Equivalent Single Objective Research Articles

Risk-Averse Multiobjective Optimization for Integrated Electricity and Heating System: An Augment Epsilon-Constraint Approach

Uncertainties including demand and environmental factors would increase the operational risk of the energy supply networks. It significantly affects the technical and financial aspects of the integrated electricity and heating system (IEHS). This article presents a risk-averse multiobjective optimization strategy for short-term decision-making. The objective is to optimize the total cost and the technical dissatisfaction in a way that the economy of system operation and energy supply quality for the risk-averse scheme is guaranteed simultaneously. Based on the trapezoidal fuzzy membership function, the fuzzy constraint is constructed to quantify the technical dissatisfaction of the nodal voltage and supply temperature. Then, a multiobjective min–max–min problem is formulated to hedge the IEHS against risk imposed by the uncertain variables. Since the formulated two objectives compete with each other, a risk-averse multiobjective solution procedure based on the augmented epsilon-constraint algorithm is developed to recast the multiobjective problem into its equivalent single objective problem. And the accurate Pareto fronts under different risk levels are obtained with several iterations. Numerical case studies are conducted to evaluate the effectiveness and applicability of the proposed method. It provides benefits in the aspect of balancing the economy and energy supply quality under network constraints and uncertainties.

An Active-Set Fischer–Burmeister Trust-Region Algorithm to Solve a Nonlinear Bilevel Optimization Problem

In this paper, the Fischer–Burmeister active-set trust-region (FBACTR) algorithm is introduced to solve the nonlinear bilevel programming problems. In FBACTR algorithm, a Karush–Kuhn–Tucker (KKT) condition is used with the Fischer–Burmeister function to transform a nonlinear bilevel programming (NBLP) problem into an equivalent smooth single objective nonlinear programming problem. To ensure global convergence for the FBACTR algorithm, an active-set strategy is used with a trust-region globalization strategy. The theory of global convergence for the FBACTR algorithm is presented. To clarify the effectiveness of the proposed FBACTR algorithm, applications of mathematical programs with equilibrium constraints are tested.

An interior-point trust-region algorithm to solve a nonlinear bilevel programming problem

<abstract><p>In this paper, a nonlinear bilevel programming (NBLP) problem is transformed into an equivalent smooth single objective nonlinear programming (SONP) problem utilized slack variable with a Karush-Kuhn-Tucker (KKT) condition. To solve the equivalent smooth SONP problem effectively, an interior-point Newton's method with Das scaling matrix is used. This method is locally method and to guarantee convergence from any starting point, a trust-region strategy is used. The proposed algorithm is proved to be stable and capable of generating approximal optimal solution to the nonlinear bilevel programming problem.</p> <p>A global convergence theory of the proposed algorithm is introduced and applications to mathematical programs with equilibrium constraints are given to clarify the effectiveness of the proposed approach.</p></abstract>

An active-set with barrier method and trust-region mechanism to solve a nonlinear Bilevel programming problem

<abstract><p>Nonlinear Bilevel programming (NBLP) problem is a hard problem and very difficult to be resolved by using the classical method. In this paper, Karush-Kuhn-Tucker (KKT) condition is used with Fischer-Burmeister function to convert NBLP problem to an equivalent smooth single objective nonlinear programming (SONP) problem. An active-set strategy is used with Barrier method and trust-region technique to solve the smooth SONP problem effectively and guarantee a convergence to optimal solution from any starting point. A global convergence theory for the active-set barrier trust-region (ACBTR) algorithm is studied under five standard assumptions. An applications to mathematical programs are introduced to clarify the effectiveness of ACBTR algorithm. The results show that ACBTR algorithm is stable and capable of generating approximal optimal solution to the NBLP problem.</p></abstract>

Multi-response optimisation of machining parameters in wire EDM process using grey relational analysis

Wire electrical discharge machining (WEDM) is extensively used in machining of materials when precision is of prime importance. It is a specialised process for cutting complex contours or fragile geometries that would be difficult to be produced using conventional cutting methods. In the present work, the WEDM machining of EN-31 alloy steel has been studied with multiple performance characteristics such as cutting rate (CR), surface roughness (Ra) and dimensional deviation (DD) using grey-Taguchi method. The process parameters considered for optimisation are pulse on time (Ton), pulse off time (Toff), wire feed (WF), wire tension (WT), spark gap set voltage (SV) and servo feed (SF). For experimentation Taguchi's L27 orthogonal array (OA) has been used. The application of grey relational analysis is adopted to convert multi-objective criterion into an equivalent single objective function; overall grey relational grade (GRG), which has been maximised by using Taguchi technique. Additionally, the analysis of variance (ANOVA) for GRG is utilised to determine the most significant process parameters. Optimal setting has been verified through confirmatory test; found good agreement with predicted value. The experimental results confirm that the proposed method effectively improves the machining performance of WEDM process.

Multi-response optimisation of machining parameters in wire EDM process using grey relational analysis

Wire electrical discharge machining (WEDM) is extensively used in machining of materials when precision is of prime importance. It is a specialised process for cutting complex contours or fragile geometries that would be difficult to be produced using conventional cutting methods. In the present work, the WEDM machining of EN-31 alloy steel has been studied with multiple performance characteristics such as cutting rate (CR), surface roughness (Ra) and dimensional deviation (DD) using grey-Taguchi method. The process parameters considered for optimisation are pulse on time (Ton), pulse off time (Toff), wire feed (WF), wire tension (WT), spark gap set voltage (SV) and servo feed (SF). For experimentation Taguchi's L27 orthogonal array (OA) has been used. The application of grey relational analysis is adopted to convert multi-objective criterion into an equivalent single objective function; overall grey relational grade (GRG), which has been maximised by using Taguchi technique. Additionally, the analysis of variance (ANOVA) for GRG is utilised to determine the most significant process parameters. Optimal setting has been verified through confirmatory test; found good agreement with predicted value. The experimental results confirm that the proposed method effectively improves the machining performance of WEDM process.

Application of fuzzy-assisted grey Taguchi approach for engine parameters optimization on performance-emission of a CI engine

ABSTRACT With the prevalent interest in diesel engine performance and emission, it is necessary to define optimum engine operating condition with less number of experiments for the efficient and effective outcome. In this article, the combined effect of input parameters viz. engine load and types of fuel blend in controlling BSFC, NOx, UHC, and CO output variables in a diesel engine are investigated. In this study, a fuzzy-assisted grey Taguchi method has been proposed to optimize the engine load and types of fuel used. The main purpose of using fuzzy inference system is to convert the multi-response into an equivalent single objective optimization. Optimum input factor corresponding to estimated values of output response has been obtained by employing fuzzy grey reasoning grade. The computed factor combination based on the highest ranking of fuzzy grey grade is validated through a confirmation experiment. Based on grey-fuzzy approach optimum engine parameter is found D85B10E5 at 100% load. ANOVA analysis of Grey Fuzzy Grade reveals engine load is the most significant input factor influencing engine output. Based on the results it is concluded that grey-fuzzy-Taguchi approach can be a more useful tool to ameliorate performance and emission of an engine compared to simple grey relational grade.Abbreviations: CI: compression ignition; BSEC: break specific energy consumption; NOx: nitrogen oxides; UHC: unburned hydrocarbon; CO: carbon monoxide; GRA: grey relational analysis; GRC: grey relational coefficient; GRG: grey relational grade; ANOVA: analysis of variance; DAQ: data acquisition; S/N: signal to noise ratio; FIS: fuzzy interface system; GFG: grey fuzzy grade

Relative partial efficiency: network and black box SBM DEA interpretations in multiplier form

In traditional black-box DEA when the ratio-based multiplier DEA model is estimated to obtain a technical efficiency score, the estimated multipliers (shadow prices) serve as the weights that maximize the ratio of the aggregation of weighted sum of outputs (virtual output) to that of inputs (virtual input) of the assessed DMU in comparison with the other decision making units (DMUs). With respect to the ratio-based multiplier model of non-radial slack-based measure (SBM), however, there does not exist such a nice efficiency interpretation. For the purpose of providing a reasonable efficiency interpretation for both black-box and network SBM models, this paper introduces a concept called relative partial efficiency (RPE). In the black box structure, RPEs are defined for each input–output pair and a multi objective programming is formed in order to maximize RPEs. Then, it is proved that its equivalent single objective programming problem is the same SBM multiplier DEA model. The obtained explicit efficiency interpretation coming from this novel concept is then generalized for the multiplier network SBM DEA model represented by Boloori (Comput Ind Eng 95:83–96, 2016).

Robust solution for a minimax regret hub location problem in a fuzzy-stochastic environment

In the present paper, a robust approach is used to locate hub facilities considering network risks. An additional objective function, minimax regret, is added to the classical objective function in the hub location problem. In the proposed model, risk factors such as availability, security, delay time, environmental guidelines and regional air pollution are considered using triangular fuzzy-stochastic numbers. Then an equivalent crisp single objective model is proposed and solved by the Benders decomposition method. Finally, the results of both Benders decomposition and commercial optimization software are compared for different instances. Numerical instances were developed based on the well-known Civil Aeronautics Board (CAB) data set, considering different levels of uncertainty in parameters. The results show that the proposed model is capable of selecting nodes as sustainable hubs. Also, the results confirm that using Benders decomposition is more efficient than using classical solution methods for large-scale problems.

Effect of Process Parameters on MRR and Surface Roughness in ECM of EN 31 Tool Steel Using WPCA

Weighted principal component analysis is used to predict the optimal machining parameters for EN 31 tool steel in electrochemical machining for minimum surface roughness and maximum material removal rate based on L27 Taguchi orthogonal design. For this, multi-response performance index is calculated to derive an equivalent single objective function and then Taguchi method is used to optimize the process parameters. The separable influence of individual machining parameters and the interaction between these parameters are also investigated by using analysis of variance (ANOVA). Results show that the main significant factor on MRR and surface roughness is electrolyte concentration. The effects of process parameters viz. electrolyte concentration, voltage, feed rate and inter-electrode gap on MRR and surface roughness are also investigated using 3D surface and contour plots. Finally, the surface morphology is studied with the help of scanning electron microscopy (SEM) images.

Integrating Principal Component Analysis, Fuzzy Linguistic Reasoning and Taguchi Philosophy for Quality-Productivity Optimization

The present work demonstrates a multi-response optimization problem for selection of optimal cutting parameters (optimal process environment) for machining (turning) of nylon 6; by using Principal Component Analysis (PCA) followed by fuzzy linguistic reasoning in combination with Taguchi’s robust design technique. In this study, three controllable process parameters: cutting speed, feed, and depth of cut have been considered for obtaining desired Material Removal Rate (MRR) of the process and favorable multiple surface roughness features for the machined product; based on L9 orthogonal array experimental design. The study has been aimed to search an appropriate process environment for simultaneous optimization of quality-productivity favorably. Various surface roughness parameters of statistical importance (of the machined product) have been considered as product quality characteristics whereas; MRR has been treated as productivity measure for the said machining process. To avoid assumptions, limitations, uncertainties and imprecision in application of existing multi-response optimization techniques; Principal Component Analysis (PCA) has been proposed to convert correlated responses into uncorrelated quality indices (called individual principal components); next, a fuzzy inference system (FIS) has been proposed for meaningful and feasible aggregation of individual principal components into an equivalent single quality index, thereby, converting such a multi-objective optimization problem into an equivalent single objective optimization situation. A Multi-Performance Characteristic Index (MPCI) has been defined based on the FIS output. MPCI has been optimized finally using Taguchi method. The study exhibits application feasibility of the proposed approach with satisfactory result of confirmatory test.

Design of a Reliable Bi-objective Relief Routing Network in the Earthquake Response Phase

One of the most critical issues in areas which have recently faced natural disasters is transportation of both injured people to medical centers and relief commodities to their desired destinations. In such situation, due to disruptions, some routes may lose all or part of their capacities and not be able to accept as much vehicles as before. Consequently, the relief vehicles face difficulties to follow their itinerary. Such critical circumstance calls for finding reliable solutions. This study develops a new bi-objective, multi-mode and multi-commodity model, in which the reliability is taken into account to help managers in making more reliable decisions. To solve this model, the TH method is used in order to find the equivalent single objective model and this new model is exactly solved by coding in GAMS software.

Robust multiobjective optimization method using satisficing trade-off method

This study proposes a robust multiobjective optimization approach using the satisficing tradeoff method (STOM). STOM is a multiobjective optimization method that obtains a highly accurate single Pareto solution. Conventionally, a robust design is formulated as a single-objective optimization problem, where the objective function is defined as the weighted sum of the mean and standard deviation of the performance index. In this study, the mean and standard deviation are formulated as individual objective function. The effect of uncertainty can be investigated through Pareto surface. In STOM, the multiobjective optimization problem is transformed into the equivalent single objective problem by introducing an aspiration level. As the obtained single Pareto solution corresponds to the aspiration level that implies the ratio of the designer's desired objective function, the designer can investigate only the desired space in detail through setting the aspiration without obtaining full Pareto surfaces. The validity of using STOM for a robust multiobjective optimization problem is discussed using numerical examples.

Fuzzy assisted grey Taguchi approach for optimisation of multiple weld quality properties in friction stir welding process

Friction stir welding (FSW) is gaining its popularity for a wide range of high strength/weight ratio materials such as aluminium, magnesium, composites and plastics. With the projected prevalent application of FSW, it is necessary to identify the optimal welding condition with a small number of experiments for effective product quality and productivity. In this study, a fuzzy assisted grey Taguchi method is proposed for optimising the FSW process parameters with multiple weld quality characteristics. The fuzzy inference system was adapted to convert the multiresponse optimisation problem into an equivalent single objective optimisation problem, which was solved by the Taguchi approach. Eight input process parameters have been varied to observe their effects on output responses, namely, ultimate tensile strength, yield strength, % elongation, weld bead thickness and nugget zone hardness. Confirmation test showed that the proposed approach can efficiently be used for the optimisation of multiple weld quality properties in FSW process.

Optimal coordination of directional overcurrent relays using NSGA-II

This paper presents a new method for coordination of directional overcurrent relays to reduce the discrimination time of the primary and backup relays, by using nondominated sorting genetic algorithm-II (NSGA-II). In order to achieve a reliable protective system, it is necessary to find a solution to avoid having large discrimination times, in addition to coordination time interval (CTI). The novelty of the paper is to reduce the discrimination time of the primary and backup relays and simultaneously reduce the operating time of primary and backup relays, by introducing a new method. In contrast to the conventional intelligent methods, the proposed method does not require weighting factors for conversion of multi-objective function into an equivalent single objective function. The effects of both near and far-end faults are considered to solve the proposed problem formulation. Also, various overcurrent relays characteristics are considered within the program to select the best of them for each relay by optimization algorithm. The proposed method is implemented in three different test cases, i.e. three, eight and IEEE 30-bus network. The results are compared with previously proposed methods.

Taguchi approach followed by fuzzy linguistic reasoning for quality‐productivity optimization in machining operation

PurposeThe study has been aimed to search an appropriate process environment for simultaneous optimization of quality‐productivity favorably. Various surface roughness parameters (of the machined product) have been considered as product quality characteristics whereas material removal rate (MRR) has been treated as productivity measure for the said machining process.Design/methodology/approachIn this study, three controllable process parameters, cutting speed, feed, and depth of cut, have been considered for optimizing material removal rate (MRR) of the process and multiple surface roughness features for the machined product, based on L9 orthogonal array experimental design. To avoid assumptions, limitation, uncertainty and imprecision in application of existing multi‐response optimization techniques documented in literature, a fuzzy inference system (FIS) has been proposed to convert such a multi‐objective optimization problem into an equivalent single objective optimization situation by adapting FIS. A multi‐performance characteristic index (MPCI) has been defined based on the FIS output. MPCI has been optimized finally using Taguchi method.FindingsThe study demonstrates application feasibility of the proposed approach with satisfactory result of confirmatory test. The proposed procedure is simple, and effective in developing a robust, versatile and flexible mass production process.Originality/valueIn the proposed model it is not required to assign individual response weights; no need to check for response correlation. FIS can efficiently take care of these aspects into its internal hierarchy thereby overcoming various limitations/assumptions of existing optimization approaches.

Multiobjective Service Restoration Considering Primary Customers using Hybrid GA-ACO Algorithm

To restore electricity service in healthy area outside the faulted zone in power distribution system is known as service restoration. In this paper, a technique based on hybrid Genetic Algorithm-Ant Colony Optimization (GA-ACO) is presented for solving the service restoration problem in electric power distribution system. Due the presence of various conflicting objectives and constraints, the task of service restoration is multi-objective and multi-constraint optimization problem. In contrast to conventional optimization technique, this approach does not require tunable weighting factors to convert multiple objectives into equivalent single objective. In this work various practical distribution systems issues such as presence of priority customers, remotely and manually controlled switches etc have been considered as objective functions. Based on simulation results on four different distribution networks, the performance of hybrid GA-ACO is found significantly better than Non Dominated Sorting of Genetic Algorithm-II (NSGA-II) and conventional Genetic Algorithm.

Bead Geometry Optimization of Submerged Arc Weld: Exploration of Weighted Principal Component Analysis (WPCA)

The present work attempts to overcome underlying assumptions in traditional Taguchi based optimization techniques highlighted in literature. Taguchi method alone fails to solve multi-response optimization problems. In order to overcome this limitation, exploration of grey relation theory, desirability function approach, utility theory etc. have been found amply applied in literature in combination with Taguchi method. But aforesaid approaches relies on the assumption that individual response features are uncorrelated i.e. independent of each other which are really impossible to happen in practice. The study takes into account this response correlation and proposes an integrated methodology in a case study on optimization of multiple bead geometry parameters of submerged arc weldment. Weighted Principal Component Analysis (WPCA) has been applied to eliminate response correlation and to convert correlated responses into equal or less number of uncorrelated quality indices called principal components. Based on individual principal components a Multi-response Performance Index (MPI) has been introduced to derive an equivalent single objective function which has been optimized (maximized) using Taguchi method. Experiments have been conducted based on Taguchi’s L25 Orthogonal Array design with combinations of process control parameters: voltage, wire feed, welding speed and electrode stick-out. Different bead geometry parameters: bead width, bead height, penetration depth and HAZ dimensions have been optimized. Optimal result has been verified by confirmatory test. The study highlights effectiveness of the proposed method for solving multi-objective optimization of submerged arc weld.

Solution of Correlated Multi-Response Optimization Problem

This paper highlights an integrated approach to solve the correlated multi-response optimization problem through a case study in submerged arc welding (SAW). The proposed approach has been presented to overcome different limitations and drawbacks of existing optimization techniques available in literature. Traditional Taguchi optimization technique is based under the assumption that quality responses are independent to each other; however, this assumption may not always be valid. A common trend in the solution of a multi-objective optimization problem is to convert these multi-objectives into an equivalent single objective function. While deriving this equivalent objective function, different weightage are assigned to different responses according to their relative priority. In this regard, it seems that no specific guideline is available for assigning individual response weighs. To avoid this, Principal Component Analysis (PCA) has been adopted to eliminate correlation among individual desirability values and to calculate uncorrelated quality indices that have been aggregated to calculate overall grey relational grade. This study combines PCA, Desirability Function (DF) approach, and grey relation theory to the entropy measurement technique. Finally, the Taguchi method has been used to derive optimal process environment capable of producing desired weld quality related to bead geometry.

Modeling, simulation and parametric optimization of wire EDM process using response surface methodology coupled with grey-Taguchi technique

In the present work, quadratic mathematical models have been derived to represent the process behavior of wire electrical discharge machining (WEDM) operation. Experiments have been conducted with six process parameters: discharge current, pulse duration, pulse frequency, wire speed, wire tension and dielectric flow rate; to be varied in three different levels. Data related to the process responses viz. material removal rate (MRR), roughness value of the worked surface (a measure of surface finish, SF) and kerf have been measured for each of the experimental runs; which correspond to randomly chosen different combinations of factor setting. These data have been utilized to fit a quadratic mathematical model (Response Surface Model) for each of the responses, which can be represented as a function of the aforesaid six process parameters. Predicted data have been utilized for identification of the parametric influence in the form of graphical representation for showing influence of the parameters on selected responses. Predicted data given by the models (as per Taguchi’s L27 (3*6) Orthogonal Array (OA) design) have been used in search of an optimal parametric combination to achieve desired yield of the process: maximum MRR, good surface finish (minimum roughness value) and dimensional accuracy of the product. Grey relational analysis has been adopted to convert this multi-objective criterion into an equivalent single objective function; overall grey relational grade, which has been optimized (maximized) by using Taguchi technique. Optimal setting has been verified through confirmatory test; showed good agreement to the predicted value. This indicates utility of the grey-Taguchi technique as multi-objective optimizer in the field of wire EDM. Keywords: Wire EDM; MRR; response surface methodology; Orthogonal Array (OA)