Evdokia Nikolova

Ali Khodabakhsh, Ger Yang, Soumya Basu et al.

Distribution network reconfiguration (DNR) is a tool used by operators to balance line load flows and mitigate losses. As distributed generation and flexible load adoption increases, the impact of DNR on the security, efficiency, and reliability of the grid will increase as well. Today, heuristic-based actions like branch exchange are routinely taken, with no theoretical guarantee of their optimality. This paper considers loss minimization via DNR, which changes the on/off status of switches in the network. The goal is to ensure a radial final configuration (called a spanning tree in the algorithms literature) that spans all network buses and connects them to the substation (called the root of the tree) through a single path. We prove that the associated combinatorial optimization problem is strongly NP-hard and thus likely cannot be solved efficiently. We formulate the loss minimization problem as a supermodular function minimization under a single matroid basis constraint, and use existing algorithms to propose a polynomial time local search algorithm for the DNR problem at hand and derive performance bounds. We show that our algorithm is equivalent to the extensively used branch exchange algorithm, for which, to the best of our knowledge, we pioneer in proposing a theoretical performance bound. Finally, we use a 33-bus network to compare our algorithm's performance to several algorithms published in the literature.

Yutong Wu, Ali Khodabakhsh, Bo Li et al.

We consider a repeated game where a player self-reports her usage of a service and is charged a payment accordingly by a center. The center observes a partial signal, representing part of the player's true consumption, which is generated from a publicly known distribution. The player can report any value that does not contradict the signal and the center issues a payment based on the reported information. Such problems find application in net metering billing in the electricity market, where a customer's actual consumption of the electricity network is masked and complete verification is impractical. When the underlying true value is relatively constant, we propose a penalty mechanism that elicits truthful self-reports. Namely, besides charging the player the reported value, the mechanism charges a penalty proportional to her inconsistent reports. We show how fear of the uncertainty in the future incentivizes the player to be truthful today. For Bernoulli distributions, we give the complete analysis and optimal strategies given any penalty. Since complete truthfulness is not possible for continuous distributions, we give approximate truthful results by a reduction from Bernoulli distributions. We also extend our mechanism to a multi-player cost sharing setting and give equilibrium results.

Ali Khodabakhsh, Evdokia Nikolova

We consider the problem of maximizing a non-monotone DR-submodular function subject to a cardinality constraint. Diminishing returns (DR) submodularity is a generalization of the diminishing returns property for functions defined over the integer lattice. This generalization can be used to solve many machine learning or combinatorial optimization problems such as optimal budget allocation, revenue maximization, etc. In this work we propose the first polynomial-time approximation algorithms for non-monotone constrained maximization. We implement our algorithms for a revenue maximization problem with a real-world dataset to check their efficiency and performance.