Search results for "Mathematical optimization"

Geometric constraint solving: The witness configuration method

2006

Geometric constraint solving is a key issue in CAD, CAM and PLM. The systems of geometric constraints are today studied and decomposed with graph-based methods, before their numerical resolution. However, graph-based methods can detect only the simplest (called structural) dependences between constraints; they cannot detect subtle dependences due to theorems. To overcome these limitations, this paper proposes a new method: the system is studied (with linear algebra tools) at a witness configuration, which is intuitively similar to the unknown one, and easy to compute.

Notice of Violation of IEEE Publication Principles: Robust Observer Design for Unknown Inputs Takagi–Sugeno Models

2013

This paper deals with the observer design for Takagi-Sugeno (T-S) fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system. Sufficient conditions to design an unknown input T-S observer are given in linear matrix inequality (LMI) terms. Both continuous-time and discrete-time cases are studied. Relaxations are introduced by using intermediate variables. Extension to the case of unmeasured decision variables is also given. A numerical example is given to illustrate the effectiveness of the given results.

A variational inequality approach to the problem of the design of the optimal covering of an obstacle

2005

Reinforcement Learning Based Mobility Load Balancing with the Cell Individual Offset

2021

In this study, we focus on the cell individual offset (CIO) parameter in the handover process, which represents the willingness of a cell to admit the incoming handovers. However, it is challenging to tune the CIO parameter, as any poor implementation can lead to undesired outcomes, such as making the neighboring cells over-loaded while decreasing the traffic load of the cell. In this work, a reinforcement learning-based approach for parameter selection is introduced, since it is quite convenient for dynamically changing environments. In that regard, two different techniques, namely Q-learning and SARSA, are proposed, as they are known for their multi-objective optimization capabilities. Mo…

A fuzzy mathematical programming approach to the assessment of efficiency with DEA models

2003

In many real applications, the data of production processes cannot be precisely measured. This is particularly worrying when assessing efficiency with frontier-type models, such as data envelopment analysis (DEA) models, since they are very sensitive to possible data errors. For this reason, the possibility of having available a methodology that allows the analyst to deal with imprecise data becomes an issue of great interest in these contexts. To that end, we develop some fuzzy versions of the classical DEA models (in particular, the BCC model) by using some ranking methods based on the comparison of α-cuts. The resulting auxiliary crisp problems can be solved by the usual DEA software. We…

Non-dominated “trade-off” solutions in television scheduling optimization

2014

The main approaches for the television scheduling design are commonly based on the ratings or revenues maximization objective, and thus, only a single optimal solution can be obtained, corresponding to the best result for the considered objective. Therefore, these approaches lead up to the alternative solutions loss which, even if less effective from the ratings or revenues maximization viewpoint, may be more suitable for the decision maker because of better compromise in relation to factors influencing the decision process. Specifically, such a compromise could be achieved through a suitable “trade-off” between these factors, with reference to the decision context in which the decision mak…

General mathematical concept of compensation in sports science with quantitative analysis in the case of sprinting performance

1995

In many of the known sports disciplines, especially in athletics, the criterion which determines the positions of the competitors is a simple physical value, mostly a time or a distance, and the athlete with the minimum or maximum, respectively, takes the first place. Moreover, sports science explains this criterion by a set of the so-called basic abilities. Compensation means the balance of the inferiority of such a basic ability by the superiority of another one. In the following paper, a general abstract concept to analyse compensation in a quantitative way is presented first. It can be applied to any discipline with a measurable criterion, if, in addition, the performance can be describ…

Simultaneous Airline Scheduling

2008

Currently, there are no solution approaches available to construct and optimize airline schedules within a single model. All existing approaches decompose the problem into smaller and less complex subproblems and solve those subproblems separately. This chapter presents a metaheuristic for simultaneous airline scheduling where several different subproblems are integrated into one single optimization model, except for crew scheduling. The problem-specific metaheuristic uses an adaptive procedure for operator selection to allow an efficient choice between a variety of different operators. Experiments are conducted as proof-of-concept and to calibrate free parameters. Comparing different searc…

Surrogate-Assisted Evolutionary Optimization of Large Problems

2019

This chapter presents some recent advances in surrogate-assisted evolutionary optimization of large problems. By large problems, we mean either the number of decision variables is large, or the number of objectives is large, or both. These problems pose challenges to evolutionary algorithms themselves, constructing surrogates and surrogate management. To address these challenges, we proposed two algorithms, one called kriging-assisted reference vector guided evolutionary algorithm (K-RVEA) for many-objective optimization, and the other called cooperative swarm optimization algorithm (SA-COSO) for high-dimensional single-objective optimization. Empirical studies demonstrate that K-RVEA works…

Recent Developments on Fixed Point Theory in Function Spaces and Applications to Control and Optimization Problems

2015

1Department of Mathematics, Disha Institute of Management and Technology, Satya Vihar, Vidhansabha-Chandrakhuri Marg, Mandir Hasaud, Raipur, Chhattisgarh 492101, India 2Department of Mathematics and AppliedMathematics, University of Pretoria, Private Bag X20, Hatfield, Pretoria 0028, South Africa 3Departement de Mathematiques et de Statistique, Universite de Montreal, CP 6128, Succursale Centre-Ville, Montreal, QC, Canada H3C 3J7 4Department of Mathematics and Informatics, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy