Resumo da Palestra:

Combinatorial optimization involves selecting the best option from the combination of several factors. As the number of factors increases, the number of possible combinations increases exponentially, often resulting in unpractical solution times for many problems in general-purpose computers. Fujitsu developed the Digital Annealer, a quantum-inspired architecture to solve combinatorial optimization problems in their quadratic unconstrained binary optimization (QUBO) form. This talk provides and introduction the QUBO approach to combinatorial optimization problems, solution methods involving the Digital Annealer, and examples of recent applications of the Digital Annealer to solve problems in the healthcare and energy industries. 

Resumo da Palestra:

Energy management is about efficiently employing resources to balance energy demands. With the increasing share of intermittent renewable sources of power generation, the need to handle uncertainty in such optimization problems has become of paramount importance for higher reliability and higher profitability. Although minimization of expected cost and maximization of expected income are the most common objectives, conservation of resources and climate protection gain protagonism as new legislation on the energy system evolution comes in. Unfortunately, in such a contemporary context, many stochastic energy management problems lack recourse, meaning that no corrective actions can be taken in the future to compensate for possible wrong decisions made today. The absence of recourse in stochastic optimization triggers the use of models involving probability functions. While such models are generally intuitive and straightforward to explain, they give rise to challenging optimization problems as probability functions are neither convex nor concave and often lack differentiability. Furthermore, accessing a multidimensional probability function amounts to evaluating numerically a multidimensional integral, a task that can be accomplished in reasonable CPU times only if precision is not a concern. For these reasons, specialized optimization methods must come into play. This talk will discuss two classes of stochastic programs: chance-constrained optimization and probability maximation problems. Our presentation will cover some basic concepts and properties of multidimensional probability functions along with some recent methods for nonconvex smooth and nonsmooth optimization problems involving a probability function.

Resumo da Palestra:

In this talk, we deal with special graph colorings and polyhedral combinatorics for MILP formulations, to better solve channel assignment problems in artificial/real-world mobile wireless networks. We consider graph coloring problems involving distance constraints as weighted edges. Some more general graph coloring problems were proposed in the literature that constitutes models for real applications, such as channel assignment in mobile wireless networks. Hale (1980) proposed he generalized coloring problem (GCP) where, for each edge, the absolute difference between colors assigned to each vertex must not be in a given forbidden set, problem that was later named T-coloring. Also, the bandwidth coloring problem (BCP), is a special case of T-coloring where the absolute difference between colors assigned to each vertex must be greater than or equal to a certain value (Malaguti and Toth, 2010; Lai and Lu, 2013; Dias et al., 2017), and the coloring problem with restrictions of adjacent colors (COLRAC, GEOM), where there is a restriction graph for which adjacent colors in it cannot be assigned to adjacent vertices (Trick et al, 2002, Akihiro et al., 2002).

In our research, we proposed theoretical modeling based on distance geometry and defined a hierarchy of coloring problems that we called distance graph coloring problems (DeFreitas et al., 2019). Thus, the vertices of the graph are considered as embedded on the real line and the coloring is treated as an assignment of positive integers to the vertices, while the distances correspond to line segments, where the goal is to find a feasible intersection. We proposed mixed-integer and constraint programming formulations and showed feasibility and optimality conditions for some problems (Dias et al., 2021). We also propose implicit enumeration methods for some of the optimization problems based on branch-and-prune algorithms proposed for DGPs in the literature. A polyhedral combinatorics study was conducted to define a distance polytope and facet-inducing inequalities (Dias et al. 2018). We propose new variations of vertex coloring problems in graphs, involving a new theoretical model in distance geometry (DG) for vertex coloring problems with generalized adjacency constraints, promoting the correlation between graph theory and DG fields. We also give a characterization and formal proof of polynomial cases for special graph classes, since the general main problem is NP-complete. We have also been developing technologies for data collection, antenna location, network throughput, connectivity path assurance, navigation, and exploring modern digital telecommunication technologies, including 5G, in a technological innovation R&D project with a large multinational telecommunications company.

Resumo da Palestra:

A maior penetração das fontes eólicas e solares mudou o paradigma do planejamento energético, requerendo uma ponte direta entre o planejamento de mais longo prazo e a programação diária, e trazendo desafios interessantes na modelagem e resolução dos problemas de otimização, tais como: o  tratamento da incerteza e variabilidade horária das fontes intermitentes; a redução e deslocamento de cargas requerido por programas de resposta da demanda; a necessidade de modelagem de componentes adicionais como usinas reversíveis e dispositivos de armazenamento de energia; a resolução de problemas de unit commitment estocásticos. Esta palestra discute essas questões do ponto de vista conceitual e de modelagem, e como vêm sendo tratadas e podem ser aprimoradas nos modelos de otimização energética utilizados oficialmente para o planejamento, despacho e formação de preço no sistema elétrico brasileiro.