The superiorization method (SM) is situated between feasibility-seeking and constrained optimization. Instead of aiming at the minimum of a given objective function over a constraint set, it seeks a feasible point at which the objective function value is reduced — though not necessarily minimal — compared to that reached by the feasibility-seeking algorithm alone. This … Read more
Human activities increasingly fragment natural habitats, placing many species at risk of population decline. This creates an urgent need to preserve biodiversity and maintain ecological connectivity through wildlife corridors. We present two spatial optimization models for corridor design that explicitly incorporate corridor width as a key ecological criterion. The first model minimizes total corridor cost … Read more
The global demand for grid-scale energy storage continues to increase. Carnot batteries (CBs) are not geographically constrained and consist of mature components. Furthermore, charging power, discharging power, and storage capacity can be sized independently and tailored to the intended use case. Designing an optimal CB also requires considering the resulting operational behavior. While design and … Read more
We propose a new mathematical model to describe equilibria in competitive markets. Our approach transforms the well-known complementary formulation into a numerically more efficient optimization framework. In complementarity models, the actions of all elastic consumers in the market are implicitly represented by their aggregate demand. Instead, we introduce demand-induced utilities, which can be explicitly constructed individually for each consumer. … Read more
Participants in energy markets make sequential decisions across multiple time horizons under uncertainty, leading to large-scale multistage stochastic optimization problems. Stochastic dual dynamic programming is widely used for its tractability, but its application to modern energy markets is challenged by nested dependencies induced by participation across multiple interrelated markets under increasing uncertainty from distributed energy … Read more
We propose a betweenness centrality measure and algorithms for stochastic networks, where edges can fail and weights vary across realizations, making the most central node random. Our approach models the sequence of reported central nodes as an absorbing Markov chain and measures node importance by the share of pre-absorption time spent at each node. This … Read more
Electricity storage is used for intertemporal price arbitrage and for ancillary services that balance unforeseen supply and demand fluctuations via frequency regulation. We present an optimization model that computes bids for both arbitrage and frequency regulation and ensures that storage operators can honor their market commitments at all times for all fluctuation signals in an … Read more
Many large-scale optimization problems decompose into a master problem and scenario subproblems, a structure that can be exploited by Benders decomposition. In Benders decomposition, each iteration may generate many cuts from scenario subproblems, and adding all of them as constraints then causes the master problem to grow rapidly. These are constraints that may need to … Read more
Modern energy grid expansion planning, by necessity, includes timeseries data to accurately model storage and renewable assets. Representative time periods are commonly used as a way to decrease problem size and therefore mitigate the increased complexity from this inclusion. However, there are many choices around these representative periods: length; location in planning horizon; boundary conditions. … Read more
We study computational aspects of a key problem in robust statistics—the penalized least trimmed squares (LTS) regression problem, a robust estimator that mitigates the influence of outliers in data by capping residuals with large magnitudes. Although statistically attractive, penalized LTS is NP-hard, and existing mixed-integer optimization (MIO) formulations scale poorly due to weak relaxations and … Read more