scholarly journals Lower bounds and compact mathematical formulations for spacing soft constraints for university examination timetabling problems

2019 ◽  
Vol 106 ◽  
pp. 133-142
Author(s):  
Taha Arbaoui ◽  
Jean-Paul Boufflet ◽  
Aziz Moukrim
Keyword(s):  
Lower Bounds ◽  
Soft Constraints ◽  
Examination Timetabling ◽  
University Examination

scholarly journals Lower-Bound Synthesis Using Loop Specialization and Max-SMT

2021 ◽  
pp. 863-886
Author(s):  
Elvira Albert ◽  
Samir Genaim ◽  
Enrique Martin-Martin ◽  
Alicia Merayo ◽  
Albert Rubio
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Soft Constraints ◽  
Worst Case ◽  
New Framework

AbstractThis paper presents a new framework to synthesize lower-bounds on the worst-case cost for non-deterministic integer loops. As in previous approaches, the analysis searches for a metering function that under-approximates the number of loop iterations. The key novelty of our framework is the specialization of loops, which is achieved by restricting their enabled transitions to a subset of the inputs combined with the narrowing of their transition scopes. Specialization allows us to find metering functions for complex loops that could not be handled before or be more precise than previous approaches. Technically, it is performed (1) by using quasi-invariants while searching for the metering function, (2) by strengthening the loop guards, and (3) by narrowing the space of non-deterministic choices. We also propose a Max-SMT encoding that takes advantage of the use of soft constraints to force the solver look for more accurate solutions. We show our accuracy gains on benchmarks extracted from the 2020 Termination and Complexity Competition by comparing our results to those obtained by the "Image missing" system.

Chapter 23. MaxSAT, Hard and Soft Constraints

2021 ◽  
Author(s):  
Chu Min Li ◽  
Felip Manyà
Keyword(s):  
Combinatorial Optimization ◽  
Lower Bounds ◽  
Branch And Bound ◽  
Data Structures ◽  
Optimization Problems ◽  
Soft Constraints ◽  
Inference Rules ◽  
Combinatorial Optimization Problems ◽  
Definition Of ◽  
Hard And Soft Constraints

MaxSAT solving is becoming a competitive generic approach for solving combinatorial optimization problems, partly due to the development of new solving techniques that have been recently incorporated into modern MaxSAT solvers, and to the challenge problems posed at the MaxSAT Evaluations. In this chapter we present the most relevant results on both approximate and exact MaxSAT solving, and survey in more detail the techniques that have proven to be useful in branch and bound MaxSAT and Weighted MaxSAT solvers. Among such techniques, we pay special attention to the definition of good quality lower bounds, powerful inference rules, clever variable selection heuristics and suitable data structures. Moreover, we discuss the advantages of dealing with hard and soft constraints in the Partial MaxSAT formalims, and present a summary of the MaxSAT Evaluations that have been organized so far as affiliated events of the International Conference on Theory and Applications of Satisfiability Testing.

scholarly journals Genetic Algorithm and Tabu Search Memory with Course Sandwiching (GATS_CS) for University Examination Timetabling

2020 ◽  
Vol 26 (3) ◽  
pp. 385-396
Author(s):  
Abayomi-Alli Adebayo ◽  
Sanjay Misra ◽  
Luis Fern醤dez-Sanz ◽  
Abayomi-Alli Olusola ◽  
A. R. Edun
Keyword(s):  
Genetic Algorithm ◽  
Tabu Search ◽  
Examination Timetabling ◽  
University Examination
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