On the Impact of Multiobjective Scalarizing Functions

Recently, there has been a renewed interest in decomposition-based approaches for evolutionary multiobjective optimization. However, the impact of the choice of the underlying scalarizing function(s) is still far from being well understood. In this paper, we investigate the behavior of different scalarizing functions and their parameters. We thereby abstract firstly from any specific algorithm and only consider the difficulty of the single scalarized problems in terms of the search ability of a (1+lambda)-EA on biobjective NK-landscapes. Secondly, combining the outcomes of independent single-objective runs allows for more general statements on set-based performance measures. Finally, we investigate the correlation between the opening angle of the scalarizing function's underlying contour lines and the position of the final solution in the objective space. Our analysis is of fundamental nature and sheds more light on the key characteristics of multiobjective scalarizing functions.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII, Ljubljana : Slovenia (2014

Network Interdiction under Uncertainty

We consider variants to one of the most common network interdiction formulations: the shortest path interdiction problem. This problem involves leader and a follower playing a zero-sum game over a directed network. The leader interdicts a set of arcs, and arc costs increase each time they are interdicted. The follower observes the leader\u27s actions and selects a shortest path in response. The leader\u27s optimal interdiction strategy maximizes the follower\u27s minimum-cost path. Our first variant allows the follower to improve the network after the interdiction by lowering the costs of some arcs, and the leader is uncertain regarding the follower\u27s cardinality budget restricting the arc improvements. We propose a multiobjective approach for this problem, with each objective corresponding to a different possible improvement budget value. To this end, we also present the modified augmented weighted Tchebychev norm, which can be used to generate a complete efficient set of solutions to a discrete multi-objective optimization problem, and which tends to scale better than competing methods as the number of objectives grows. In our second variant, the leader selects a policy of randomized interdiction actions, and the follower uses the probability of where interdictions are deployed on the network to select a path having the minimum expected cost. We show that this continuous non-convex problem becomes strongly NP-hard when the cost functions are convex or when they are concave. After formally describing each variant, we present various algorithms for solving them, and we examine the efficacy of all our algorithms on test beds of randomly generated instances

Cooperative control of multi-uavs under communication constraints.

This research aims to develop an analysis and control methodology for the multiple un-manned aerial vehicles (UAVs), connected over a communication network. The wireless communication network between the UAVs is vulnerable to errors and time delays, which may lead to performance degradation or even instability. Analysis on the effects of the potential communication constraints in the multiple UAV control is a critical issue for successful operation of multiple UAVs. Therefore, this thesis proposes a systematic method by incorporating three steps: proposing the analysis method and metrics considering the wireless communication dynamics, designing the structure of the cooperative controller for UAVs, and applying the analysis method to the proposed control in representative applications. For simplicity and general insights on the effect of communication topology, a net-worked system is first analysed without considering the agent or communication dynamics. The network theory specifies important characteristics such as robustness, effectiveness, and synchronisability with respect to the network topology. This research not only reveals the trade-off relationship among the network properties, but also proposes a multi-objective optimisation (MOO) method to find the optimal network topology considering these trade-offs. Extending the analysis to the networked control system with agent and communication dynamics, the effect of the network topology with respect to system dynamics and time delays should be considered. To this end, the effect of communication dynamics is then analysed in the perspective of robustness and performance of the controller. The key philosophy behind this analysis is to approximate the networked control system as a transfer function, and to apply the concepts such as stability margin and sensitivity function in the control theory. Through the analysis, it is shown that the information sharing between the agents to determine their control input deteriorates the robustness of their stability against system uncertainties. In order to compensate the robustness and cancel out the effect of uncertainties, this thesis also develops two different adaptive control methods. The proposed adaptive control methods in this research aim to cope with unmatched uncertainty and time-varying parameter uncertainty, respectively. The effect of unmatched uncertainty is reduced on the nominal performance of the controller, using the parameter-robust linear quadratic Gaussian method and adaptive term. On the other hand, time-varying parameter uncertainty is estimated without requiring the persistent excitation using concurrent learning with the directional forgetting algorithm. The stability of the tracking and parameter estimation error is proved using Lyapunov analysis. The proposed analysis method and control design are demonstrated in two application examples of a formation control problem without any physical interconnection between the agents, and an interconnected slung-load transportation system. The performance of the proposed controllers and the effect of topology and delay on the system performance are evaluated either analytically or numerically.PhD in Aerospac