX for nearly all the problem instances, particularly for larger problems with 1000 binary variables. The experimental results show that optimally locating jamming devices can increase the impact of flow-jamming attacks. Specifically, as the number of possible locations increases the jammers’ efficacy increases as well, but there is a clear point of diminishing returns. Also, adding lower-powered jammers to work in conjunction with higher powered jammers significantly increases overall efficacy in spite of the power difference.
We study a security problem in which an adversary seeks to attack a landscape by setting a wildfire in a strategic location, whereas wildfire managers wish to mitigate the damage of the attack by implementing a fuel treatment in the landscape. We model the problem as a min–max Stackelberg game with the goal of identifying an optimal fuel treatment plan that minimizes the impact of a pyro-terror attack. As the adversary’s problem is discrete, we use a decomposition algorithm suitable for integer bi-level programs. We test our model on three test landscape cases located in the Western United States. The results indicate that fuel treatment can effectively mitigate the effects of an attack: implementing fuel treatment on 2, 5, and 10% of the landscape, on average, reduces the damage caused by a pyro-terror attack by 14, 27, and 43%, respectively. The resulting fuel treatment plan is also effective in mitigating natural wildfires with randomly placed ignition points. The pyro-terrorism mitigation problem studied in this article is equivalent to the b-interdiction-covering problem where the intermediate nodes are subject to interdiction. It can also be interpreted as the problem of identifying the b-most-vital nodes in a one-to-all shortest path problem.
There is significant value in the data collected by satellites during and after a natural disaster. The current operating paradigm in practice is for satellites to passively collect data when they happen to fly over a disaster location. Conversely, this article considers the alternative approach of actively maneuvering satellites to fly directly overhead of the disaster site on a routine basis. Toward this end, we seek to compute a satellite constellation design that minimizes the expected maneuver costs for monitoring an unknown forest fire. In this article, we present a 2‐stage stochastic programing model for this problem as well as a accelerated L‐shaped decomposition approach. A comparison between our approach and the current operating paradigm indicates that our solution provides longer duration data collections and a greater number of data collections. Analysis also shows that our proposed solution is robust over a wide array of scenarios.