Multiple Objective Functions Research Articles

Multi-Objective Binomial Scrambled Bumble Bees Mating Optimization for D2D Communication in 5G Networks

Device-to-Device (D2D) communication is a gifted component for 5G as it has two innate returns such as traffic reduction and consistent quality of services. Also, D2D is more elastic and efficient and exploits less power than other techniques. Few research works have been designed to provide better D2D communication but, providing maximum throughput is still a demanding one. A novel nature-inspired approach called Multi-Objective Binomial Scrambled Bumble Bees Mating Optimization (MOBSBBMO) technique is proposed to perform D2D communication with higher throughput and lesser loss rate. The MOBSBBMO technique uses multiple objective functions to obtain the optimal mobile device for D2D communication. First, the population (i.e. number of mobile devices) gets initialized arbitrarily. The fitness function is calculated for the number of mobile devices depending on multiple objectives such as energy efficiency, bandwidth capacity, and device cooperativeness. According to the fitness, tournament selection is applied to determine the optimal mobile device. If the fitness criterion is satisfied, then the mobile device is said to be optimal. The MOBSBBMO technique uses the binomial crossover applied to obtain broods by the mating process. Next, scramble mutation is employed to get the best drone bees. Yet, again the mating process is carried out to obtain the optimal solution for the best mobile device. The proposed MOBSBBMO technique is compared with benchmark methods in terms of throughput, data delivery rate, energy efficiency, packet loss rate, and latency. Simulation results show that the proposed MOBSBBMO can notably improve network throughput.

Optimization over the Pareto front of nonconvex multi-objective optimal control problems

Simultaneous optimization of multiple objective functions results in a set of trade-off, or Pareto, solutions. Choosing a, in some sense, best solution in this set is in general a challenging task: In the case of three or more objectives the Pareto front is usually difficult to view, if not impossible, and even in the case of just two objectives constructing the whole Pareto front so as to visually inspect it might be very costly. Therefore, optimization over the Pareto (or efficient) set has been an active area of research. Although there is a wealth of literature involving finite dimensional optimization problems in this area, there is a lack of problem formulation and numerical methods for optimal control problems, except for the convex case. In this paper, we formulate the problem of optimizing over the Pareto front of nonconvex constrained and time-delayed optimal control problems as a bi-level optimization problem. Motivated by existing solution differentiability results, we propose an algorithm incorporating (i) the Chebyshev scalarization, (ii) a concept of the essential interval of weights, and (iii) the simple but effective bisection method, for optimal control problems with two objectives. We illustrate the working of the algorithm on two example problems involving an electric circuit and treatment of tuberculosis and discuss future lines of research for new computational methods.

Matrix-augmentation approach for machine repair problem with generally distributed repair times during working breakdown periods

In the manufacturing industry, production facilities for product manufacturing often contain unreliable operating machines and standbys. The machines can break down and result in productivity loss, and have to be repaired by the repairmen. To evaluate the system performance in operations and production management accurately, a general mathematical model is proposed to investigate the machine repair problem with an unreliable repairman, working breakdowns, and multiple vacations. A novel matrix-augmentation approach is introduced to simplify the analysis process and to derive the stationary distribution of the number of failed machines in the system when the classical supplementary variable technique cannot evolve the steady-state probability recursively. Furthermore, explicit formulas of various performance metrics are developed and numerically computed corresponding to various repair time distributions during working breakdown periods. Finally, an optimization problem with multiple objective functions is formulated with two different objective functions: the expected cost and machine availability. The NSGA-II algorithm is applied to perform numerical experiments and to provide Pareto-efficient solutions for managers and decision-makers.

A Survey on Multi-Objective Based Parameter Optimization for Deep Learning

Deep learning models form one of the most powerful machine learning models for the extraction of important features. Most of the designs of deep neural models, i.e., the initialization of parameters, are still manually tuned. Hence, obtaining a model with high performance is exceedingly time-consuming and occasionally impossible. Optimizing the parameters of the deep networks, therefore, requires improved optimization algorithms with high convergence rates. The single objective-based optimization methods generally used are mostly time-consuming and do not guarantee optimum performance in allcases. Mathematical optimization problems containing multiple objective functions that must be optimized simultaneously fall under the category of multi-objective optimization sometimes referred to as Pareto optimization. Multi-objective optimization problems form one of the alternatives yet useful options for parameter optimization. However, this domain is a bit less explored. In this survey, we focus on exploring the effectiveness of multi-objective optimization strategies for parameter optimization in conjunction with deep neural networks. The case studies used in this study focus on how the twomethods are combined to provide valuable insights into the generation of predictions and analysis in multiple applications.

FUZZY MULTI-OBJECTIVE NONLINEAR PROGRAMMING PROBLEMS UNDER VARİOUS MEMBERSHIP FUNCTIONS: A COMPARATİVE ANALYSIS

Fuzzy sets have been applied to various decision-making problems when there is uncertainty in real-life problems. In decision-making problems, objective functions and constraints sometimes cannot be expressed linearly. In such cases, the problems discussed are expressed by nonlinear programming models. Fuzzy multi-objective programming models are problems containing multiple objective functions, where objective functions and/or constraints include fuzzy parameters. Membership functions are crucial to obtain optimal solution of fuzzy multi-objective programming model. In this study, a green supply chain network model with fuzzy parameters is proposed. Proposed model with nonlinear constraints is a fuzzy multi-objective nonlinear programming model that minimizes both transportation costs and emissions generated by two vehicle types during transportation. The model is used in Zimmermann's Min-Max approach by considering triangular, hyperbolic and exponential membership functions and optimal solutions are obtained. When optimal solutions are compared, it is seen that optimal solution obtained using the hyperbolic membership function is better than the optimal solutions obtained from triangular and exponential ones. Maximum common satisfaction level calculated using hyperbolic membership function for proposed model is λ=0.97. Sensitivity analysis is also carried out by taking into account distances between suppliers, manufacturers, distribution centers and customers, as well as customer demands.

An ANN-based Hong-Lagrange algorithm (ANN-based HLA) for auto design-based building application (ABBA) with prestressed precast piperack frame

ABSTRACT Building optimization using traditional approaches based on explicit objective functions is difficult because of large numbers of variables and constraints. Many studies, thus, developed derivative-free optimizations using evolutionary programming, particle swarm methods, swarm intelligence, etc. Applications of artificial neural networks (ANNs) in frame designs are not common, although ANN is an evolutionary technology in many areas. This study presents novel holistic designs and optimizations of prestressed multi-story frames in general and piperack frames in particular, using the ANN-based Hong-Lagrange Algorithm. The proposed method provides optimized designs in terms of multiple objective functions such as costs, CO2 emissions, weights, and energy consumptions. A software is developed based on MATLAB codes for generating big datasets following American standards. A big data of 120,000 samples is used to train ANNs, formulating objective and constraint functions of 38 input and 69 output parameters. Designs minimizing multiple objective functions are performed by applying sequential quadratic programming to ANN-based functions constrained by equalities and inequalities imposed by architectural and code requirements. Examples show reductions up to 31.81%, 38.63%, 5.06%, and 37.36% in costs, CO2 emissions, weights, and energy consumption, respectively, compared with the minima of those identified from 340,000 samples.

A Solver for Multiobjective Mixed-Integer Convex and Nonconvex Optimization

AbstractThis paper proposes a general framework for solving multiobjective nonconvex optimization problems, i.e., optimization problems in which multiple objective functions have to be optimized simultaneously. Thereby, the nonconvexity might come from the objective or constraint functions, or from integrality conditions for some of the variables. In particular, multiobjective mixed-integer convex and nonconvex optimization problems are covered and form the motivation of our studies. The presented algorithm is based on a branch-and-bound method in the pre-image space, a technique which was already successfully applied for continuous nonconvex multiobjective optimization. However, extending this method to the mixed-integer setting is not straightforward, in particular with regard to convergence results. More precisely, new branching rules and lower bounding procedures are needed to obtain an algorithm that is practically applicable and convergent for multiobjective mixed-integer optimization problems. Corresponding results are a main contribution of this paper. What is more, for improving the performance of this new branch-and-bound method we enhance it with two types of cuts in the image space which are based on ideas from multiobjective mixed-integer convex optimization. Those combine continuous convex relaxations with adaptive cuts for the convex hull of the mixed-integer image set, derived from supporting hyperplanes to the relaxed sets. Based on the above ingredients, the paper provides a new multiobjective mixed-integer solver for convex problems with a stopping criterion purely in the image space. What is more, for the first time a solver for multiobjective mixed-integer nonconvex optimization is presented. We provide the results of numerical tests for the new algorithm. Where possible, we compare it with existing procedures.

Stochastic Transportation Problem with Multichoice Random Parameter

This paper deals with the situation of multiple random choices along with multiple objective functions of the transportation problem. Due to the uncertainty in the environment, the choices of the cost coefficients are considered multichoice random parameters. The other parameters (supply and demand) are replaced by random variables with Gaussian distributions, and each multichoice parameter alternative is treated as a random variable. In this paper, the Newton divided difference interpolation technique is used to convert the multichoice parameter into a single choice in the objective function. Then, the chance-constrained method is applied to transform the probabilistic constraints into deterministic constraints. Due to the consideration of multichoices in the objective function, the expectation minimization model is used to get the deterministic form. Moreover, the fuzzy programming approach with the membership function is utilized to convert the multiobjective function into a single-objective function. A case study is also illustrated for a better understanding of the methodology.

Two-Stage Multicriteria Decision-Making Framework for Aircraft Conflict Resolution

In this study, a two-stage multicriteria decision-making framework for aircraft conflict resolution in the air traffic management system is proposed. Aircraft conflict resolution has been commonly solved based on single-objective optimization. However, the existing approach may not provide a satisfactory solution to all stakeholders involved in the air traffic management system. Therefore, in the first stage of the proposed algorithm, a new conflict resolution strategy is presented based on multiobjective optimization in which multiple-objective functions are optimized simultaneously. Each objective function is designed to take into account the interests of various stakeholders, and the augmented epsilon-constraint method is applied to determine Pareto optimal solutions. In the second stage, the best compromise solution among the Pareto optimal solutions is determined based on the technique for order performance by similarity to the ideal solution. The numerical simulation results show that the proposed algorithm provides a better solution from the perspective of mitigating the competing interests among stakeholders than the existing approach based on single-objective optimization.

Involving energy security and a Water–Energy-Environment nexus framework in the optimal integration of rural water–energy supply systems

This paper addresses the problem of evaluating the Water–Energy-Environment nexus and energy security in the design of water and energy supply systems in isolated off-grid rural communities. Since the evaluation of the nexus requires addressing multiple design objectives, a strategy, based on normalization and sub-setting of objective functions, is proposed to visualize conflicts in problems with many objective functions. To test this idea, the optimal design of a water and energy supply system in a rural indigenous community with traditional household buildings in central Mexico is presented. The Water–Energy-Environment nexus is dealt with using the objective functions of water consumption from local sources, energy efficiency of the system, land use and local CO2 balance. The focus of the analysis is the performance of the nexus components contrasted with the economic performance and energy security of the system. The energy security is evaluated using the Shannon–Wiener index. The results indicate that diversification of primary supply sources increases the impacts and accentuates conflicts in both the nexus and economic performance. For the case study presented, maximizing the Shannon–Wiener Index increases the participation of photovoltaic and wind power, but the total annual cost of the system increases up to 63%. On the other hand, there are considerable impacts on land use and CO2 emissions associated with wood combustion. The proposed strategy for visualizing conflicts in problems with multiple objective functions has the potential to be used as a complement to traditional tools such as the Pareto front.

Application of the Goal Programming Method in Nurse Scheduling at RSUD Dr. Hadrianus Sinaga Pangururan

The purpose of this study was to establish an effective and optimal nurse schedule at the Regional General Hospital dr. Hadrianus sinaga Pangururan. RSUD dr.Hadrianus Sinaga Pangururan is still scheduling nurses manually with a total of 20 nurses and has three work shifts namely morning, afternoon and evening. As a result of manual scheduling, it takes quite a long time and is less efficient due to imbalances in the distribution of shifts. The method used to solve nurse scheduling problems is Goal Programming. Goal Programming is the development of linear programs that are used to solve linear programming problems with multiple objective functions. In modeling this scheduling problem, there are two systems of constraints that must be met, namely the main constraints and additional constraints. The main obstacle is hospital rules that must be complied with while additional obstacles are hospital rules that are still given tolerance for violations. In modeling the nurse scheduling problem, each problem is converted into a mathematical model and the completion of the goal programming model is assisted by LINGO software. From the LINGO output, the results show that nurse scheduling using goal programming meets all system constraints, while the hospital's manual schedule does not meet system constraints.

On first and second order multiobjective programming with interval-valued objective functions

The growing use of optimization models to help decision making has created a demand for such tools that allow formulating and solving more models of real-world processes and systems related to human activity in which hypotheses are not verify in a way specific for classical optimization. One of the approaches for real-world extremum problems under uncertainty is interval-valued optimization. In this paper, a twice differentiable vector optimization problem with multiple interval-valued objective function and both inequality and equality constraints is considered. In this paper, the first order necessary optimality conditions of Karush-Kuhn-Tucker type are proved for differentiable interval-valued vector optimization problems under the first order constraint qualification. If the interval-valued objective function is assumed to be twice weakly differentiable and constraints functions are assumed to be twice differentiable, then two types of second order necessary optimality conditions under two various constraint qualifications are proved for such smooth interval-valued vector optimization problems. Finally, in order to illustrate the Karush-Kuhn-Tucker type necessary optimality conditions established in the paper, an example of an interval-valued optimization is given.

Physics-enhanced machine learning-based optimization of tuned mass damper parameters for seismically-excited buildings

Optimal design of tuned mass damper (TMD) parameters should be implemented before device installation to achieve the desired vibration reduction effects for tall and quite slender buildings. Although various optimization algorithms have been developed for searching TMD parameters, there has been very limited exploration of machine learning-based optimization approach in this domain. In this paper, two machine learning-based algorithms are proposed to optimize the natural frequency and damping ratio of a TMD device for seismically excited building. The first algorithm investigates the single-objective optimization of a TMD parameters on a linear building structure. It is based on physics-enhanced generative and adversarial network (GAN) architecture. A generative network randomly generates the primary TMD parameters within the specified parameter ranges, while an adversarial network guides the evolution of parameters to acquire updated parameters, a physical evaluation network assesses the performance of the updated and primary parameters, subsequently providing training data for both the generated network and adversarial network. Furthermore, a second physics-enhanced machine learning algorithm is proposed for the multi-objective optimization of a TMD parameters on a nonlinear building structure under various seismic excitations. The physical evaluation network is extended to consider multiple objective functions, in which the multiple objective functions are integrated through a kind of decomposition scheme, i.e., weighted sum approach. Then, a better set of parameters can be determined and a Pareto optimal solution is obtained. To verify the effectiveness of the two proposed algorithms, single-objective optimization of a TMD parameters for a linear shear-type structure under seismic excitation and a multiple-objectives optimization of a TMD parameters for a seismically excited nonlinear moment-resisting frame (MRF) are conducted and the optimizations are validated by comparing with those by the conventional particle swarm optimization (PSO) approach.

A parallel variable population multi-objective optimizer for accelerator beam dynamics optimization

The simultaneous optimization of multiple objective functions is needed in many particle accelerator applications. In this paper, we present a parallel evolution based multi-objective optimizer that uses a variable population from generation to generation and an external storage to save good solutions. Two heuristic optimization methods, one uses the unified differential evolution and the other uses the real-coded genetic algorithm, are included in the optimizer to generate next generation candidate solutions, and are compared in the test examples. As an application, we applied this optimizer to the beam dynamics design optimization of a photoinjector and attained the optimal front solutions after 200 generations with the unified differential evolution offspring production scheme.

Optimality conditions in a class of generalized convex optimization problems with the multiple interval-valued objective function

In this paper, a new class of generalized convex optimization problems with a multiple interval-valued objective function is considered. The concepts of B-preinvexity, B-invexity, and the generalized of B-invexity are extended to interval-valued functions. Additionally, several properties of interval-valued B-preinvex and B-invex functions are investigated. The Karush–Kuhn–Tucker necessary optimality conditions for a (weak LU-Pareto) LU-Pareto solution are established for a differentiable vector optimization problem with a multiple interval-valued objective function. Furthermore, the sufficient optimality conditions for both LU and UC order relations are derived for such interval-valued vector optimization problems under appropriate (generalized) B-invexity hypotheses. Suitable examples are provided to illustrate the aforementioned results.

Multi-Criteria Optimization for the Decision Making in Building Envelope Thermal Design

The increase of energy utilization reinforced the need of reducing the primary energy consumption based on fossil fuels and the limitation of carbon dioxide (CO2) emissions to the atmosphere. Such goals aim at the provision of affordable and generally clean energy for the citizens. However, the final decision making is hard to be achieved, due not only to the multitude variety of such proposed technologies, but also to the consideration of different criteria and scenarios, that in many cases are conflicting with each other. This paper deals with the optimization of the building envelope design considering thermal insulation, economic, and environmental aspects. The Life Cycle Assessment perspective is implemented for the data of the environmental criterion, focusing on the CO2 emissions and the cumulative energy demand. The decision making refers not only to the selection of the appropriate thermal insulation material and its width, but also to the choice of the window frame material. In that way, Mathematical Programming (MP) models for the optimization of such criteria were developed. The General Algebraic Modeling System (GAMS) was used to model these problems and the BARON solver was used to solve them. The respective MP models include mixed integer nonlinear programming problems, multiple objective functions, as well as multi-criteria techniques such as goal programming. According to the results, the increase of the envelope thermal protection implies that the economic and environmental costs are higher, displaying the importance of criteria compensation. For smoothing the conflicting criteria, a weighting sensitivity analysis was conducted, showing that reference optimal values are formed for certain ranges of weights, elaborating the framework of decision-making without having to precisely prescribe them beforehand. All in all, the use of the optimization models can improve and facilitate the building design process by analyzing the advantages and drawbacks of the various materials/technologies and allowing the comparative evaluation of the considered alternatives.

Thermal-mechanical coupling topology optimization of multi-phase infill structures with a non-gradient porosity optimization method

Mechanical structures in the real world are often subject to different types of physics which affect their performance and reliability. Recent studies have revealed that porous structures can be an ideal solution for multiphysics problems due to their multifunctionality. In this paper, a full-scale topology optimization method of multi-phase infill structures, i.e. non-gradient porosity optimization method, is proposed to exploit the advantages of different phase materials and solve multiphysics problems efficiently. The method builds upon a unified multi-material density-based topology optimization framework to interpolate the thermal stress coefficient in order to characterize the dependence of the thermal stress load upon the design variables. To generate sparse but stable structures distributed in the interior of a given shape, the upper bound of the solid material volume fraction in the neighborhood of each element in the design domain is constrained. In particular, the influence radius of each element is considered as a separate variable to be optimized, which is calculated directly from field functions in finite element analysis (FEA) without additional sensitivity analysis. In the proposed method, the element pseudo-density and porosity are optimized simultaneously, which further expands the design space and improves the performance of infill structures. Subsequently, the improved weighting method is used to aggregate multiple objective functions. The whole analysis and optimization process are based on a full-scale FEA, thus avoiding scale separation and naturally ensuring the optimized spatial gradient infills to be connected smoothly. Numerical examples with different thermal and mechanical load conditions are presented to demonstrate the feasibility and effectiveness of the proposed method.

Modeling of uncertainty in the estimation of hydrograph components in conjunction with the SUFI-2 optimization algorithm by using multiple objective functions

Modeling of uncertainty in the estimation of hydrograph components in conjunction with the SUFI-2 optimization algorithm by using multiple objective functions

TextureWGAN: texture preserving WGAN with multitask regularizer for computed tomography inverse problems.

This paper presents a deep learning (DL) based method called TextureWGAN. It is designed to preserve image texture while maintaining high pixel fidelity for computed tomography (CT) inverse problems. Over-smoothed images by postprocessing algorithms have been a well-known problem in the medical imaging industry. Therefore, our method tries to solve the over-smoothing problem without compromising pixel fidelity. The TextureWGAN extends from Wasserstein GAN (WGAN). The WGAN can create an image that looks like a genuine image. This aspect of the WGAN helps preserve image texture. However, an output image from the WGAN is not correlated to the corresponding ground truth image. To solve this problem, we introduce the multitask regularizer (MTR) to the WGAN framework to make a generated image highly correlated to the corresponding ground truth image so that the TextureWGAN can achieve high-level pixel fidelity. The MTR is capable of using multiple objective functions. In this research, we adopt a mean squared error (MSE) loss to maintain pixel fidelity. We also use a perception loss to improve the look and feel of result images. Furthermore, the regularization parameters in the MTR are trained along with generator network weights to maximize the performance of the TextureWGAN generator. The proposed method was evaluated in CT image reconstruction applications in addition to super-resolution and image-denoising applications. We conducted extensive qualitative and quantitative evaluations. We used PSNR and SSIM for pixel fidelity analysis and the first-order and the second-order statistical texture analysis for image texture. The results show that the TextureWGAN is more effective in preserving image texture compared with other well-known methods such as the conventional CNN and nonlocal mean filter (NLM). In addition, we demonstrate that TextureWGAN can achieve competitive pixel fidelity performance compared with CNN and NLM. The CNN with MSE loss can attain high-level pixel fidelity, but it often damages image texture. TextureWGAN can preserve image texture while maintaining pixel fidelity. The MTR is not only helpful to stabilize the TextureWGAN's generator training but also maximizes the generator performance.

Evolutionary Optimization of Multiple Machine-Learned Objectives for PET Image Reconstruction

This article proposes optimizing machine-learned objective functions to estimate a set of images optimal for multiple tasks. Tomographic image reconstruction commonly relies on optimizing an objective function that dictates the goodness of an image estimate. We propose a novel use of deep learning in which we train models to perform blind estimation of the goodness of an image. The trained model that maps an image to a target figure of merit serves as the objective function. Using simulated PET images, we train convolutional neural networks (CNNs) to estimate for a single image the root mean square error (RMSE), signal-to-noise ratio, and full width half maximum (FWHM) of a point source. These figures of merit serve as surrogates for the common medical task performance in terms of quantitation, detection, and spatial resolution, respectively. These multiple objective functions are optimized using our recently proposed multiobjective evolutionary algorithm for PET image reconstruction. The evolutionary algorithm seeks to identify the Pareto-optimal front of image solutions, optimal for multiple objectives. Additionally, we propose a reference point method to focus the evolutionary optimization on regions of the multiobjective space to reduce computation. Likewise, we integrate optimality conditions to estimate how close a solution is to optimal without any prior knowledge about the Pareto-optimal front in an effort to guide termination conditions. The multiobjective approach is compared with conventional maximum-likelihood reconstruction with increasing explicit regularization and maximum a posteriori reconstruction with varying penalty strength. The approaches are tested with simulated PET data from a digital phantom and patient data. Results suggest that the proposed machine-learned objectives can estimate quantification, detection, and spatial resolution performance and that the evolutionary algorithm estimates a set of solutions with a good balance for convergence and diversity across different multiobjective combinations. In general, the evolutionary algorithm estimates images with superior performance compared to conventional techniques. Future work is needed to ensure and improve generalizability of the machine-learned objectives for different imaging conditions and to explore other target figures of merit for training machine-learned objectives. This proof-of-concept effort demonstrates a new use of deep learning for tomographic image reconstruction.