Goal Attainment Method Research Articles

A novel multi-objective decision-making model to determine optimum resource and capacity configuration for hybrid electricity generation systems: A comparative case study in Türkiye

The rapid depletion of fossil fuels, their negative environmental impacts due to harmful carbon emissions, and the drawbacks of the sole use of intermittent renewable energy resources on system reliability necessitate the use of more advanced energy system technologies. As a result, hybrid electricity generation systems offer an innovative alternative to conventional energy systems. However, the technical complexity and variability of these systems require the application of multi-objective optimization techniques to determine the optimal sizing and system design. Therefore, in this study, we suggest a multi-objective decision-making (MODM) model that involves five conflicting objectives to find the optimal resource configuration and auxiliary source capacity allocation within the framework of the multi-source electricity production method in Türkiye. The MODM model aims to maximize the utilization of resource potentials and the jobs created, while simultaneously minimizing the levelized cost of energy (LCOE), construction duration, and carbon emissions. The MODM model was solved using fmincon and fgoalattain multi-objective optimization algorithms using the Goal Attainment Method in MATLAB and the model results were subsequently compared to the real-world data. According to the model results, the optimal capacity to be allocated for the auxiliary source units is 13,749.58 MWm, while the capacity allocated according to the real-world data as of March 2024 is 2495.49 MWm. In contrast to the model's prediction of 90.8 % solar-based auxiliary unit installations, 99.8 % of auxiliary units are based on solar PV in the actual case. Furthermore, hydro or geothermal-based auxiliary sources are not allocated any capacity, which is consistent with the actual situation. The capacity allocated for the wind (primary source) + solar (auxiliary source) configuration is 76.2 %, whereas in reality, it accounts for 65.6 % of the total installations. Consequently, the model findings suggest that the maximum capacity allocation is for the wind (primary source) + solar (auxiliary source) type hybrid electricity generation system.

A Bi-Objective Inventory Model for Strategic Items in a Stochastic Environment with Partial Shortage: A Base-Stock Approach

This paper suggests an ordering policy for strategic items. Based on the base stock policy, we modeled a bi-objective, multi-product inventory control system with partial back-ordering. The model aims to minimize total costs and maximize the average service level, considering stochastic constraints such as storage space, maximum allowable shortage, and maximum allowable lost sales to match real-world conditions. We used three Multi-Objective Decision-Making methods, namely Individual optimization, Desirability function, and Goal attainment, to solve the problem. TOPSIS method showed the Goal attainment method’s superiority over the others. The sensitivity analysis revealed that the mean of storage space had the most significant impact on objective functions. Also, increasing the back-order percentage can reduce the system’s total costs.

An optimization model for energy project scheduling problem with cost-risk-quality-social consideration trade-off under uncertainty: A real-world application

To complete a successful energy project, all aspects and criteria which can influence the project should be considered. Classic time-cost trade-off (TCT) is used when the completion time of project is not acceptable for customers or top managers. This paper proposes a new cost-risk-quality-social consideration trade-off (CRQST) model for energy projects in a time-constrained problem for achieving specified due date under uncertainty. Moreover, a new comprehensive definition of risk criterion is proposed, and a novel approach for the quality criterion of project based on the dependence of the quality of activities with each other is presented. The internal and external environment of the energy project are considered simultaneously and a new criterion in TCT problem, called social consideration criterion, is introduced. A developed fuzzy augmented ε-constraint method is introduced for the presented multi-objective model to generate Pareto-optimal solutions. To depict the accuracy of results, the proposed model is solved by goal attainment method, and the results of two methods are compared. As a case study, a real oil and gas project is presented, and results show that the proposed method enables managers to effectively handle construction projects in real-world uncertain environments.

A machine learning model with linear and quadratic regression for designing pharmaceutical supply chains with soft time windows and perishable products

Product perishability is an important problem in Pharmaceutical Supply Chains (PSC). Demand perishability and unpredictability add enormous complexity to successfully implementing efficient Pharmaceutical Supply Chain Network Design (PSCND). This study develops a mathematical model for the PSCND. The two objective functions used in the model minimize the total cost and the delivery penalty due to schedule violations involving Soft Time Windows (STWs). Using a STW strategy in the Distribution Center (DC) allocation model empowers decision-makers to include a time-based performance metric for DC evaluation based on the degree of urgency or need for a part. Moreover, Linear Regression (LR) and Quadratic Regression (QR) Machine Learning (ML) algorithms are proposed to forecast the demand and decrease the possibility of a shortage in the PSCND. We show that QR has better performance than LR in PSCND. In the proposed approach, the demand for medicine is forecasted by the QR technique. The Goal Attainment (GA) method is used to solve the suggested model. Finally, sensitivity analysis and managerial perspectives are offered. The numerical outcomes show that the suggested model leads to an efficient PSC, reducing cost, decreasing shortage, and increasing customer satisfaction with STW consideration.

Artificial intelligence assisted optimization of rammed aggregate pier supported raft foundation systems based on parametric three-dimensional finite element analysis

The increased usage of rammed aggregate piers has demanded optimizing the design parameters of this technique. In this study, numerous parametric three-dimensional finite element analyses were conducted to optimize the parameters of the rammed aggregate pier-supported raft foundation with novel methods. Three-dimensional finite element simulations were validated using a field loading test for a single rammed aggregate pier at Neola, Iowa (USA). After the validation, elasticity modules of the rammed aggregate piers, raft foundation thicknesses, and column spacings were varied. The raft foundation-rammed aggregate pier groups system in 81 different combinations was subjected to parametric three-dimensional finite element analyses to provide data for the optimization study. The effect of the changes in the elasticity modulus of the rammed aggregate piers, the raft foundation thickness, and column spacing on the settlement was investigated. Optimization analyses were performed using the artificial intelligence-supported novel Goal Attainment Method and the Response Surface Method. The novel coding developed in this study, which automatically selects the most reasonable prediction function with the support of artificial intelligence, created a prediction function with a high correlation coefficient used in the optimization analyses. Two different optimization methods specified in the optimization study performed as multi-objectives were compared, and the solution system with the highest desirability value was selected. Therefore, optimum design parameters were reached by using novel methods for general raft foundation-rammed aggregate pier group systems to guide researchers.

Evaluation of SPT-N values and internal friction angle correlation using artificial intelligence methods in granular soils

Context Artificial neural networks (ANNs) and genetic algorithms (GAs) have become widely used in various engineering fields due to their ability to solve complicated issues directly. Aims In this study, internal friction angle (ϕ) values for granular soils were calculated using ANNs, GAs, and empirical methods based on standard penetration test (SPT) data to designate the system that produced the best statistical outcomes. Methods Utilising the literature, experimentally determined internal friction angle (Eϕ) values were obtained for a significant quantity of standard penetration test data. Analysis of variance was performed to ascertain whether there was a significant correlation between SPT-N60 values and Eϕ. A simulated network was created with ANNs, and a function was obtained with GAs for SPT-N60–ϕ correlation. The outcomes obtained with ANNs and GAs were compared with empirical equations and experimental results. Optimisation analysis was conducted with the novel Improved Goal Attainment method to minimise the margin of error. Key results Compared to the GAs and empirical equations, the ANN has been determined to have a reasonable correlation with experimental results. Conclusions It was determined that by utilising ANNs, the current empirical equations indicating the relationship between different soil parameters and the data of tests such as SPT and cone penetration test (CPT) could be produced in improved correlations by employing a large number of data sets obtained from different regions. Implications Effective predictions can be achieved instead of present methods.

Optimization of fiber-reinforced deep cement-fly ash mixing column materials

The flexural and compressive strength requirements of deep cement mixing (DCM) columns subjected to lateral loading have brought forth the demand to specify how the incorporation of fiber and fly ash improves these properties and the mixture quality, including the construction design characteristics of segregation and swelling. The paper addresses this issue considering the experimental results from the extensive parametric study in which various lengths and content of carbon fiber (4-, 6-, and 12-mm lengths and 0.1, 0.4, 0.8% by volume of the mixture) are incorporated into the cement-based mixtures with and without the optimized fly ash content. Along the strength parameters, the effects of mixture quality responses on the performance of DCM columns are also investigated. The segregation results of the fresh mixtures, unconfined compression strength (UCS), flexural strength, and swelling values from the 28-day cured specimens are presented. The novel version of the Goal Attainment Method is used for the optimizations, in which the procedures of high-order regression equations and the multi-objective desirability contents are included to obtain more accurate optimization results in terms of the controlling parameters of segregation, swelling, UCS, and flexural strength. The setting time and workability results from the mixtures having the optimized parameters are also presented to demonstrate the fluidity of the optimized mixtures. The addition of carbon fiber led to significant improvements in the segregation and swelling ratios, with gains of up to 35%. Moreover, the three-point flexural strength and unconfined compressive strength were enhanced by 278% and 54%, respectively. The paper specifically reveals that the incorporation of carbon fiber significantly improves the mixture quality characteristics of segregation and swelling as well as the parameters of flexural strength and UCS.

Multi-Objective Optimization of a Crude Oil Hydrotreating Process with a Crude Distillation Unit Based on Bootstrap Aggregated Neural Network Models

This paper presents the multi-objective optimization of a crude oil hydrotreating (HDT) process with a crude atmospheric distillation unit using data-driven models based on bootstrap aggregated neural networks. Hydrotreating of the whole crude oil has economic benefit compared to the conventional hydrotreating of individual oil products. In order to overcome the difficulty in developing accurate mechanistic models and the computational burden of utilizing such models in optimization, bootstrap aggregated neural networks are utilized to develop reliable data-driven models for this process. Reliable optimal process operating conditions are derived by solving a multi-objective optimization problem incorporating minimization of the widths of model prediction confidence bounds as additional objectives. The multi-objective optimization problem is solved using the goal-attainment method. The proposed method is demonstrated on the HDT of crude oil with crude distillation unit simulated using Aspen HYSYS. Validation of the optimization results using Aspen HYSYS simulation demonstrates that the proposed technique is effective.

Optimized Design of a Self-Biased Amplifier for Seizure Detection Supplied by Piezoelectric Nanogenerator: Metaheuristic Algorithms versus ANN-Assisted Goal Attainment Method.

This work is dedicated to parameter optimization for a self-biased amplifier to be used in preamplifiers for the diagnosis of seizures in neuro-diseases such as epilepsy. For the sake of maximum compactness, which is obligatory for all implantable devices, power is to be supplied by a piezoelectric nanogenerator (PENG). Several meta-heuristic optimization algorithms and an ANN (artificial neural network)-assisted goal attainment method were applied to the circuit, aiming to provide us with the set of optimal design parameters which ensure the minimal overall area of the preamplifier. These parameters are the slew rate, load capacitor, gain–bandwidth product, maximal input voltage, minimal input voltage, input voltage, reference voltage, and dissipation power. The results are re-evaluated and compared in the Cadence 180 nm SCL environment. It has been observed that, among the metaheuristic algorithms, the whale optimization technique reached the best values at low computational cost, decreased complexity, and the highest convergence speed. However, all metaheuristic algorithms were outperformed by the ANN-assisted goal attainment method, which produced a roughly 50% smaller overall area of the preamplifier. All the techniques described here are applicable to the design and optimization of wearable or implantable circuits.

A Mathematical Model and Two Fuzzy Approaches Based on Credibility and Expected Interval for Project Cost-Quality-Risk Trade-Off Problem in Time-Constrained Conditions

To successfully finalize projects and attain their determined purposes, it is indispensable to control all success criteria of a project. The time–cost trade-off (TCT) is known as a prevalent and efficient approach applied when the planned finish date of a project is not admitted by stakeholders, and consequently, the project duration must be decreased. This paper proposes a new mathematical model under fuzzy uncertainty to deal with the project cost–risk–quality trade-off problem (CRQT) under time constraints. Because of the unique nature of projects and their uncertain circumstances, applying crisp values for some project parameters does not seem appropriate. Hence, this paper employs fuzzy sets to resolve these weaknesses. In this study, two approaches are presented to handle proposed fuzzy multi-objective mathematical model. First, fuzzy credibility theory and then goal attainment method are used. Secondly, the model is solved by a fuzzy method based on expected interval and value and augmented ɛ-constraint method. A project from the literature review is adopted and solved by the presented methodology. The results demonstrate the accuracy and efficiency of the two proposed approaches for the introduced practical problem.

A NOVEL BI-OBJECTIVE MODEL FOR A MULTI-PERIOD MULTI-PRODUCT CLOSED-LOOP SUPPLY CHAIN

Closed-loop supply chain (CLSC) is a kind of supply chain which contains forward and backward flows of commodities within a logistics network. In the decision-making process of CLSC, locational, inventory control and transportation issues are addressed to deal with strategic, tactical and operational decisions. This paper utilizes a novel bi-objective mixed-integer linear programming (MILP) model to formulate a multi-period multi-product CLSC design problem considering aggregate cost minimization and service level maximization at the same time. To tackle the bi-objectiveness of the model, goal attainment method (GAM) is applied which is then executed by Gurobi Python API to test the applicability of the suggested model for three different scales (small, medium and large). It is demonstrated that the proposed methodology can find the optimal solutions for different problems in a maximum of 500 seconds. Finally, a set of sensitivity analyses is carried out on the main parameters in order to test the behaviors of the objective functions and suggest managerial insights as well as decision aids. The results reveal that the model is highly dependent on the demand parameter, that is, an increase in demand is closely related to an increase in the aggregate cost and a simultaneous downward trend in the service level.

Multi-Objective Optimal Design and Development of a Four-Bar Mechanism for Weed Control

Weeds compete with crops for water, nutrients, and light consequently, have adverse effects on the crop yield and overall productivity. Mechanical weeding is the most common non-chemical method for weed control, which is applied in organic farming, and the weed cultivator is the most common implement in mechanical weeding. This study aimed to design and develop an innovative active tool to optimize the cultivation depth, which can avoid damage to crop roots and improve the key performance indicators of an inter-row cultivator. A quasi-Newton optimization method and a hybrid of the non-dominated sorting genetic algorithm (NSGA-II) and goal attainment method were separately applied to synthesize and develop a four-bar mechanism for weeding requirements. The transmission angle of the mechanism and the desired path of the weeding blade were simultaneously optimized using these multi-objective optimization techniques. The performance of the developed four-bar cultivator based on the optimization techniques was compared with the ones developed based on the classic methods and also with several conventional tools evaluated in other studies. The results showed that applying the quasi-Newton optimization method and hybrid genetic algorithm can propose a more effective weed cultivator in terms of performance indicators, namely weeding performance, mechanical damage to crop plants and cultivation depth. In addition, the optimization of the transmission angle guaranteed the smooth rotations in the mechanism’s joints.

Tuning of Model Predictive Controllers Based on Hybrid Optimization

A tuning procedure for a model predictive controller (MPC) is presented for multi-input multi-output systems. The approach consists of two steps based on a hybrid method: the goal attainment method and a variable neighborhood search. In the first step, the weights of the MPC objective function are obtained, minimizing the square error between the closed-loop response of the internal controller model and a predefined desired reference trajectory. In the second step, the integer variables of the problem (prediction and control horizons) are obtained, minimizing the square error between the closed-loop response and an optimal trajectory, aiming a controller with low computational cost and good performance. The proposed method was tested in two benchmark processes using different MPC formulations, showing satisfactory results.

Multi-objective sustainable capacitated location routing problem formulation in sustainable supply-chain management

Conflicting sustainability dimensions are considered in a multi-objective formulation, focusing on the capacitated location routing problem (CLRP). The proposed sustainable version (S-CLRP) addresses the location of facilities, the routing of vehicles, the balance of the working load among drivers, and the environmental impact of operations due to the emission of greenhouse gases. In this work, both a mixed integer linear programming model solved using the goal attainment method and an approximated method based on iterated local search (ILS) and decomposition (ILS/D) are proposed. The results show the generation of non-dominated fronts with adequate dispersion and convergence characteristics with which supply-chain decision-makers can evaluate the impact of their decisions on the financial, environmental and social dimensions of their operations.

Over-Actuated Underwater Robots: Configuration Matrix Design and Perspectives.

In general, for the configuration designs of underwater robots, the positions and directions of actuators (i.e., thrusters) are given and installed in conventional ways (known points, vertically, horizontally). This yields limitations for the capability of robots and does not optimize the robot’s resources such as energy, reactivity, and versatility, especially when the robots operate in confined environments. In order to optimize the configuration designs in the underwater robot field focusing on over-actuated systems, in the paper, performance indices (manipulability, energetic, reactive, and robustness indices) are introduced. The multi-objective optimization problem was formulated and analyzed. To deal with different objectives with different units, the goal-attainment method, which can avoid the difficulty of choosing a weighting vector to obtain a good balance among these objectives, was selected to solve the problem. A solution design procedure is proposed and discussed. The efficiency of the proposed method was proven by simulations and experimental results.

A Dynamic Framework for Multiobjective Mixed-Integer Optimal Power Flow Analyses

This paper proposes a reliable and computationally efficient framework for solving multiobjective mixed-integer Optimal Power Flow problems. The main idea is to apply the interior point theory and the goal-attainment method to recast a generic OPF problem with both real and integer decision variables by an equivalent scalar optimization problem with equality constraints. Then, thanks to the adoption of the Lyapunov theory, an asymptotically stable dynamic system is designed such that its equilibrium points coincide with the stationary points of the Lagrangian function of the equivalent problem. Thanks to this approach, the OPF solutions can be promptly and reliably obtained by solving a set of ordinary differential equations, rather than using an iterative Newton-based scheme, which can fail to converge due to several numerical issues. Detailed numerical results are presented and discussed in order to prove the effectiveness of the proposed framework in solving real world problems.

Artificial Intelligence-Based Optimization of a Bimorph-Segmented Tapered Piezoelectric MEMS Energy Harvester for Multimode Operation

This paper presents a study on the design and multiobjective optimization of a bimorph-segmented linearly tapered piezoelectric harvester for low-frequency and multimode vibration energy harvesting. The procedure starts with a significant number of FEM simulations of the structure with different geometric dimensions—length, width, and tapering ratio. The datasets train the artificial neural network (ANN) that provides the fitting function to be modified and used in algorithms for optimization, aiming to achieve minimal resonant frequency and maximal generated power. Levenberg–Marquardt (LM) and scaled conjugate gradient (SCG) methods were used to train the ANN, then the goal attainment method (GAM) and genetic algorithm (GA) were used for optimization. The dominant solution resulted from optimization by the genetic algorithm integrated with the ANN fitting function obtained by the SCG training method. The optimal piezoelectric harvester is 121.3 mm long and 71.56 mm wide and has a taper ratio of 0.7682. It ensures over five times greater output power at frequencies below 200 Hz, which benefits the low frequency of the vibration spectrum. The optimized design can harness the power of higher-resonance modes for multimode applications.

Multi-Objective Optimization for Healthcare Waste Management Network Design with Sustainability Perspective

Healthcare Waste Management (HWM) is considered as one of the important urban decision-making problems due to its potential environmental, economic, and social risks and damages. The network of the HWM system involves important decisions such as facility locating, inventory management, and transportation management. Moreover, with growing concerns towards sustainable development objectives, HWM systems should address its environmental and social aspects as well as its economic and technical characteristics. In this regard, this paper formulates a novel multi-objective optimization model to empower companies in making optimized decisions considering the economic, environmental, and social aspects. Within the proposed model, the first objective function aims to minimize the transportation costs, processing costs, and establishment costs. The second objective function aims to minimize environmental risks and emissions related to the transportation of waste between facilities. The third objective function aims to maximize job creation opportunities. Formulating these three functions, an Improved Multi-Choice Goal Programing (IMCGP) approach is proposed to solve the multi-objective optimization model, which is then compared with the Goal Attainment Method (GAM). Finally, to show the applicability and feasibility of the proposed model, an illustrative example of healthcare waste management is analyzed, and the results are discussed.

Green closed-loop supply chain network design: a novel bi-objective chance-constraint approach

In this paper, a novel chance-constrained programming model has been proposed for handling uncertainties in green closed loop supply chain network design. In addition to locating the facilities and establishing a flow between them, the model also determines the transportation mode between facilities. The objective functions are applied to minimize the expected value and variance of the total cost CO2 released is also controlled by providing a novel chance-constraint including a stochastic upper bound of emission capacity. To solve the mathematical model using the General Algebraic Modeling System (GAMS) software, four multi-objective decision-making (MODM) methods were applied. The proposed methodology was subjected to various numerical experiments. The solutions provided by different methods were compared in terms of the expected value of cost, variance of cost, and CPU time using Pareto-based analysis and optimality-based analysis. In Pareto-based analysis, a set of preferable solutions were presented using the Pareto front; then optimality-based optimization was chosen as the best method by using a Simple Additive Weighting (SAW) method. Experimental experiments and sensitivity analysis demonstrated that the performance of the goal attainment method was 13% and 24% better that of global criteria and goal programming methods, respectively.

Multi-objective optimum design for FS welded 7039 aluminium alloy considering weld quality issues

The optimization techniques gain immense exposure as a potential methodology for attaining the optimal process parameters for manufacturing problems. The present study deals with optimizing approaches in analyzing and predicting the tensile behavior of friction stir welded AA7039. Rotational speed, welding speed, and tilt angle are used as input variables; ultimate tensile strength (UTS) and tensile elongation (TE) is observed as a response parameter. Central composite design (CCD) of response surface methodology (RSM) is used to perform the experiment. Multi-objective genetic algorithm (MOGA) and HMOGA (Hybrid multi-objective genetic algorithm) using goal attainment method are employed to determine the optimal values of input parameters. It is observed that both techniques give better optimal process parameters for attaining maximum values of UTS and TE. Moreover, HMOGA provides better results than MOGA owing to the presence of consistency in the solution.