Objective Function Research Articles

An adaptive fractional controller design for automatic voltage regulator system: sigmoid-based fractional-order PID controller

AbstractThe primary objective of a power system is to provide safe and reliable electrical energy to consumers. This objective is achieved by maintaining the stability of the power system, a multifaceted concept that can be divided into three distinct classes. The focus of this study is on one of these classes, voltage stability. A critical component in maintaining voltage stability is the automatic voltage regulator (AVR) system of synchronous generators. In this paper, a novel control method, the sigmoid-based fractional-order PID (SFOPID), is introduced with the aim of improving the dynamic response and the robustness of the AVR system. The dandelion optimizer (DO), a successful optimization algorithm, is used to optimize the parameters of the proposed SFOPID control strategy. The optimization process for the DO-SFOPID control strategy includes a variety of objective functions, including error-based metrics such as integral of absolute error, integral of squared error, integral of time absolute error, and integral of time squared error, in addition to the user-defined Zwee Lee Gaing’s metric. The effectiveness of the DO-SFOPID control technique on the AVR system has been rigorously investigated through a series of tests and analyses, including aspects such as time domain, robustness, frequency domain, and evaluation of nonlinearity effects. The simulation results are compared between the proposed DO-SFOPID control technique and the fractional-order PID (FOPID) and sigmoid-based PID (SPID) control techniques, both of which have been tuned using different metaheuristic algorithms that have gained significant recognition in recent years. As a result of these comparative analyses, the superiority of the DO-SFOPID control technique is confirmed as it shows an improved performance with respect to the other control techniques. Furthermore, the performance of the proposed DO-SFOPID control technique is validated within an experimental setup for the AVR system. The simulation results show that the proposed DO-SFOPID control technique is highly successful in terms of stability and robustness. In summary, this study provides comprehensive evidence supporting the effectiveness and superiority of the DO-SFOPID control technique on the AVR system through both simulation and experimental results.

Linear-space-variant model for Fourier ptychographic microscopy.

Fourier ptychographic microscopy (FPM) needs to realize well-accepted reconstruction by image segmentation and discarding problematic data due to artifacts caused by vignetting. However, the imaging results have long suffered from uneven color blocks and the consequent digital stitching artifacts, failing to bring satisfying experiences to researchers and users over the past decade since the invention of FPM. In fact, the fundamental reason for vignetting artifacts lies in that the acquired data does not match the adopted linear-space-invariant (LSI) forward model, i.e., the actual object function is modulated by a quadratic phase factor during data acquisition, which has been neglected in the advancement of FPM. In this Letter, we rederive a linear-space-variant (LSV) model for FPM and design the corresponding loss function for FPM, termed LSV-FPM. Utilizing LSV-FPM for optimization enables the efficient removal of wrinkle artifacts caused by vignetting in the reconstruction results, without the need of segmenting or discarding images. The effectiveness of LSV-FPM is validated through data acquired in both 4f and finite conjugate single-lens systems.

Optimization of Temperature Modulation for Gas Classification Based on Bayesian Optimization.

This study proposes an optimization method for temperature modulation in chemiresistor-type gas sensors based on Bayesian optimization (BO), and its applicability was investigated. As voltage for a sensor heater, our previously proposed waveform was employed, and the parameters determining the voltage range were optimized. Employing the Bouldin-Davies index (DBI) as an objective function (OBJ), BO was utilized to minimize the DBI calculated from a feature matrix built from the collected data followed by pre-processing. The sensor responses were measured using five test gases with five concentrations, amounting to 2500 data points per parameter set. After seven trials with four initial parameter sets (ten parameter sets were tested in total), the DBI was successfully reduced from 2.1 to 1.5. The classification accuracy for the test gases based on the support vector machine tends to increase with decreasing the DBI, indicating that the DBI acts as a good OBJ. Additionally, the accuracy itself increased from 85.4% to 93.2% through optimization. The deviation from the tendency that the accuracy increases with decreasing the DBI for some parameter sets was also discussed. Consequently, it was demonstrated that the proposed optimization method based on BO is promising for temperature modulation.

Cooperative lane-changing for connected autonomous vehicles merging into dedicated lanes in mixed traffic flow

Connected and automated vehicles (CAVs) have enormous potential to enhance traffic safety, efficiency, and emissions reduction. However, in the initial phases of CAV development, mixed traffic comprising CAVs and human-driven vehicles (HDVs) will inevitably coexist in the traffic system. To fully exploit the benefits of CAVs, dedicated lanes with independent rights of way will be established. This paper proposes an optimal control strategy for coordinating the mandatory lane-changing of CAVs from ordinary lanes to dedicated lanes. The strategy develops a centralized two-stage cooperative optimal control model to optimize the lane-changing sequence and trajectories of CAVs. In the first stage, a dynamic programming formulation is designed to determine the lane-changing sequence decisions. The model predictive control (MPC) controller is adopted to dynamically solve the optimal control problem with a fixed terminal state. In the second stage, we dynamically and cooperatively designed the longitudinal trajectories of related CAVs. The lateral trajectories of lane-changing CAVs are planned with a cubic polynomial. The objective function considers driving comfort and state tracking to ensure traffic smoothness. Simulation results show that: (1) the proposed strategy can improve the negative impact of lane-changing behavior under different traffic demand levels. (2) Compared to the benchmark approach, the proposed strategy can significantly enhance traffic efficiency and driving comfort, particularly in medium-traffic demand. The strategy can improve the average speed of CAVs by approximately 12 % and decrease the average acceleration by over 45 %. (3) The average fuel consumption is positively correlated with traffic demands and the difference in arrival speeds between lane-changing and dedicated lane CAVs. (4) The effectiveness of the strategy increases with the length of the lane-changing segment. However, the marginal benefit becomes negligible when the segment exceeds 300 m. Therefore, the findings of this paper can provide theoretical support for the cooperative control of CAVs in dedicated lanes of highways in the future.

Numerical algorithm for estimating a conditioned symmetric positive definite matrix under constraints

SummaryWe present RCO (regularized Cholesky optimization): a numerical algorithm for finding a symmetric positive definite (PD) matrix with a bounded condition number that minimizes an objective function. This task arises when estimating a covariance matrix from noisy data or due to model constraints, which can cause spurious small negative eigenvalues. A special case is the problem of finding the nearest well‐conditioned PD matrix to a given matrix. RCO explicitly optimizes the entries of the Cholesky factor. This requires solving a regularized non‐linear, non‐convex optimization problem, for which we apply Newton‐CG and exploit the Hessian's sparsity. The regularization parameter is determined via numerical continuation with an accuracy‐conditioning trade‐off criterion. We apply RCO to our motivating educational measurement application of estimating the covariance matrix of an empirical best linear prediction (EBLP) of school growth scores. We present numerical results for two empirical datasets, state and urban. RCO outperforms general‐purpose near‐PD algorithms, obtaining ‐smaller matrix reconstruction bias and smaller EBLP estimator mean‐squared error. It is in fact the only algorithm that solves the right minimization problem, which strikes a balance between the objective function and the condition number. RCO can be similarly applied to the stable estimation of other posterior means. For the task of finding the nearest PD matrix, RCO yields similar condition numbers to near‐PD methods, but provides a better overall near‐null space.

Study of biocapacity areas to reduce ecological footprint deficits: A case study of Turkey

Our world has had difficulty meeting humans' needs in recent years. To ensure that the world can sustain its inhabitability and self-sufficiency in terms of natural resources, it is required to make the total amount of biocapacity areas equal to or higher than the ecological footprint. An analytical study has been carried out to remedy the biocapacity deficit by utilizing this information for Turkey and then these areas are optimized with heuristic optimization techniques. As a result, Artificial Bee Colony provides better objective function results (fewer errors) compared to Particle Swarm Optimization and Global Optimization Method Based on Clustering and Parabolic Approximation in terms of minimum, maximum, average value, and standard deviation. The rates of change according to the current situation of the biocapacity areas in 2016 are 277.97 %, 30.28 %, −29.28 %, 14.97 %, and −44.85 % for cropland, grazing land, forestland, fishing grounds, and built-up land, respectively. Depending on the population growth, these rates should additionally change by 83.24 %, −0.69 %, 3.97 %, 6.22 %, and −14.24 % respectively in 2050. The developed model can be used in industry or within the frame of government development policy and thus the balance between ecological footprint and biocapacity can be kept under control.

A short-term wind-hydrothermal operational framework in the presence of pumped-hydro storage

Short-term operation is one of the most significant aspects of power systems operation and planning and it mainly includes resource scheduling including renewable and non-renewable energy sources. The mentioned problem is modeled as an optimization problem with one or more objectives depending upon the priorities of the decision maker (system operator) and several equality and inequality constraints. In this respect, this paper proposes a short-term operational model for the hydrothermal power systems in the presence of wind power generation and pumped-hydro storage (PHS) units. The problem is formulated as a single-objective optimization problem that aims to minimize the total operating cost including the fuel cost of thermal units. The problem has been comprehensively investigated through five case studies where the first case study is used for the sake of validation. Then, the other case studies assessed the impacts of wind power generation, PHS unit, and uncertainty on the problem. The five case studies are as follows: Case 1: Short-term hydrothermal (STH) scheduling which aims to minimize the total cost. Case 2: Deterministic short-term hydrothermal-wind (STHTW) scheduling which aims to minimize the total cost. Case 3: Stochastic wind-hydro-thermal scheduling that seeks to minimize the total cost taking into consideration the uncertainty of the wind power generation. Case 4: Deterministic wind-hydro-thermal scheduling in the presence of the PHS unit with the total cost minimization as the objective function. Case 5: Stochastic wind-hydro-thermal scheduling in the presence of the PHS unit that is used to evaluate the impact of uncertainty of wind power generation with the total cost minimization as the objective function. It is noteworthy that the first three case studies have been formulated using a non-linear programming (NLP) model and solved using the CONOPT solver in GAMS. Case studies 4 and 5 have been presented using a mixed-integer non-linear programming (MINLP) model and solved using the DICOPT solver in GAMS. A sensitivity analysis has also been carried out to assess the system's performance with different loading conditions. In this respect, the total cost and PHS operation with different amounts of load demand were evaluated and the results have been presented and discussed.

Failure Behavior and Vulnerability of Containment Structures Subjected to Overpressure Loads Considering Different Failure Criteria

This paper investigates the failure behavior and vulnerability of the containment structure (CS) under internal pressure according to different functional and structural failure criteria. Through nonlinear numerical analysis, the deformation of the structure, degree of concrete cracking, and the distribution of stresses and strains in the prestressing tendons and steel liner under different failure criteria are compared. Combined with probabilistic analysis methods, the vulnerability curves, HCLPF capacities, and total failure probabilities of CS determined by different failure criteria are systematically discussed. Results show that there are some differences in the failure behavior and pressure capacity of CS under different failure criteria for both functional and structural failure modes. Under the same failure mode, the variability of the pressure capacities obtained using different criteria is relatively small. Generally, the total failure probabilities of CS subjected to overpressure loads determined by different failure criteria exhibit significant differences. If it is considered that all the investigated failure criteria have a certain ability to predict containment failure, the probabilistic assessment results derived from the functional failure criterion based on the fracture strain of steel liners and the structural failure criterion based on the global strain are deemed to be more reasonable.

Investigating the feasibility of the double-play strategy: evidence from Hong Kong’s speculative attacks

ABSTRACT This paper examines the ‘double-play’ strategy adopted by speculators during currency attacks in Hong Kong. We modify the speculators’ objective function to interpret how they earned potential returns from the automatic mechanism of the linked exchange rate system. Furthermore, we investigate the dynamic conditional correlations among currency, stock and derivatives markets, and identify the key determinants for these relationships during speculative attacks. Our findings offer a comprehensive insight into the behaviour of speculators during currency attacks, and provide compelling empirical support for the impact of central bank interventions on market dynamics.

Optimal declutching control of hinged multiple floating bodies

In deep seas, there is an increasing utilisation of multiple floating structures as devices for harnessing renewable energy, such as hybrid wind-wave energy systems and multi-body wave energy converters. The control strategies have a great influence on the motion characteristics and energy conversion efficiency of these systems. The control technology brings more benefits to the system's performance, yet also introduces more complex challenges. This paper aims to fill the research gap in the control of multiple floating bodies and to propose a novel optimal declutching control method. Declutching control enables discontinuous loading and releasing of the force from power take-off system between bodies. It was found that the feasibility of the proposed method is highly dependent on the choice of objective functions, iteration numbers, and wave frequencies. With appropriate parameters, the declutching control can achieve a variety of objectives for a hinged floating multibody system, such as reducing pitch motion, improving extracted wave power, increasing relative rotational speed, and enhancing power extraction. The control effects on the velocity and the force-velocity phase relationship and how they benefit the objectives are discussed. All objective functions show a better control effect (at least 7.76%) on their respective performance indices than others.

High-order residual moveout correction with global optimization in local time windows

Residual moveout (RMO) correction is significant for optimizing the common image gathers (CIGs) and migration stacked sections, which is a vital step in seismic data processing. The conventional RMO correction methods flatten the migrated gathers by inverse normal moveout and then pick up the velocity parameters, which require high labor of manual picking with low efficiency. The existing high-order RMO correction methods by scanning technology need a bispectral picking process. To address these issues, we propose a novel high-order RMO correction method based on a crosscorrelation-based objective function with global optimization in local time windows. The selected time windows covering the reflected events in the stacked section are used for parameter estimation. Then the very fast simulated annealing (VFSA) algorithm is used to simultaneously invert the two effective parameters (migration velocity and anellipticity anisotropic parameter) with the local CIGs in the time window, which has relatively high computational efficiency. The Hess model example test results show that the proposed method can effectively deal with the RMO problem in the case of anisotropic media, and the developed high-order RMO correction based on anisotropic assumption significantly improved the imaging performance compared to the conventional isotropic RMO correction methods, especially for steep structures. The application to a real 3D land data set further confirms the effectiveness and practicability of the proposed method.

Stability and Reactive Power Sharing Enhancement in Islanded Microgrid via Small-Signal Modeling and Optimal Virtual Impedance Control

In the context of integrating Renewable Energy Sources, Microgrid (MG) development is pivotal, particularly as a foundational technology for Smart-Grid evolution. Despite advancements in control techniques, challenges persist in ensuring system stability and accurate power sharing across diverse operational conditions and load types. The objective of this research is to control numerous paralleled inverters-based distributed generators (DGs) that contribute to power sharing in an island MG. The proposed methodology involves developing an innovative small-signal model for islanding MGs that incorporate virtual impedances. Subsequently, optimization algorithms based on Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are proposed and compared for designing the virtual impedances. These algorithms analyze all potential operating points, aiming to minimize reactive power mismatches while maximizing MG stability. The suggested objective function facilitates the simultaneous achievement of these objectives. The proposed approaches were tested using MATLAB-Simulink software, and the comparison of the results between conventional approach and the proposed optimal approaches shows significant improvement in terms of the dynamic response during load changes, such as a decrease in response time by up to 20%, a reduction in overshoot percentage by approximately 15%, and a settling time improvement of nearly 25%. These quantified improvements highlight the effectiveness of the GA and PSO methods in minimizing the reactive power-sharing error while optimizing MG performance and stability.

Topology optimization and bionic analysis of heat sink fin configuration based on additive manufacturing technology

Fins are extensively employed in heat sinks for high heat flux components. In this study, three distinct objective functions, namely temperature gradient minimization (TO-I type fin), average temperature minimization (TO-II type fin), and entransy dissipation minimization (TO-III type fin), are established for topology optimization design of the heat sink fin structure to effectively minimize the temperature of the heat source. By conducting a comparative analysis of the configuration features and thermal performance of optimized fins with different objective functions, it is evident that the TO-I type fin exhibits superior thermal performance. When the fin volume fraction φ is 0.3, the heat source center temperature of TO-I type fin is 2.67 K and 4.55 K lower than that of TO-II type fin and TO-III type fin, respectively. Meanwhile, the bionic analysis of the optimized fins under different objective functions using fractal theory reveals that the fractal dimension of the TO-I type fin is 1.4038, which is the closest to the average fractal dimension of many kinds of leaf veins in nature (D¯f= 1.3762), which indicates that the optimized fins have the bionic characteristics most similar to those of the leaf blade. Finally, the three topology optimization fins were fabricated using boundary-filtering optimization 3D printing technology. Comparative tests verified the advantage of minimizing the temperature gradient as the objective function of topology optimization and demonstrated its potential for thermal performance and lightweighting applications, especially under high heat source operating conditions.

Advancing Healthcare Networks: Optimizing Multi-Objective RPL for Diverse Traffic in Low-Power, Lossy Environments

RPL: Powering modern healthcare IoT Networks. The Routing Protocol for Low Power and Lossy Networks(RPL) is a protocol specifically designed for routing in networks characterized by low power and lossy connections built on IPv6. It is specifically designed for the growing use of Instantaneous IoT (Internet of Things) applications. These networks cater to the specialized requirements of Low Power (resource-constrained) and Lossy Networks(unstable networks), also known as LLNs, where routing data smoothly and prioritizing traffic types are the significant challenges. Studies have shown that standard RPL, which makes use of a set of routing rules, struggles to provide the level of performance that many IoT applications in modern-day healthcare demand. This limits RPL’s potential in scenarios where we have a mix of data traffic, which is very common in healthcare settings. To handle the diverse data traffic found in healthcare settings, our method involves distributing several instances of RPL settings throughout the network. The main objective of this strategy is to improve the effectiveness of important and critical healthcare applications. We have developed and thoroughly tested our system using Contiki, which is an open-source IoT operating system. We have three instances in our MultiInstance RPL setup, each of which is intended to handle different kinds of network traffic and provide varying Quality of Service (QoS) measures. Different sets of Objective Function (OF) rules are used by each instance to decide which route is optimal for the data it processes. We have made use of OF0 (Objective Function 0) and MRHOF (Minimum Rank with Hysteresis Objective Function). We have rigorously tested our solution. Our focus has been on metrics like delay, average energy consumption and Packet Delivery Ratio (PDR). Compared to standard RPL, our approach improved packet delivery rates and significantly reduced delays for high priority data packets. This research shows how to better address the complex data traffic needs of real-time healthcare IoT networks.

Reactive Power Management in Loss and Voltage Control via Integrated Clonal Accelerated Evolutionary Programming

Optimal Reactive Power Dispatch (ORPD) plays a crucial role in maintaining voltage stability, enhance power transfer capability, improve system efficiency, regulate voltages, manage congestion, facilitate renewable energy integration, and achieve cost savings in power systems. This paper presents a new optimization technique for optimal reactive power management in power transmission system, called Integrated Clonal Accelerated Evolutionary Programming (ICAEP) algorithm to optimize the reactive power to be dispatched by the generator buses under 3 scenarios with cases. The ICAEP was developed based on hybridization of the traditional Artificial Immune System (AIS) and Evolutionary Programming (EP). The two cases demonstrate the effect of reactive load increment at the chosen load buses; while the three scenarios represent the ORPD schemes which indicate the involvement of generator buses either 3 generators, 4 generators or 5 generators. Implementation of ICAEP outperformed AIS and EP in both objective functions either in minimum voltage maximization or power loss minimization, involving all the cases under the three scenarios. The performance of the ICAEP is evaluated on the IEEE 30-bus test system. The results would be beneficial to power system operators and planning expansion and knowing the status of their systems in their utilities. The developed optimization engine is also robust and feasible for further optimization problem solving initiatives.

Inverse optimization in semi-definite programs to impute unknown constraint matrices

In a typical (forward) optimization problem, a decision-maker uses given values of model parameters to compute the values of decision variables. The goal in inverse optimization (IO) is instead to infer parameters that render given values of decision variables optimal. Most papers on IO utilize duality to impute objective function parameters. A corresponding literature for imputing constraint parameters is essentially non-existent, even for linear programs. The difficulty is that these IO problems include nonconvex bilinear constraints and/or objectives. We study inverse semi-definite programs (SDPs) where matrices on the left-hand-sides of constraints are unknown. These unknown matrices must satisfy some side constraints. We consider two types of such problems, depending on which SDP decision variable values are given: primal or dual. In each situation, we study three sub-cases based on whether both the right-hand-side coefficients and the objective function matrix are known or only one of these two is known. This creates six variants of the inverse problem. For each variant, we first look for sufficient conditions, either on the side constraints or on problem structure, under which the nonconvex bilinear inverse problem can be simplified substantially. In particular, it either has a trivial solution or can be reformulated as a (set of) convex program(s). When such conditions are not evident, we propose three tailored heuristics called the Convex–Concave Procedure, Sequential Semi-definite Programming, and Alternate Convex Search. We perform computational experiments to gain insights into the performance of these three methods.

Multi-objective design optimization of polymer spur gears using a hybrid approach

Polymer gears are used in applications requiring small to moderate loads to effectively transmit power and use the limited place available as possible. Various commercial standards have been provided designers with the rating criteria and acquaintance of different polymer material properties for the process of design. However, the result was unsatisfactory in terms of economy, time, and the optimality of the product. Thus, classic and stochastic algorithms have been embraced to reach the best design of polymer gears. Taking advantage of the former and latter algorithm’ methods, optimal design of gears could be attained with an increased gear life span and decreased failure modes. In this study, polyoxymethylene (POM) spur gear set has been optimized combining the mathematical model from plastic standards and hybrid optimization approach of multi-objective genetic algorithm (MOGA) and sequential quadratic programming (SQP). Weight and power loss were the objective functions. Five design variables were optimized with the satisfaction of bending and contact stresses, temperature, wear, and deformation as constraints. Solutions of the problem were formulated as Pareto optimal set. The results of multi-objective were compared with previously published single-objective optimization. The results favored multi-objective optimization (82.67%, 31.39% reduction in weight and power loss respectively) as it gave the best applicable solution fitting in real life situations. The results also went hand in hand with literature confirming the efficiency of the proposed algorithm. With the variation of operating parameters, various optimal designs could be obtained where the designers can choose the design that is suitable for a particular application.

Research on the optimal capacity configuration of green storage microgrid based on the improved sparrow search algorithm

Green storage plays a key role in modern logistics and is committed to minimizing the environmental impact. To promote the transformation of traditional storage to green storage, research on the capacity allocation of wind-solar-storage microgrids for green storage is proposed. Firstly, this paper proposes a microgrid capacity configuration model, and secondly takes the shortest payback period as the objective function, and uses the improved sparrow search algorithm (ISSA) for optimization. Firstly, the Logistic-Tent compound chaotic mapping method is added to the population initialization of the sparrow search algorithm (SSA). Secondly, the adaptive t-distribution mutation is used to improve the discoverer, and the overall optimization ability of the algorithm is improved. Finally, the hybrid decreasing strategy is adopted in the process of vigilance position update. The ISSA can improve the search efficiency of the algorithm, avoid premature convergence and enhance the robustness of the algorithm, which is helpful to better apply to the optimal configuration of wind-solar-storage microgrid capacity in green storage. By analyzing the optimal capacity allocation results of two typical days, the system can better adapt to the dynamic storage requirements and improve the flexibility and sustainability of the supply chain.

Energy management strategies based on soft actor critic reinforcement learning with a proper reward function design based on battery state of charge constraints

The environmental concerns have pushed our society to find solutions to reduce the emission of transportation systems. One promising solution is the fuel cell hybrid electric vehicle (FCHEV), with a proton exchange membrane fuel cell (PEMFC) and a lithium-ion battery. The presence of two different energy sources requires a smart energy management strategy (EMS) which must not only optimize energy consumption (conventional approaches), but also mitigate component’s degradation (New approaches : Health-conscious strategies). For that, a wide range of techniques has been proposed in the literature, and the most recent techniques are based on machine learning. Reinforcement learning (RL) is usually the most chosen strategy, but as in the optimization techniques, a strong design of the objective function (called reward function in RL) is required. The main challenge in the reward function is to encourage a proper battery state of charge (SOC) management, while reducing the energy consumption and avoiding the factors that accelerate the FC aging. The current advancement in the literature shows satisfactory results, but the reward function design have great improvement potential in the chosen approach. Indeed, most approaches in RL for SOC management with continuous actions are based on the reference SOC principle, which reduces the EMS ability to optimize the other part of the reward function. This paper reveals the challenges associated with the introduction of SOC limits in the reward function and proposes an approach, based on SOC boundaries in the reward function. The contribution allows to better consider the parts to optimize, as it gives more freedom than previous reference SOC techniques all reducing the consumption by 12.9%.

Multi-objective optimization of wire electrical discharge machining process using multi-attribute decision making techniques and regression analysis

Wire electrical discharge machining (WEDM) is one of the most important non-traditional machining methods that is widely used in various industries. The present research work is concerned with the influences of process variables on quality of machined specimen obtained from WEDM process. The process parameters to manufacture mold structure included wire feed speed, wire tension and generator power, and in the current research, the effects of these variables on the aim factors, namely dimensional accuracy, hardness and roughness of product surface have been investigated, simultaneously. In order to obtain the optimal experiment, the multi-objective optimization with discrete solution area has been employed. Method based on the removal effects of criteria (MEREC) and weighted aggregates sum product assessment (WASPAS) techniques have been used with the aim of weighting the objective functions and discovering the best practical experiment. In the following, the regression analysis has been employed to study the effects of variables on response factors. A good correlation between the results gained from two analysis methods was observed. Based on MEREC-WASPAS hybrid technique, the weights of roughness, hardness and dimensional accuracy of machined part were calculated to about 89%, 9% and 2%, respectively. In the selected optimal experiment, the amount of wire feed speed, wire tension and generator power variables were considered to, in turn, 2 cm/s, 2.5 kg, and 10%.