Real life optimization often concerns difficult objective functions, in two aspects, namely that gradients are unavailable, and that evaluation of the objective function takes a long time. Such problems are often attacked with model building algorithms, where an approximation of the function is constructed and solved, in order to find a new promising point to evaluate. We study several ways of saving time by using parallel calculations in the context of model building algorithms, which is not trivial, since such algorithms are inherently sequential. We present a number of ideas that has been implemented and tested on a large number of known test functions, and a few new ones. The computational results reveal that some ideas are quite promising.

This thesis is divided into two parts that each is concerned with a specific problem.

The problem under consideration in the first part is to find suitable graph representations, abstractions, cost measures and algorithms for calculating placements of unmanned aerial vehicles (UAVs) such that they can keep one or several static targets under constant surveillance. Each target is kept under surveillance by a surveillance UAV, which transmits information, typically real time video, to a relay UAV. The role of the relay UAV is to retransmit the information to another relay UAV, which retransmits it again to yet another UAV. This chain of retransmission continues until the information eventually reaches an operator at a base station.

When there is a single target, then all Pareto-optimal solutions, i.e. all relevant compromises between quality and the number of UAVs required, can be found using an efficient new algorithm. If there are several targets, the problem becomes a variant of the Steiner tree problem and to solve this problem we adapt an existing algorithm to find an initial tree. Once it is found, we can further improve it using a new algorithm presentedin this thesis.

The second problem is optimization of time-consuming problems where the objective function is seen as a black box, where the input parameters are sent and a function valueis returned. This has the important implication that no gradient or Hessian information is available. Such problems are common when simulators are used to perform advanced calculations such as crash test simulations of cars, dynamic multibody simulations etc. It is common that a single function evaluation takes several hours.

Algorithms for solving such problems can be broadly divided into direct search algorithms and model building algorithms. The first kind evaluates the objective function directly, whereas the second kind builds a model of the objective function, which is then optimized in order to find a new point where it is believed that objective function has agood value. Then the objective function is evaluated in that point.

Since the objective function is very time-consuming, it is common to focus on minimizing the number of function evaluations. However, this completely disregards the possibility to perform calculations in parallel and to exploit this we investigate different ways parallelization can be used in model-building algorithms. Some of the ways to do this is to use several starting points, generate several new points in each iteration, new ways of predicting a point’s value and more.

We have implemented the parallel extensions in one of the state of the art algorithms for derivative-free optimization and report results from testing on synthetic benchmarksas well as from solving real industrial problems.

We present results from testing of parallel versions of algorithms for derivativefree optimization. Such algorithms are required when an analytical expression for the objective function is not available, which often happens in simulator-driven product development. Since the objective function is unavailable, we cannot use the common algorithms that require gradient and Hessian information. Instead special algorithms for derivative-free optimization are used. Such algorithms are typically sequential, and here we present the rst test results of parallelization of such algorithms. The parallel extensions include using several start points, generating several points from each start point in each iteration, alternative model building, and more. We also investigate whether we can generate synergy between the di erent start points through information sharing. Examples of this include using several models to predict the objective function value of a point in order to prioritize the order in which points are sent for evaluation. We also present results for higher-level control of the optimization algorithms.

Surveillance is an important application for unmanned aerial vehicles (UAVs). The sensed information often has high priority and it must be made available to human operators as quickly as possible. Due to obstacles and limited communication range, it is not always possible to transmit the information directly to the base station. In this case, other UAVs can form a relay chain between the surveillance UAV and the base station. Determining suitable positions for such UAVs is a complex optimization problem in and of itself, and is made even more difficult by communication and surveillance constraints.

To solve different variations of finding positions for UAVs for surveillance of one target, two new algorithms have been developed. One of the algorithms is developed especially for finding a set of relay chains offering different trade-offs between the number of UAVsand the quality of the chain. The other algorithm is tailored towards finding the highest quality chain possible, given a limited number of available UAVs.

Finding the optimal positions for surveillance of several targets is more difficult. A study has been performed, in order to determine how the problems of interest can besolved. It turns out that very few of the existing algorithms can be used due to the characteristics of our specific problem. For this reason, an algorithm for quickly calculating positions for surveillance of multiple targets has been developed. This enables calculation of an initial chain that is immediately made available to the user, and the chain is then incrementally optimized according to the user’s desire.

An important use of unmanned aerial vehicles is surveillance of distant targets, where sensor information must quickly be transmitted back to a base station. In many cases, high uninterrupted bandwidth requires line-of-sight between sender and transmitter to minimize quality degradation. Communication range is typically limited, especially when smaller UAVs are used. Both problems can be solved by creating relay chains for surveillance of a single target, and relay trees for simultaneous surveillance of multiple targets. In this paper, we show how such chains and trees can be calculated. For relay chains we create a set of chains offering different trade-offs between the number of UAVs in the chain and the chain’s cost. We also show new results on how relay trees can be quickly calculated and then incrementally improved if necessary. Encouraging empirical results for improvement of relay trees are presented.

We consider a constrained optimization problem with mixed integer and real variables. It models optimal placement of communications relay nodes in the presence of obstacles. This problem is widely encountered, for instance, in robotics, where it is required to survey some target located in one point and convey the gathered information back to a base station located in another point. One or more unmanned aerial or ground vehicles (UAVs or UGVs) can be used for this purpose as communications relays. The decision variables are the number of unmanned vehicles (UVs) and the UV positions. The objective function is assumed to access the placement quality. We suggest one instance of such a function which is more suitable for accessing UAV placement. The constraints are determined by, firstly, a free line of sight requirement for every consecutive pair in the chain and, secondly, a limited communication range. Because of these requirements, our constrained optimization problem is a difficult multi-extremal problem for any fixed number of UVs. Moreover, the feasible set of real variables is typically disjoint. We present an approach that allows us to efficiently find a practically acceptable approximation to a global minimum in the problem of optimal placement of communications relay nodes. It is based on a spatial discretization with a subsequent reduction to a shortest path problem. The case of a restricted number of available UVs is also considered here. We introduce two label correcting algorithms which are able to take advantage of using some peculiarities of the resulting restricted shortest path problem. The algorithms produce a Pareto solution to the two-objective problem of minimizing the path cost and the number of hops. We justify their correctness. The presented results of numerical 3D experiments show that our algorithms are superior to the conventional Bellman-Ford algorithm tailored to solving this problem.

When unmanned aerial vehicles (UAVs) are used to survey distant targets, it is important to transmit sensor information back to a base station. As this communication often requires high uninterrupted bandwidth, the surveying UAV often needs afree line-of-sight to the base station, which can be problematic in urban or mountainous areas. Communication ranges may also belimited, especially for smaller UAVs. Though both problems can be solved through the use of relay chains consisting of one or more intermediate relay UAVs, this leads to a new problem: Where should relays be placed for optimum performance? We present two new algorithms capable of generating such relay chains, one being a dual ascent algorithm and the other a modification of the Bellman-Ford algorithm. As the priorities between the numberof hops in the relay chain and the cost of the chain may vary, wecalculate chains of different lengths and costs and let the ground operator choose between them. Several different formulations for edge costs are presented. In our test cases, both algorithms are substantially faster than an optimized version of the original Bellman-Ford algorithm, which is used for comparison.

When unmanned aerial vehicles (UAVs) are used for surveillance, information must often be transmitted to a base station in real time. However, limited communication ranges and the common requirement of free line of sight may make direct transmissions from distant targets impossible. This problem can be solved using relay chains consisting of one or more intermediate relay UAVs. This leads to the problem of positioning such relays given known obstacles, while taking into account a possibly mission-specific quality measure. The maximum quality of a chain may depend strongly on the number of UAVs allocated. Therefore, it is desirable to either generate a chain of maximum quality given the available UAVs or allow a choice from a spectrum of Pareto-optimal chains corresponding to different trade-offs between the number of UAVs used and the resulting quality. In this article, we define several problem variations in a continuous three-dimensional setting. We show how sets of Pareto-optimal chains can be generated using graph search and present a new label-correcting algorithm generating such chains significantly more efficiently than the best-known algorithms in the literature. Finally, we present a new dual ascent algorithm with better performance for certain tasks and situations.

We provide an overview of ongoing research which targets development of a principled framework for mixed-initiative interaction with unmanned aircraft systems (UAS). UASs are now becoming technologically mature enough to be integrated into civil society. Principled interaction between UASs and human resources is an essential component in their future uses in complex emergency services or bluelight scenarios. In our current research, we have targeted a triad of fundamental, interdependent conceptual issues: delegation, mixed- initiative interaction and adjustable autonomy, that is being used as a basis for developing a principled and well-defined framework for interaction. This can be used to clarify, validate and verify different types of interaction between human operators and UAS systems both theoretically and practically in UAS experimentation with our deployed platforms.

We consider a constrained optimization problem with mixed integer and real variables. It models optimal placement of communications relay nodes in the presence of obstacles. This problem is widely encountered, for instance, in robotics, where it is required to survey some target located in one point and convey the gathered information back to a base station located in another point. One or more unmanned aerial or ground vehicles (UAVs or UGVs) can be used for this purpose as communications relays. The decision variables are the number of unmanned vehicles (UVs) and the UV positions. The objective function is assumed to access the placement quality. We suggest one instance of such a function which is more suitable for accessing UAV placement. The constraints are determined by, firstly, a free line of sight requirement for every consecutive pair in the chain and, secondly, a limited communication range. Because of these requirements, our constrained optimization problem is a difficult multi-extremal problem for any fixed number of UVs. Moreover, the feasible set of real variables is typically disjoint. We present an approach that allows us to efficiently find a practically acceptable approximation to a global minimum in the problem of optimal placement of communications relay nodes. It is based on a spatial discretization with a subsequent reduction to a shortest path problem. The case of a restricted number of available UVs is also considered here. We introduce two label correcting algorithms which are able to take advantage of using some peculiarities of the resulting restricted shortest path problem. The algorithms produce a Pareto solution to the two-objective problem of minimizing the path cost and the number of hops. We justify their correctness. The presented results of numerical 3D experiments show that our algorithms are superior to the conventional Bellman-Ford algorithm tailored to solving this problem.