No Arabic abstract
Search and detection of objects on the ocean surface is a challenging task due to the complexity of the drift dynamics and lack of known optimal solutions for the path of the search agents. This challenge was highlighted by the unsuccessful search for Malaysian Flight 370 (MH370) which disappeared on March 8, 2014. In this paper, we propose an improvement of a search algorithm rooted in the ergodic theory of dynamical systems which can accommodate complex geometries and uncertainties of the drifting search areas on the ocean surface. We illustrate the effectiveness of this algorithm in a computational replication of the conducted search for MH370. In comparison to conventional search methods, the proposed algorithm leads to an order of magnitude improvement in success rate over the time period of the actual search operation. Simulations of the proposed search control also indicate that the initial success rate of finding debris increases in the event of delayed search commencement. This is due to the existence of convergence zones in the search area which leads to local aggregation of debris in those zones and hence reduction of the effective size of the area to be searched.
Within the model of social dynamics determined by collective decisions in a stochastic environment (ViSE model), we consider the case of a homogeneous society consisting of classically rational economic agents (or homines economici, or egoists). We present expressions for the optimal majority threshold and the maximum expected capital increment as functions of the parameters of the environment. An estimate of the rate of change of the optimal threshold at zero is given, which is an absolute constant: $(sqrt{2/pi}-sqrt{pi/2})/2$.
Mean field games (MFGs) and the best reply strategy (BRS) are two methods of describing competitive optimisation of systems of interacting agents. The latter can be interpreted as an approximation of the respective MFG system. In this paper we present a systematic analysis and comparison of the two approaches in the stationary case. We provide novel existence and uniqueness results for the stationary boundary value problems related to the MFG and BRS formulations, and we present an analytical and numerical comparison of the two paradigms in a variety of modelling situations.
This paper shows the capability the alternating direction method of multipliers (ADMM) has to track, in a distributed manner, the optimal down-link beam-forming solution in a multiple input multiple output (MISO) multi-cell network given a dynamic channel. Each time the channel changes, ADMM is allowed to perform one algorithm iteration. In order to implement the proposed scheme, the base stations are not required to exchange channel state information (CSI), but will require to exchange interference values once. We show ADMMs tracking ability in terms of the algorithms Lyapunov function given that the primal and dual solutions to the convex optimization problem at hand can be understood as a continuous mapping from the problems parameters. We show that this holds true even considering that the problem looses strong convexity when it is made distributed. We then show that these requirements hold for the down-link, and consequently up-link, beam-forming case. Numerical examples corroborating the theoretical findings are also provided.
In this paper, we develop mixed integer linear programming models to compute near-optimal policy parameters for the non-stationary stochastic lot sizing problem under Bookbinder and Tans static-dynamic uncertainty strategy. Our models build on piecewise linear upper and lower bounds of the first order loss function. We discuss different formulations of the stochastic lot sizing problem, in which the quality of service is captured by means of backorder penalty costs, non-stockout probability, or fill rate constraints. These models can be easily adapted to operate in settings in which unmet demand is backordered or lost. The proposed approach has a number of advantages with respect to existing methods in the literature: it enables seamless modelling of different variants of the above problem, which have been previously tackled via ad-hoc solution methods; and it produces an accurate estimation of the expected total cost, expressed in terms of upper and lower bounds. Our computational study demonstrates the effectiveness and flexibility of our models.
Agents operating in unstructured environments often produce negative side effects (NSE), which are difficult to identify at design time. While the agent can learn to mitigate the side effects from human feedback, such feedback is often expensive and the rate of learning is sensitive to the agents state representation. We examine how humans can assist an agent, beyond providing feedback, and exploit their broader scope of knowledge to mitigate the impacts of NSE. We formulate this problem as a human-agent team with decoupled objectives. The agent optimizes its assigned task, during which its actions may produce NSE. The human shapes the environment through minor reconfiguration actions so as to mitigate the impacts of the agents side effects, without affecting the agents ability to complete its assigned task. We present an algorithm to solve this problem and analyze its theoretical properties. Through experiments with human subjects, we assess the willingness of users to perform minor environment modifications to mitigate the impacts of NSE. Empirical evaluation of our approach shows that the proposed framework can successfully mitigate NSE, without affecting the agents ability to complete its assigned task.