Title: Symmetrically Fair AllocationsAbstract: We consider a setting in which items need to be prepackaged into bundles and agents pick an arbitrary bundle without knowing its contents. We prove guarantees on the fairness of allocations when the values of the items to the agents are nonnegative, additive, and known, but potentially heterogeneous. As items are indivisible, a common fairness notion is “envy freeness up to one good’’ (EF1), in which bundles can be assigned to agents such that every agent is almost envy free: they weakly prefer their own bundle over any other bundle minus the value of their highest-valued item in the other bundle. We instead strive for a more stringent goal, to find what we call a “symmetrically envy free up to one good”, or symEF1, partition of the goods. With a symEF1 partition, any arbitrary assignment of one bundle each to the agents results in an EF1 allocation. We show that if agents have identical or disjoint preferences, then it is always possible to find a symEF1 partition. We give an example where a symEF1 partition may not exist for three agents. For two agents, we present strong evidence that a symEF1 partition always exists without any further assumptions on preferences.

Abstract: As more renewables are introduced into the energy mix world-wide, power systems are in demand of an increasing degree of flexibility. A grid can be adjusted to meet changed requirements by changing its topology. Such topology changes come in varying degrees of complexity – from switching off lines to reconfiguring substations. Finding feasible and improved topologies, however, is a challenging problem computationally. In this talk, the main topology control schemes are introduced. Furthermore, an outlook is giving on how solutions can be obtained for the resulting mixed-integer problems.

Abstract: Recent claims on “solving” combinatorial optimization problems via quantum computers has attracted many researchers to work on quantum algorithms. The max k-cut problem is a challenging combinatorial optimization problem with multiple notorious mixed integer linear optimization (MILO) formulations. Motivated by recent progress of classical solvers in handling quadratic optimization problems, we revisit the binary quadratic optimization (BQO) formulation of Carlson and Nemhauser (Operations Research, 1966) and provide theoretical and computational comparisons between different mixed integer optimization formulations of the max k-cut problem. While no claim on “quantum advantage” is provided, we introduce quadratic unconstrained binary optimization (QUBO) formulations with tight penalty coefficients. We also design quantum circuits for finding feasible solutions of the problem by a quantum approximate optimization algorithm (QAOA). To accelerate the solve process and to handle large-scale instances of the problem, we propose a preprocessing procedure that can be employed in both classical and quantum contexts. Finally, we test the performance of our classical and quantum-inspired formulations on an extensive set of instances. Codes and data are available on GitHub.

Bio: Hamidreza Validi is a Postdoctoral Research Associate in the Department of Computational and Applied Mathematics at Rice University. He is broadly interested in integer programming and network optimization with applications in political redistricting, machine learning, and quantum computing. Hamid has accepted papers at Operations Research, INFORMS Journal on Computing, and Networks. He is a recipient of the 2021 INFORMS Computing Society Harvey J. Greenberg Research Award.

Preceding his presentation, Dr. Smith explained that he didn’t want to dissuade anyone from choosing to get a Ph.D.; if you have the passion, then go for it. He explained that no one knows what it is they would like to research upon entering the Ph.D. program. Most students are taken through general courses for their first year to broaden their academia which helps the students decide the path that they would like to take with their classes – these paths delve deeper into the subjects that they decide to study. Eventually, students seek out the aid of advisors for these subjects and when they hit their second year the work deviates from classes to research problems. The goal of these research problems is to not only expose you to never-before-done projects, but to also help you get work published. UF ranks at the top for publications in many of the best Operations Research journals. UF’s Ph.D. program for ISE accepts about twelve students, on average, every year out of about 250 applications from all over the world. Their selection process aims to diversify the classes so you’ll always be exposed to different backgrounds. UF does not accept any Ph.D. students that do not get funded from the school (tuition plus a livable salary). As for life after an Industrial Engineering Ph.D., some go on to work for the Department of Defense, the military, or FedEx just to name a few. The biggest point that Dr. Smith wanted to drive home about getting a Ph.D. is that there’s no need to push into a Ph.D. unless you really love at least one aspect of the work. Dr. Smith proceeded to challenge attendees with a few examples of the types of problems students solve in graduate school for Operations Research.

Dr. Carrillo began her presentation by asking students if they knew they wanted to be industrial engineers when they were ten. Of course most everyone laughed at that question. Dr. Carrillo considers herself an “Accidental OM Academic” because of the ‘accidental’ way in which she became a professor and involved with research in operations management. What followed was a Q&A style presentation, in which students asked Dr. Carrillo questions about her research, the difference between operations management and operations research, and about her experience being a professor.