Objective Function Value Research Articles

Solving a Fully Intuitionistic Fuzzy Transportation Problem Using a Hybrid Multi-Objective Optimization Approach

In this study, a typical transportation problem involving intuitionistic fuzzy-type variables and parameters is focused on. The approaches proposed in the literature for such transportation problems have many shortcomings, such as the use of ranking functions and obtaining an infeasible solution with negative values for variables and objective functions in the presence of non-negative unit transportation charges. To overcome such weaknesses, a new approach without a ranking function is introduced in this paper. The proposed approach first constructs an equivalent crisp multi-objective form of the intuitionistic fuzzy transportation problem and then proposes a new hybrid multi-objective solution procedure to tackle the obtained crisp multi-objective problem. The conducted computer experiments with benchmark problems from the existing studies of the literature reflect the effectiveness of the proposed solution approach of this study in terms of the quality of the results when compared to the available approaches of the literature.

Impact analysis of uncertainty in thermal resistor-capacitor models on model predictive control performance

Model Predictive Control (MPC) is extensively utilized for optimal control in building systems. Despite substantial research being dedicated to exploring the impact of uncertainties in external and internal disturbances on the performance of MPC, the existing studies neglect the potential impact of uncertainties in model parameter identification on control performance. To address this gap, this study quantifies the impact of model uncertainty on MPC performance through a test case in a virtual environment. Various levels of uncertainties for parameters R and C are artificially introduced to assess the MPC performance. The causes of the impact of model uncertainty on control performance are further explored through analysis. We select a first-order RC model to modelling building thermal dynamics. MPC is employed to optimize the heat pump signal with the goal of minimizing the energy cost while maintaining thermal comfort. The simulation results demonstrate that a negative deviation in model parameter identification has a more pronounced impact on MPC performance than a positive deviation, which has a negligible effect on MPC control performance. Deviations in parameters from their true values affect both heat losses from the zone and thermal capacity, thereby influencing the estimated temperature by the RC model. Consequently, these factors, in turn, affect the system’s control decisions, leading to variations in the objective function values. This study can provide an insight into the relationship of model parameters uncertainties and MPC performance and facilitate the practical application of MPC in buildings.

Label Deconvolution for Node Representation Learning on Large-Scale Attributed Graphs Against Learning Bias.

Node representation learning on attributed graphs-whose nodes are associated with rich attributes (e.g., texts and protein sequences)-plays a crucial role in many important downstream tasks. To encode the attributes and graph structures simultaneously, recent studies integrate pre-trained models with graph neural networks (GNNs), where pre-trained models serve as node encoders (NEs) to encode the attributes. As jointly training large NEs and GNNs on large-scale graphs suffers from severe scalability issues, many methods propose to train NEs and GNNs separately. Consequently, they do not take feature convolutions in GNNs into consideration in the training phase of NEs, leading to a significant learning bias relative to the joint training. To address this challenge, we propose an efficient label regularization technique, namely Label Deconvolution (LD), to alleviate the learning bias by a novel and highly scalable approximation to the inverse mapping of GNNs. The inverse mapping leads to an objective function that is equivalent to that by the joint training, while it can effectively incorporate GNNs in the training phase of NEs against the learning bias. More importantly, we show that LD converges to the optimal objective function values by the joint training under mild assumptions. Experiments demonstrate LD significantly outperforms state-of-the-art methods on Open Graph Benchmark datasets.

Bio-inspired optimization technique for optimal beam angle selection in radiotherapy application

A human planner's expertise is currently the most important consideration for determining optimal beam angles for external beam radiotherapy. The necessity of automatically selecting beam angles is especially important in intensity-modulated radiation therapy (IMRT) since fewer modulated beams are utilized in conformal radiotherapy. For an automated beam angle selection (ABAS) approach, the ideal coplanar beam angles correspond to the lowest objective function (OF) value of the dose distributions produced from this collection of candidate beams' intensity-modulated maps. Because of the task's intricacy and the large search space concerned, the ABAS and optimization of intensity maps are addressed independently and repeatedly. The Modified Artificial Bee Colony (MABC) optimization, the integration of Artificial Bee Colony (ABC), and a Firefly algorithm are employed to choose suitable beam angles, and the conjugate gradient (CG) technique is employed to fasten the optimized intensity maps for every selected beam. A 3D full scatter convolution (FSC) approach based on the pencil beam is employed for dose assessment. The effectiveness of MABC is examined using a more difficult instance representing a prostate tumor, and 2 simple cases The simulated MABC output is compared to the ABC optimization method. The results illustrate the reliability and efficiency of the suggested MABC-based ABAS can improve dosage distributions with clinically acceptable computation time.

Precision parameter estimation in Proton Exchange Membrane Fuel Cells using depth information enhanced Differential Evolution

Proton Exchange Membrane Fuel Cell (PEMFC) models require parameter tuning for their design and performance improvement. In this study, Depth Information-Based Differential Evolution (Di-DE) algorithm, a novel and efficient metaheuristic approach, is applied to the complex, nonlinear optimization problem of PEMFC parameter estimation. The Di-DE algorithm was tested on twelve PEMFCs (BCS 500 W PEMFC, Nedstack 600 W PS6 PEMFC, SR-12 500 W PEMFC, H-12 PEMFC, STD 250 W PEMFC, HORIZON 500 W PEMFC and four 250W PEMFC and two H-12 12W PEMFC) and showed excellent accuracy. The Di-DE algorithm is was compared with other advanced evolutionary algorithms like iwPSO, CLPSO, DNLPSO, SLPSO, SaDE, SHADE, JADE, QUATRE, LSA, QUATRE-EMS and C-QUATRE, which obtained a minimum objective function value of 0.0255 and an average runtime improvement of 98.8%. The optimized parameters of the proposed method yielded the Sum of Squared Errors (SSE) as low as 0.00002 in some cases, which indicates better precision and stability. Moreover, the voltage–current (V–I) and power–voltage (P–V) characteristics predicted by Di-DE were within 1% error relative to the experimental data for all tested PEMFCs. The results of this work highlight the potential of the Di-DE algorithm to enable more sophisticated modelling and optimization of PEMFCs, which in turn will help to broaden the use of PEMFCs in clean energy applications.

A multi-objective improved horse herd optimizer based on convex lens imaging for stochastic optimization of wind energy resources in distribution networks considering reliability and uncertainty

In this study, stochastic multi-objective allocation of wind turbines (WTs) in radial distribution networks is performed using a new multi-objective improved horse herd optimizer (MOIHHO) and an unscented transformation (UT) method for modeling the uncertainties of WTs power and network load. The objective function aims to minimize power loss, improve reliability, and reduce the costs associated with wind turbines (WTs), presenting these goals as a three-dimensional function. The Multi-Objective Improved Horse Herd Optimizer (MOIHHO) is derived from an enhanced version of the traditional horse herd optimizer. This enhancement utilizes mirror imaging based on convex lens principles to address issues of premature convergence. Additionally, the decision-making process is designed to identify the final fuzzy solution among the non-dominant solutions within the Pareto front set. The simulation results are presented with and without considering uncertainty in two scenarios of deterministic and stochastic WT allocation on 33- and 69-bus distribution networks and different objectives are compared. Also, the effect of incorporating uncertainties are evaluated on power loss and reliability using the MOIHHO. Moreover, the superiority of the MOIHHO is investigated in achieving better objective function value compared with conventional MOHHO, multi-objective particle swarm optimization (MOSPO), multi-objective gray wolf optimizer (MOGWO), and multi-objective gazelle optimization algorithm (MOGOA). The obtained results demonstrated that considering the UT-based stochastic scenario, the power losses cost is increased, and the reliability is weakened for 33- and 69-bus networks in comparison with the deterministic scenario.

Optimizing Wind and Solar Integration in a Hybrid Energy System for Enhanced Sustainability

ABSTRACTA hybrid energy system, comprising a diesel engine as the prime mover, electrical and absorption chillers, a backup boiler, and a multi‐effect distillation through thermal vapor compression (MED‐TVC) unit, has been utilized to meet the requirements of a residential complex. This study focuses on redesigning and optimizing the system to enhance environmental conditions, reduce pollutants, and minimize the use of fossil energy. The feasibility and design of renewable energy systems, including wind turbines (WTs), photovoltaic panels (PVs), and flat plate collectors (FPCs), have been examined. Genetic algorithm (GA) has been employed for optimization. The hybrid system employs 21 design variables, with 24 design variables chosen for optimization alongside renewable energies. The total annual cost (TAC), encompassing investment, operation, and pollution emission fines, has been chosen as the objective function for minimization. The results indicate that the use of WTs has not been cost‐effective, and solar energy can enhance the system's performance in Bandar Abbas, Hormozgan province in Iran. In the case of using a combined system, the objective function value was 2.0472 × 106 $/year, and when using renewable energies, the objective function became 1.6795 × 106 $/year. Thus, the proposed combined‐renewable system has reduced the objective function by 17.96%.

Characterization of the temporal profile of the antinociceptive effects of an intravenous bolus of ketamine using the analgesia nociception index in no-anesthetized adult patients.

An effect-site target-controlled infusion (TCI) would allow a more precise titration of intravenous analgesics effect. The analgesia nociception index (ANI) continuously monitors the analgesia/nociception balance during general anesthesia. This study aims to derive a PKPD model of ketamine antinociceptive effect using the Domino PK parameter set and the ANI response data in awake patients without other drugs affecting the ANI response. Twenty awake adult patients were prospectively studied before general anesthesia. Patients received a single intravenous bolus of ketamine 0.1mg·kg- 1, and the subsequent ANI values were recorded. An effect compartment model incorporating the Domino PK parameter set was used to characterize the time lag between ketamine plasma concentrations and the ANI response. The model was parameterized with a single parameter Ke0. An Emax pharmacodynamic model was used to fit the ANI response data. Model parameters were estimated with NONMEM® 7.5. The minimum objective function value guided the model construction. After the ketamine administration, basal ANI values increased from 38.5 ± 4.95 to a maximum of 53.5 ± 4.95 with an observed time-to-peak effect of 1.83 ± 0.74min. Modeling analysis revealed hysteresis between predicted plasma concentrations from the Domino model and observed ANI data. Hysteresis was characterized, incorporating an estimated Keo of 0.238 (CI95% 0.20-0.28) min-1 to the described PK parameters set. The developed PKPD model, using Domino's PK parameters and the ANI response data, adequately characterized the temporal profile of ketamine's antinociceptive effect. The current estimated model parameters can be used to perform an effect-site TCI of ketamine for analgesic purposes.

Orbit-finite linear programming

An infinite set is orbit-finite if, up to permutations of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of linear inequalities. As our principal contribution we provide a decision procedure for checking if such a system has a real solution, and for computing the minimal/maximal value of a linear objective function over the solution set. We also show undecidability of these problems in case when only integer solutions are considered. Therefore orbit-finite linear programming is decidable, while orbit-finite integer linear programming is not.

A Novel k-Means Framework via Constrained Relaxation and Spectral Rotation.

Owing to its simplicity, the traditional k - means (Lloyd heuristic) clustering method plays a vital role in a variety of machine-learning applications. Disappointingly, the Lloyd heuristic is prone to local minima. In this article, we propose k - mRSR, which converts the sum-of-squared error (SSE) (Lloyd) into a combinatorial optimization problem and incorporates a relaxed trace maximization term and an improved spectral rotation term. The main advantage of k - mRSR is that it only needs to solve the membership matrix instead of computing the cluster centers in each iteration. Furthermore, we present a nonredundant coordinate descent method that brings the discrete solution infinitely close to the scaled partition matrix. Two novel findings from the experiments are that k - mRSR can further decrease (increase) the objective function values of the k - means obtained by Lloyd (CD), while Lloyd (CD) cannot decrease (increase) the objective function obtained by k - mRSR. In addition, the results of extensive experiments on 15 datasets indicate that k - mRSR outperforms both Lloyd and CD in terms of the objective function value and outperforms other state-of-the-art methods in terms of clustering performance.

Bi-objective ranking and selection using stochastic kriging

We consider bi-objective ranking and selection problems, where the goal is to correctly identify the Pareto-optimal solutions among a finite set of candidates for which the objective function values have to be estimated from noisy evaluations. When identifying these solutions, the noise perturbing the observed performance may lead to two types of errors: solutions that are truly Pareto-optimal may appear to be dominated, and solutions that are truly dominated may appear to be Pareto-optimal. We propose a novel Bayesian bi-objective ranking and selection method that sequentially allocates extra samples to competitive solutions, in view of reducing the misclassification errors when identifying the solutions with the best expected performance. The approach uses stochastic kriging to build reliable predictive distributions of the objectives, and exploits this information to decide how to resample. The experiments are designed to evaluate the algorithm on several artificial and practical test problems. The proposed approach is observed to consistently outperform its competitors (a well-known state-of-the-art algorithm and the standard equal allocation method), which may also benefit from the use of stochastic kriging information.

Stochastic optimal PV placement and command based power control for voltage and power factor correction using MOPSO algorithm

This paper addresses a multi-objective particle swarm optimization (MOPSO) algorithm to locate the best position at which a single distributed generator (DG) with optimum voltage amplitude and phase can be installed. The objective is to maximize the power factor and voltage in IEEE 9-Bus system and voltage in IEEE 15-Bus system using MATLAB/SIMULINK software. Systematic simulations revealed that a single DG at Bus-5 with voltage amplitude/phase of 230 kV/-13∘ caused highest objective function value of 1.9919 with an improvement in power factor and voltage of 1.39% and 1.15% respectively. In IEEE 15-Bus system, DG at Bus-3 caused the highest objective function (0.8828) with DG voltage amplitude/phase of 10.735 kV/23.12∘ and 11.89% voltage improvement. Finally, a robust control program in dq0 domain is developed to achieve calculated powers from photovoltaic generator at DG bus whose effect is validated to be the same at all buses as given by the MOPSO algorithm.

Adaptive Free-Form Deformation Parameterization Based on Spring Analogy Method for Aerodynamic Shape Optimization

An adaptive Free-Form Deformation parameterization method based on a spring analogy is presented for aerodynamic shape optimization problems. The proposed method effectively incorporates the gradients of the objective and constraint functions, achieving automatic control point adjustment based on variances in design variable components. To evaluate the performance of the adaptive FFD parameterization method, two 2D airfoil optimization design problems are examined. The optimization of the RAE2822 airfoil with 12, 18 and 24 design variables demonstrates superior results for the adaptive method compared to uniform parameterization. The adaptive method requires fewer iterations and achieves lower objective function values. Additionally, the optimization design from NACA0012 to RAE2822 airfoil with 18 design variables shows that the adaptive parameterization method achieves a lower drag coefficient while satisfying the optimization objective. This validates the method’s capability to finely adjust airfoil shapes and capture more optimal design points by exerting stronger control over local shapes. The proposed adaptive FFD parameterization method proves highly effective for optimizing aerodynamic shapes, offering stability and efficiency in the early stages of optimization, even with a limited number of design variables.

Design of Shape Forming Elements for Architected Composites via Bayesian Optimization and Genetic Algorithms: A Concept Evaluation.

This article presents the first use of shape forming elements (SFEs) to produce architected composites from multiple materials in an extrusion process. Each SFE contains a matrix of flow channels connecting input and output ports, where materials are routed between corresponding ports. The mathematical operations of rotation and shifting are described, and design automation is explored using Bayesian optimization and genetic algorithms to select fifty or more parameters for minimizing two objective functions. The first objective aims to match a target cross-section by minimizing the pixel-by-pixel error, which is weighted with the structural similarity index (SSIM). The second objective seeks to maximize information content by minimizing the SSIM relative to a white image. Satisfactory designs are achieved with better objective function values observed in rectangular rather than square flow channels. Validation extrusion of modeling clay demonstrates that while SFEs impose complex material transformations, they do not achieve the material distributions predicted by the digital model. Using the SSIM for results comparison, initial stages yielded SSIM values near 0.8 between design and simulation, indicating a good initial match. However, the control of material processing tended to decline with successive SFE processing with the SSIM of the extruded output dropping to 0.023 relative to the design intent. Flow simulations more closely replicated the observed structures with SSIM values around 0.4 but also failed to predict the intended cross-sections. The evaluation highlights the need for advanced modeling techniques to enhance the predictive accuracy and functionality of SFEs for biomedical, energy storage, and structural applications.

Optimization of architectural design and construction with integrated BIM and PLM methodologies.

Digital transformation in the architecture industry encounters challenges such as data silos within design stages, between design and construction, and across the entire industry chain, including BIM and project management. This study introduces a pioneering approach for seamlessly integrating building information modeling (BIM) and product lifecycle management (PLM) within the management framework and collaborative workflows of architectural design and construction. The proposed methodology was implemented in two major projects, namely, the Wuhan Next-Generation Weather Radar Construction Project and the Hubei Center for Disease Control and Prevention Comprehensive Capacity Enhancement Project (Phase I), with the former being China's first end-to-end digitally integrated construction project. Compared with traditional projects, these implementations achieved improvements of 24.39% and 38.04%, respectively, in objective function values. The findings highlight the unique advantages of BIM-PLM integration in optimizing lifecycle management, enhancing cross-disciplinary, cross-enterprise, and cross-regional collaboration, improving project design efficiency and quality, and reducing costs and waste. This integration provides valuable insights into the digital advancement of the construction industry.

Parameter estimation in vapor-liquid equilibrium modeling of compounds related to biodiesel production using opposite point-based differential evolution algorithm.

Biodiesel stands out as the most favorable alternatives to fossil-derived diesel, offering a multitude of environmental benefits. At various stages of biodiesel production, the separation processes necessitate thermodynamic models with the capability to correlate and predict phase equilibria of mixtures. In this study, application of the classical differential evolution (DE) and its new enhanced version, the OPDE algorithm, for modeling vapor-liquid equilibrium (VLE) associated with components related to biodiesel production is presented. The algorithms were analysed and contrasted in terms of their performance, in estimating parameters for Wilson, NRTL and UNIFAC models. Additionally, classical least-squares (LS) and error-in-variable (EIV) approaches were examined and compared. Also, VLE datasets for a specific system have been merged, and parameters have been estimated. The findings suggest that parameters obtained through LS approach align with those reported in literature, indicating faster convergence in all problems. In contrast, the EIV approach achieved a higher objective function value compared to the LS approach, exhibiting low deviation. OPDE outperformed DE in terms of performance. The enhancement in RMSTD value has been found within range 91%-99% for EIV approach. Further, novel findings derived from some of the studied VLE datasets are presented.

Dynamic load frequency control in Power systems using a hybrid simulated annealing based Quadratic Interpolation Optimizer

Ensuring the stability and reliability of modern power systems is increasingly challenging due to the growing integration of renewable energy sources and the dynamic nature of load demands. Traditional proportional-integral-derivative (PID) controllers, while widely used, often fall short in effectively managing these complexities. This paper introduces a novel approach to load frequency control (LFC) by proposing a filtered PID (PID-F) controller optimized through a hybrid simulated annealing based quadratic interpolation optimizer (hSA-QIO). The hSA-QIO uniquely combines the local search capabilities of simulated annealing (SA) with the global optimization strengths of the quadratic interpolation optimizer (QIO), providing a robust and efficient solution for LFC challenges. The key contributions of this study include the development and application of the hSA-QIO, which significantly enhances the performance of the PID-F controller. The proposed hSA-QIO was evaluated on unimodal, multimodal, and low-dimensional benchmark functions, to demonstrate its robustness and effectiveness across diverse optimization scenarios. The results showed significant improvements in solution quality compared to the original QIO, with lower objective function values and faster convergence. Applied to a two-area interconnected power system with hybrid photovoltaic-thermal power generation, the hSA-QIO-tuned controller achieved a substantial reduction in the integral of time-weighted absolute error by 23.4%, from 1.1396 to 0.87412. Additionally, the controller reduced the settling time for frequency deviations in Area 1 by 9.9%, from 1.0574 s to 0.96191 s, and decreased the overshoot by 8.8%. In Area 2, the settling time was improved to 0.89209 s, with a reduction in overshoot by 4.8%. The controller also demonstrated superior tie-line power regulation, achieving immediate response with minimal overshoot.

Quantum search algorithm for binary constant weight codes

A binary constant weight code is a type of error-correcting code with a wide range of applications. The problem of finding a binary constant weight code has long been studied as a combinatorial optimization problem in coding theory. In this paper, we propose a quantum search algorithm for binary constant weight codes. Specifically, the search problem is formulated as a polynomial binary optimization problem and Grover adaptive search is used for providing the quadratic speedup. Focusing on the inherent structure of the problem, we derive an upper bound on the minimum of the objective function value and a lower bound on the exact number of solutions. By exploiting these two bounds, we successfully reduced the constant overhead of the algorithm, although the overall query complexity remains exponential due to the NP-complete nature of the problem. In our algebraic analysis, it was found that this proposed algorithm is capable of reducing the number of required qubits, thus enhancing the feasibility. Additionally, our simulations demonstrated that it reduces the average number of classical iterations by 63% as well as the average number of total Grover rotations by 31%. The proposed approach may be useful for other quantum search algorithms and optimization problems.

Hydrodynamic model-driven evolutionary algorithm-based operation optimization of an experimental drainage pumping station

ABSTRACT The effective operation of pumping stations plays a crucial role in urban flood management. However, challenges persist in optimizing pumping station operations, including inaccuracies in characterizing flood propagation and the high computational costs associated with optimization. This study introduces a novel optimization approach for pumping station operation that integrates a hydrodynamic model with evolutionary algorithms, leveraging data-driven technology. The method iteratively computes operation rules using the adaptive particle swarm optimization (APSO) algorithm to identify optimal solutions. The hydrodynamic model accurately simulates flood propagation and provides hydraulic parameters for the objective function and constraints of the APSO algorithm. With the predictive capability of the Kriging model, the optimization enhances efficiency by reducing the frequency of calls to the hydrodynamic model. A study case of a flood management digital twin experimental platform was then taken for the application. Compared to initial operation rules, the objective function value of the proposed method is reduced by 28.7, 32.5, and 25%, respectively, under varying magnitudes of unsteady flood inflows, demonstrating high performances in both flood mitigation and operation cost control. Moreover, the method only requires 70 calls to the hydrodynamic model to formulate the decision operation rule.

Explicable AI-based modeling for the compressive strength of metakaolin-derived geopolymers

Geopolymers (GPs) are produced using a variety of alumina and silica-rich ingredients, including natural sources, such as calcined clays, as well as waste by-products, like fly ash and slag. It is difficult to measure the effect of each parameter on the strength of GP composites via experimental research. In this regard, this research aimed to build artificial intelligence (AI)-aided estimation models to quantify the impact of mix proportions on the compressive strength (CS) of MK-based GP mortar. Gene expression programming (GEP) and multi-expression programming (MEP) tools were used for models' development due to their advantage of yielding model equations for future predictions. Hyperparameters in GEP and MEP were systematically adjusted to enhance the models' optimal predictability. The regression and error analysis proved the superiority of MEP models over GEP models. In comparison to the GEP model, which had R2, MAE, MSE, RMSE, and objective function values of 0.90, 4.02, 25.3, 5.03, and 0.08, respectively, the MEP model demonstrated greater accuracy with values of 0.96, 3.24, 16.4, 4.05, and 0.02 respectively. Furthermore, SHapley Additive exPlanations (SHAP) analysis was conducted to determine the effect of various parameters on the CS of MK-based GP mortar. The established models' equations may be exploited to assess the CS of MK-based GP composites with various input parameters, hence reducing the need for further laboratory testing. Implementing this approach not only improves the efficiency of material design but also encourages the sustainable utilization of locally accessible resources in the manufacturing of geopolymers.