An exact method for a discrete multiobjective linear fractional optimization

Integer linear fractional programming problem with multiple objective MOILFP is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions, then generate an integer feasible solution. Using the reduced gradients of the objective functions, an efficient cut is built and a part of the feasible domain not containing efficient solutions is truncated by adding this cut. A sample problem is solved using this algorithm, and the main practical advantages of the algorithm are indicated.multiobjective programming, integer programming, linear fractional programming, branch and cut

A Novel Multiobjective Cell Switch-Off Framework for Cellular Networks

Cell Switch-Off (CSO) is recognized as a promising approach to reduce the energy consumption in next-generation cellular networks. However, CSO poses serious challenges not only from the resource allocation perspective but also from the implementation point of view. Indeed, CSO represents a difficult optimization problem due to its NP-complete nature. Moreover, there are a number of important practical limitations in the implementation of CSO schemes, such as the need for minimizing the real-time complexity and the number of on-off/off-on transitions and CSO-induced handovers. This article introduces a novel approach to CSO based on multiobjective optimization that makes use of the statistical description of the service demand (known by operators). In addition, downlink and uplink coverage criteria are included and a comparative analysis between different models to characterize intercell interference is also presented to shed light on their impact on CSO. The framework distinguishes itself from other proposals in two ways: 1) The number of on-off/off-on transitions as well as handovers are minimized, and 2) the computationally-heavy part of the algorithm is executed offline, which makes its implementation feasible. The results show that the proposed scheme achieves substantial energy savings in small cell deployments where service demand is not uniformly distributed, without compromising the Quality-of-Service (QoS) or requiring heavy real-time processing

An exact method for a discrete multiobjective linear fractional optimization

Integer linear fractional programming problem with multiple objective MOILFP is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions, then generate an integer feasible solution. Using the reduced gradients of the objective functions, an efficient cut is built and a part of the feasible domain not containing efficient solutions is truncated by adding this cut. A sample problem is solved using this algorithm, and the main practical advantages of the algorithm are indicated

Multiple Criteria Decision Making

Abstract This paper introduces a new method to estimate the weakly e cient set for the Multiobjective Linear Fractional Programming problem. The main idea is based on the procedure proposed by Tzeng and Hsu (In: G.H. Tzeng, H.F. Wang, U.P. Wen, L. Yu (Eds.), Multiple Criteria Decision Making, Springer, New York, 1994, pp. 459 -470), called CONNISE. However, as we will explain in this paper, the CONNISE method is not always convergent for problems with more than two objectives. For this reason, we have developed a new method, called "The Controlled Estimation Method", based on the same concept as CONNISE regarding the decision-maker being able to control distances between points from the estimation set he/she wants to ÿnd, while ensuring the method is convergent with problems with more than two objectives. Thus, we propose an algorithm able to calculate a discrete estimation of the weakly e cient set that veriÿes this property of the CONNISE method, but further, improves it thanks to its convergence and the fact that it satisÿes the three good properties suggested by Sayin (Math. Programming 87(3) (2000) 543): Coverage, Uniformity, and Cardinality.

Multi-objective Active Control Policy Design for Commensurate and Incommensurate Fractional Order Chaotic Financial Systems

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.In this paper, an active control policy design for a fractional order (FO) financial system is attempted, considering multiple conflicting objectives. An active control template as a nonlinear state feedback mechanism is developed and the controller gains are chosen within a multi-objective optimization (MOO) framework to satisfy the conditions of asymptotic stability, derived analytically. The MOO gives a set of solutions on the Pareto optimal front for the multiple conflicting objectives that are considered. It is shown that there is a trade-off between the multiple design objectives and a better performance in one objective can only be obtained at the cost of performance deterioration in the other objectives. The multi-objective controller design has been compared using three different MOO techniques viz. Non Dominated Sorting Genetic Algorithm-II (NSGA-II), epsilon variable Multi-Objective Genetic Algorithm (ev-MOGA), and Multi Objective Evolutionary Algorithm with Decomposition (MOEA/D). The robustness of the same control policy designed with the nominal system settings have been investigated also for gradual decrease in the commensurate and incommensurate fractional orders of the financial system

Effective and efficient algorithm for multiobjective optimization of hydrologic models

Practical experience with the calibration of hydrologic models suggests that any single-objective function, no matter how carefully chosen, is often inadequate to properly measure all of the characteristics of the observed data deemed to be important. One strategy to circumvent this problem is to define several optimization criteria (objective functions) that measure different (complementary) aspects of the system behavior and to use multicriteria optimization to identify the set of nondominated, efficient, or Pareto optimal solutions. In this paper, we present an efficient and effective Markov Chain Monte Carlo sampler, entitled the Multiobjective Shuffled Complex Evolution Metropolis (MOSCEM) algorithm, which is capable of solving the multiobjective optimization problem for hydrologic models. MOSCEM is an improvement over the Shuffled Complex Evolution Metropolis (SCEM-UA) global optimization algorithm, using the concept of Pareto dominance (rather than direct single-objective function evaluation) to evolve the initial population of points toward a set of solutions stemming from a stable distribution (Pareto set). The efficacy of the MOSCEM-UA algorithm is compared with the original MOCOM-UA algorithm for three hydrologic modeling case studies of increasing complexity

Tuning Rules for Active Disturbance Rejection Controllers via Multiobjective Optimization - A Guide for Parameters Computation Based on Robustness

[EN] A set of tuning rules for Linear Active Disturbance Rejection Controller (LADRC) with three different levels of compromise between disturbance rejection and robustness is presented. The tuning rules are the result of a Multiobjective Optimization Design (MOOD) procedure followed by curve fitting and are intended as a tool for designers who seek to implement LADRC by considering the load disturbance response of processes whose behavior is approximated by a general first-order system with delay. The validation of the proposed tuning rules is done through illustrative examples and the control of a nonlinear thermal process. Compared to classical PID (Proportional-Integral-Derivative) and other LADRC tuning methods, the derived functions offer an improvement in either disturbance rejection, robustness or both design objectives.This work was supported in part by the Ministerio de Ciencia, Innovacion y Universidades, Spain, under Grant RTI2018-096904-B-I00.Martínez, BV.; Sanchís Saez, J.; Garcia-Nieto, S.; Martínez Iranzo, MA. (2021). Tuning Rules for Active Disturbance Rejection Controllers via Multiobjective Optimization - A Guide for Parameters Computation Based on Robustness. Mathematics. 9(5):1-34. https://doi.org/10.3390/math90505171349

Theoretical Investigation of Immiscible Multiphase Flow Mechanisms in Porous Media with Capillarity

The correct description of multiphase flow mechanism in porous media is an important aspect of research in fluid mechanics, water resources and petroleum engineering. The thorough understanding of these mechanisms is important for many applications such as waterflood, CO2 sequestration, and enhanced oil recovery. Being different from single phase flow that is well described by Darcy’s law and well understood for over 160 years, the multiphase flow mechanism requires more mathematical involvement with more complex fluid interaction which inevitably will incorporate relative permeability and capillary pressure into its description. For typical two-phase flow problems, especially at the conventional reservoir scale, the Buckley-Leverett flow equations are normally applied with negligible capillarity to capture the flow behavior. However, as we extend our studies to higher resolution using multiscale calculations, or evaluate tighter or higher contrast heterogeneous reservoirs, capillarity becomes increasingly important. Also, for situations such as spontaneous imbibition that wetting fluid is displaced by non-wetting invading fluid, it is possible that capillary force becomes the dominating driving force with negligible viscous and gravity contributions. To better characterize the multiphase flow mechanism with capillarity, in this research, a detailed investigation is carried out in pursuit of more rigorous mathematical description and broader applicability. The numerical simulation analysis of the described problem has long been a subject of interest with numerous publications addressing it. Being different from the traditional methods where numerical simulation is used, we pursue the analytical description of the flow behavior using Lagrangian approach which is better in describing these frontal propagation problems. Also, the analytical solution tends to give more insight into the underlying physical characteristics of the problem itself. As one of the most important outcomes, the methodology derives a new dimensionless capillary group that characterizes the relative strength of capillarity at the continuum scale based on the analytical solution. Knowledge of this can be used for stability analyses, with future potential application in the design of computational grids to properly resolve the capillary physics