Minimization of Constraint Violation in Fuzzy Multiobjective Programming

Fuzzy multiobjective programming for a deterministic case involves maximizing the minimum goal satisfaction level among conflicting goals of different stakeholders using Max-min approach. Uncertainty due to randomness in a fuzzy multiobjective programming may be addressed by modifying the constraints using probabilistic inequality (e.g., Chebyshev’s inequality) or by addition of new constraints using statistical moments (e.g., skewness). Such modifications may result in the reduction of the optimal value of the system performance. In the present study, a methodology is developed to allow some violation in the newly added and modified constraints, and then minimizing the violation of those constraints with the objective of maximizing the minimum goal satisfaction level. Fuzzy goal programming is used to solve the multiobjective model. The proposed methodology is demonstrated with an application in the field of Waste Load Allocation (WLA) in a river system.

Fuzzy waste load allocation model: a multiobjective approach

Fuzzy Waste Load Allocation Model (FWLAM), developed in an earlier study, derives the optimal fractional levels, for the base flow conditions, considering the goals of the Pollution Control Agency (PCA) and dischargers. The Modified Fuzzy Waste Load Allocation Model (MFWLAM) developed subsequently is a stochastic model and considers the moments (mean, variance and skewness) of water quality indicators, incorporating uncertainty due to randomness of input variables along with uncertainty due to imprecision. The risk of low water quality is reduced significantly by using this modified model, but inclusion of new constraints leads to a low value of acceptability level, A, interpreted as the maximized minimum satisfaction in the system. To improve this value, a new model, which is a combination Of FWLAM and MFWLAM, is presented, allowing for some violations in the constraints of MFWLAM. This combined model is a multiobjective optimization model having the objectives, maximization of acceptability level and minimization of violation of constraints. Fuzzy multiobjective programming, goal programming and fuzzy goal programming are used to find the solutions. For the optimization model, Probabilistic Global Search Lausanne (PGSL) is used as a nonlinear optimization tool. The methodology is applied to a case study of the Tunga-Bhadra river system in south India. The model results in a compromised solution of a higher value of acceptability level as compared to MFWLAM, with a satisfactory value of risk. Thus the goal of risk minimization is achieved with a comparatively better value of acceptability level.

A multi-objective programming approach for the optimal operation of distributed generation considering uncertainty

Due to the renewed interest in distributed generation (DG), the number of DG units incorporated in distribution systems has been rapidly increasing in the past few years. This situation requires new analysis tools for understanding system performance, and taking advantage of the potential benefits of DG. This paper presents an evolutionary multi-objective programming approach to determine the optimal operation of DG in distribution systems. The objectives are the minimization of the system power losses and operation cost of the DG units. The proposed approach also considers the inherent stochasticity of DG technologies powered by renewable resources. Some tests were carried out on the IEEE 34 bus distribution test system showing the robustness and applicability of the proposed methodology. © 2011 IEEE.

Multiobjective Genetic Algorithm applied to dengue control

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Risk minimization in water quality control problems of a river system

Methodologies are presented for minimization of risk in a river water quality management problem. A risk minimization model is developed to minimize the risk of low water quality along a river in the face of conflict among various stake holders. The model consists of three parts: a water quality simulation model, a risk evaluation model with uncertainty analysis and an optimization model. Sensitivity analysis, First Order Reliability Analysis (FORA) and Monte-Carlo simulations are performed to evaluate the fuzzy risk of low water quality. Fuzzy multiobjective programming is used to formulate the multiobjective model. Probabilistic Global Search Laussane (PGSL), a global search algorithm developed recently, is used for solving the resulting non-linear optimization problem. The algorithm is based on the assumption that better sets of points are more likely to be found in the neighborhood of good sets of points, therefore intensifying the search in the regions that contain good solutions. Another model is developed for risk minimization, which deals with only the moments of the generated probability density functions of the water quality indicators. Suitable skewness values of water quality indicators, which lead to low fuzzy risk are identified. Results of the models are compared with the results of a deterministic fuzzy waste load allocation model (FWLAM), when methodologies are applied to the case study of Tunga-Bhadra river system in southern India, with a steady state BOD-DO model. The fractional removal levels resulting from the risk minimization model are slightly higher, but result in a significant reduction in risk of low water quality. (c) 2005 Elsevier Ltd. All rights reserved.

Time-series-based maximization of distributed wind power generation integration

Energy policies and technological progress in the development of wind turbines have made wind power the fastest growing renewable power source worldwide. The inherent variability of this resource requires special attention when analyzing the impacts of high penetration on the distribution network. A time-series steady-state analysis is proposed that assesses technical issues such as energy export, losses, and short-circuit levels. A multiobjective programming approach based on the nondominated sorting genetic algorithm (NSGA) is applied in order to find configurations that maximize the integration of distributed wind power generation (DWPG) while satisfying voltage and thermal limits. The approach has been applied to a medium voltage distribution network considering hourly demand and wind profiles for part of the U.K. The Pareto optimal solutions obtained highlight the drawbacks of using a single demand and generation scenario, and indicate the importance of appropriate substation voltage settings for maximizing the connection of MPG.

Algoritomos transgenéticos aplicados ao problema da árvore geradora biobjetivo

The Multiobjective Spanning Tree is a NP-hard Combinatorial Optimization problem whose application arises in several areas, especially networks design. In this work, we propose a solution to the biobjective version of the problem through a Transgenetic Algorithm named ATIS-NP. The Computational Transgenetic is a metaheuristic technique from Evolutionary Computation whose inspiration relies in the conception of cooperation (and not competition) as the factor of main influence to evolution. The algorithm outlined is the evolution of a work that has already yielded two other transgenetic algorithms. In this sense, the algorithms previously developed are also presented. This research also comprises an experimental analysis with the aim of obtaining information related to the performance of ATIS-NP when compared to other approaches. Thus, ATIS-NP is compared to the algorithms previously implemented and to other transgenetic already presented for the problem under consideration. The computational experiments also address the comparison to two recent approaches from literature that present good results, a GRASP and a genetic algorithms. The efficiency of the method described is evaluated with basis in metrics of solution quality and computational time spent. Considering the problem is within the context of Multiobjective Optimization, quality indicators are adopted to infer the criteria of solution quality. Statistical tests evaluate the significance of results obtained from computational experiments

Invex nonsmooth alternative theorem and applications

An invex constrained nonsmooth optimization problem is considered, in which the presence of an abstract constraint set is possibly allowed. Necessary and sufficient conditions of optimality are provided and weak and strong duality results established. Following Geoffrion's approach an invex nonsmooth alternative theorem of Gordan type is then derived. Subsequently, some applications on multiobjective programming are then pursued. © 2000 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint.

Using a CGE Model to Identify the Policy Trade-Off between Unemployment and Inflation: The Efficient Phillips Curve

This paper provides a new reading of a classical economic relation: the short-run Phillips curve. Our point is that, when dealing with inflation and unemployment, policy-making can be understood as a multicriteria decisionmaking problem. Hence, we use so-called multiobjective programming in connection with a computable general equilibrium (CGE) model to determine the combinations of policy instruments that provide efficient combinations of inflation and unemployment. This approach results in an alternative version of the Phillips curve labelled as efficient Phillips curve. Our aim is to present an application of CGE models to a new area of research that can be especially useful when addressing policy exercises with real data. We apply our methodological proposal within a particular regional economy, Andalusia, in the south of Spain. This tool can give some keys for policy advice and policy implementation in the fight against unemployment and inflation.

Defining efficient policies in a general equilibrium model: a multi-objective approach

Macroeconomic policy makers are typically concerned with several indicators of economic performance. We thus propose to tackle the design of macroeconomic policy using Multicriteria Decision Making (MCDM) techniques. More specifically, we employ Multiobjective Programming (MP) to seek so-called efficient policies. The MP approach is combined with a computable general equilibrium (CGE) model. We chose use of a CGE model since they have the dual advantage of being consistent with standard economic theory while allowing one to measure the effect(s) of a specific policy with real data. Applying the proposed methodology to Spain (via the 1995 Social Accounting Matrix) we first quantified the trade-offs between two specific policy objectives: growth and inflation, when designing fiscal policy. We then constructed a frontier of efficient policies involving real growth and inflation. In doing so, we found that policy in 1995 Spain displayed some degree of inefficiency with respect to these two policy objectives. We then offer two sets of policy recommendations that, ostensibly, could have helped Spain at the time. The first deals with efficiency independent of the importance given to both growth and inflation by policy makers (we label this set: general policy recommendations). A second set depends on which policy objective is seen as more important by policy makers: increasing growth or controlling inflation (we label this one: objective-specific recommendations).

Multiobjective 0-1 integer programming for the use of sugarcane residual biomass in energy cogeneration

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Corrigendum to “The envelope theorem for multiobjective convex programming via contingent derivatives” [J. Math. Anal. Appl. 372 (1) (2010) 197–207]

The aim of this note is to formulate an envelope theorem for vector convex programs. This version corrects an earlier work, “The envelope theorem for multiobjective convex programming via contingent derivatives” by Jiménez Guerra et al. (2010) [3]. We first propose a necessary and sufficient condition allowing to restate the main result proved in the alluded paper. Second, we introduce a new Lagrange multiplier in order to obtain an envelope theorem avoiding the aforementioned error.

Multiobjective optimization of economic balances of sugarcane harvest biomass

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A class of multiobjective control problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)