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The High School Timetabling Problem consists in assigning timeslots and resources to events, satisfying constraints which heavily depend on the specific institution. This work deals with the problem of the ongoing III International Timetabling Competition (ITC), which includes a diverse set of instances from many educational institutions around the world. We proposed an approach based on Simulated Annealing and Variable Neighborhood Search metaheuristics. One important structural feature of our approach is the use of the Kingston's High School Timetabling Engine (KHE) to generate initial solutions combined with the multi-neighborhood search. Such approach led us to the finals of the ongoing competition.

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Resource Constrained Project Scheduling Problems (RCPSPs) without preemption are well-known N P-hard combinatorial optimization problems. A feasible RCPSP solution consists of a time-ordered schedule of jobs with corresponding execution modes, respecting precedence and resources constraints. In this paper, we propose a cutting plane algorithm to separate five different cut families, as well as a new preprocessing routine to strengthen resource-related constraints. New lifted versions of the well-known precedence and cover inequalities are employed. At each iteration, a dense conflict graph is built considering feasibility and optimality conditions to separate cliques, odd-holes and strengthened Chvátal-Gomory cuts. The proposed strategies considerably improve the linear relaxation bounds, allowing a state-of-the-art mixed-integer linear programming solver to find provably optimal solutions for 754 previously open instances of different variants of the RCPSPs, which was not possible using the original linear programming formulations.

Este artigo apresenta um estudo de caso sobre a formação de professores do ensino primário, fundamental e médio para o uso de tecnologias no ensino remoto de emergência, durante a pandemia da Covid-19. São analisadas uma palestra e oito aulas virtuais síncronas conduzida por web-conferência. Em todas as aulas virtuais foram aplicados questionários de avaliação para os participantes, com o objetivo de validar ou não as estratégias, conteúdos e ferramentas utilizados na formação remota. A análise dos questionamentos durante as oficinas evidenciou que muitas das preocupações e dúvidas se relacionam à falta de formação em estratégias didáticas inovadoras acompanhadas de recursos tecnológicos.

In this paper we propose a Local Search approach for NP-Hard problems expressed as binary programs. Our search method focuses on the fast production of feasible solutions. The method explicitly considers the structure of the problem as a conflict graph and uses a systematic neighbor generation procedure to jump from one feasible solution to another using chains of movements. Computational experiments comparing with two open source integer programming solvers, CBC and GLPK, in MIPLIB 2010 instances, showed that our approach is more reliable for the production of feasible solutions in restricted amounts of time.

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