Computing Pareto set in the criterion space for bicriteria linear programs using a single criterion software

2021 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
François Dubeau ◽  
Marie Emmanuel Ntigura Habingabwa
2009 ◽  
Vol 20 (02) ◽  
pp. 247-269 ◽  
Author(s):  
NATALIA V. SHAKHLEVICH ◽  
AKIYOSHI SHIOURA ◽  
VITALY A. STRUSEVICH

In scheduling with controllable processing times the actual processing time of each job is to be chosen from the interval between the smallest (compressed or fully crashed) value and the largest (decompressed or uncrashed) value. In the problems under consideration, the jobs are processed on a single machine and the quality of a schedule is measured by two functions: the maximum cost (that depends on job completion times) and the total compression cost. Our main model is bicriteria and is related to determining an optimal trade-off between these two objectives. Additionally, we consider a pair of associated single criterion problems, in which one of the objective functions is bounded while the other one is to be minimized. We reduce the bicriteria problem to a series of parametric linear programs defined over the intersection of a submodular polyhedron with a box. We demonstrate that the feasible region is represented by a so-called base polyhedron and the corresponding problem can be solved by the greedy algorithm that runs two orders of magnitude faster than known previously. For each of the associated single criterion problems, we develop algorithms that deliver the optimum faster than it can be deduced from a solution to the bicriteria problem.


Author(s):  
Д.В. Довгая ◽  
М.Х. Мальсагов

В статье описан подход к оценке функционирования высших учебных заведений на уровне кафедры, факультета и университета в целом. Он включает в себя - агрегирование показателей с помощью специальных функций; построение множества Парето в пространстве индексов; выбор наилучшей точки множества Парето с помощью скаляризации. In this paper we describe an approach to the evaluation of the higher school institutions on the levels of a chair, a faculty, and the whole university. The approach includes - an aggregation of the indicators by means of specific functions; building of Pareto set in the space of the research, teaching, and innovative criteria; a choice of the best point in the Pareto set by scalarization.


2018 ◽  
Author(s):  
Ricardo Guedes ◽  
Vasco Furtado ◽  
Tarc�sio Pequeno ◽  
Joel Rodrigues
Keyword(s):  

2018 ◽  
Author(s):  
Ricardo Guedes ◽  
Vasco Furtado ◽  
Tarcísio Pequeno ◽  
Joel Rodrigues

UNSTRUCTURED The article investigates policies for helping emergency-centre authorities for dispatching resources aimed at reducing goals such as response time, the number of unattended calls, the attending of priority calls, and the cost of displacement of vehicles. Pareto Set is shown to be the appropriated way to support the representation of policies of dispatch since it naturally fits the challenges of multi-objective optimization. By means of the concept of Pareto dominance a set with objectives may be ordered in a way that guides the dispatch of resources. Instead of manually trying to identify the best dispatching strategy, a multi-objective evolutionary algorithm coupled with an Emergency Call Simulator uncovers automatically the best approximation of the optimal Pareto Set that would be the responsible for indicating the importance of each objective and consequently the order of attendance of the calls. The scenario of validation is a big metropolis in Brazil using one-year of real data from 911 calls. Comparisons with traditional policies proposed in the literature are done as well as other innovative policies inspired from different domains as computer science and operational research. The results show that strategy of ranking the calls from a Pareto Set discovered by the evolutionary method is a good option because it has the second best (lowest) waiting time, serves almost 100% of priority calls, is the second most economical, and is the second in attendance of calls. That is to say, it is a strategy in which the four dimensions are considered without major impairment to any of them.


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