Normalized Objective Function Research Articles

An improved non-dominated sorting biogeography-based optimization algorithm for the (hybrid) multi-objective flexible job-shop scheduling problem

With the continuous advancement of intelligent manufacturing and industry 4.0, production scheduling has become a significant problem that most enterprises must deal with. Thereinto, (hybrid) multi-objective flexible job-shop scheduling problem, widely existing in the real-life manufacturing systems, is one of the NP-hard problems in various scheduling problems. Consequently, in this paper, an improved non-dominated sorting biogeography-based optimization (INSBBO) algorithm has been proposed to solve the problem. First of all, to overcome the pressure scarcity of individual selection in the Pareto dominance principle, especially in the late iteration of the algorithm, a novel V-dominance principle based on the volume enclosed by the normalized objective function values has been developed to enhance the convergence speed. Then, a hybrid variable neighborhood search (HVNS) structure is designed as a local search algorithm to amend the local search ability. Thereafter, for avoiding the loss of the partial (sub-)optimal solutions in the iteration, an elite storage strategy (ESS) is constructed to store the (sub-)optimal solutions. Additionally, we modify the internal habitat suitability index (HSI), migration and mutation operators of the NSBBO algorithm to further improve its performance. To evaluate the effectiveness of the above improved operations and the robustness of parameter setting, we compare the performances of each modified operation and critical parameter combination through multiple independent running the typical scheduling instance from the literature. The statistical results exhibit that each amended operation has a significant influence on the performance of INSBBO and its key parameter configuration is robust. Meanwhile, INSBBO has a better or similar performance among other state-of-the-art intelligent algorithms by comparing three classical benchmark scheduling datasets.

Efficient reflection waveform inversion using a locally normalized zero‐lag correlative objective function

ABSTRACTFull‐waveform inversion is characterized by cycle‐skipping when the starting background model differs significantly from the true model and low‐frequency data are unavailable. To mitigate this problem, reflection waveform inversion is applied to provide a background velocity model for full‐waveform inversion. This technique attempts to extract background velocity updates along the reflection wavepath by matching the reflection waveforms. However, two issues arise during the implementation of reflection waveform inversion: amplitude and efficiency. The amplitude is always underestimated due to the complex subsurface parameter (i.e. the source signature, density, attenuation etc.). This makes it unreasonable to match the reflection amplitude involved in waveforms, especially in the filed data cases. In addition, generating the background velocity gradient requires the simulation of the reflection wavefield. However, simulating the reflection wavefield is time‐consuming. To address the former, we introduced a locally normalized objective function, while for the latter, we used an efficient strategy by avoiding the explicit generation of the reflection wavefield. Results show that applying the proposed method to both synthetic and field data can provide a good background velocity model for full‐waveform inversion with high efficiency.

A simulation-based method to develop strategies for nitrogen pollution control in a creek watershed with sparse data

Well-defined targets for nitrogen (N) release into the local environment are essential for water management in creeks, but difficulties often arise from working with data that are too sparse to achieve reliable evaluations. Here, a simulation-optimization approach based on the QUAL2K model was developed to put forward strategies for nitrogen pollution control in a creek with sparse data in Shixi Creek, southeast China. The model showed good agreement with field observations from 22 sampling sites sampled over the period from March 2017 to February 2019, with normalized objective function (NOF) less than 0.360. Based on this model, the water pollutant sources in the creek were distinguished and analyzed. Rural sewage discharge in Shixi Creek was the major factor threatening water quality in the stream. Seasonal variations may influence the transformation of riverine N. To make more than 80% of the area in Shixi Creek meet the water quality standard of grade III, an optimized approach is to reduce more than 55% of the N pollution from point source pollution and 10% from nonpoint source pollution. This study proposed an approach that can effectively evaluate strategies for water management in a creek watershed with sparse data.

A new fuzzy strategy for size and topology optimization of truss structures

Most of the metaheuristic optimization techniques are the general optimization tools with the ability of solving various class of problems. However, in the case of more complex engineering problems, adding extra customizing procedure(s) can improve their performance. In this regard, the current study deals with introducing a new auxiliary fuzzy decision mechanism to enhance these methods’ capability on handling the structural size and topology optimization problems. The proposed mechanism aims to reduce the complexity level of the structural size and topology optimization problems by converting their complex search spaces into simpler fuzzy domains. Introduced fuzzy mechanism, during the optimization process, permanently monitors the population updating process and emphasizes either size or topology search behavior of each agent. Proposed mechanism evaluates agents via two predefined concepts so-called Normalized Objective Function (NOFi) and Normalized Members Density (NMDi). Since the presented fuzzy strategy designed as an independent regulator module, it can be integrated with different optimization algorithms. In the current work, it is combined with the Interactive Search Algorithm (ISA) optimization method and the compound method is named as Fuzzy Tuned Interactive Search Algorithm (FTISA). Eventually, its performance is comparatively assessed on solving a number of structural size and topology optimization problems with dynamic and static constraints. Achieved results demonstrate that the introduced fuzzy strategy not only significantly enhances the computational cost of the process but also improves the accuracy of the solutions and stability of the algorithm.

Retarding contaminant migration through porous media using inclined barrier walls

Abstract This study aims to assess the abilities of inclined barrier walls (BWs) to retard the migration of contaminants through porous media. Four cases of BW arrangements were considered, including a single inclined BW (BW 1) and two adjacent BWs (BW 1 and BW 2) with different combinations of inclination ratios (i.e., I 1 = θ1 /90° and I2 = θ2 /90°). Furthermore, the effect of the distance (L) between the contamination source and BW 1 on the migration time (T) was evaluated. A numerical model (GeoStudio) containing two modules (SEEP/W and CTRAN/W) was used. The model proved its reliability to simulate contaminant migration through the porous media, where the normalized objective function values between the simulated and analytical results were 0.02 and 0.04 for the discharge of seepage and concentration of contamination, respectively. The results demonstrated that the migration time was strongly influenced by the inclination ratios of the BWs. Three-dimensional regression analysis was applied to demonstrate the combined effect of the inclination ratio, L and BW arrangements on T.

Multi objective optimization of a micro-channel heat sink through genetic algorithm

In this study, fluid flow and conjugate heat transfer in a micro-channel heat sink (MCHS) is simulated with ANSYS-Fluent and optimized with multi objective genetic algorithm known as elitist Non-Dominated Sorting Genetic Algorithm (NSGA-II) coded in MATLAB. Single phase, steady and fully developed liquid flow in the range of the inlet Reynolds number 500–1000 through a 3D micro-channel is solved by the laminar flow solver. The coolant fluid is considered as deionized water with dynamic viscosity depending on temperature. The geometric variables (channel width and height) of the micro-channel related to the channel’s cross section and the inlet Reynolds number related to the flow rate are selected as design variables for the optimization. Two normalized objective functions of the Nusselt number and pumping power are chosen to assess the hydrodynamic and thermal performances of the MCHS. The optimization is performed for 20 generations with a number of population of 30. Optimal Pareto Front representing the trade-off between the objective functions is obtained, which provides useful results for the design of MCHS. The final generation of the optimization process reveals that in most of the design variable sets, the design points are identified as uniform distribution for the inlet Reynolds number within the limits and 0.29 mm for the micro-channel’s width. However, the micro-channel’s height was suggested in the range of 0.50–0.67 mm in most optimum cases.

Evaluation of a Crop Growth Model for Sweet Potato Over a Set of Agro-Climatic Conditions in India

A study was conducted to evaluate the wider applicability of sweet potato growth model, ‘SPOTCOMS’ for simulating the phenology and yield over a set of agroclimatic conditions in India. The model simulated the phenology of the crop as a function of growing degree days. The genetic coefficients required for the model were estimated from the field experiments conducted with sweet potato variety, Sree Bhadra and other local varieties at the study locations. The model simulated the yield of the sweet potato well and the statistical indices calculated between the simulated and observed yields stated the reliability of the model simulations. The agreement index (D-index) for Sree Bhadra ranged from 0.55 to 0.99, and the D-index for local varieties ranged from 0.51 to 1.00. The calculated values of normalized objective function ranged from 0.01 to 0.10 for Sree Bhadra and 0.00 to 0.22 for other local varieties, and indicated better agreement of simulated and observed yields. The normalized root mean square error ranged from 0.80% to 10.40% for Sree Bhadra and 0.00% to 22.44% for other varieties, and these results suggested the wider applicability of the model with excellent to good simulations. The model also simulated dry matter distribution in tubers pertaining to different stresses such as water, nitrogen and potassium. The study revealed that the simulation model ‘SPOTCOMS’ can be used for simulating the yield as well as to manage the stresses during the crop growth period and to optimize best management practices for the crop cultivation irrespective of the agroclimatic conditions.

Experimental Investigation of Forchheimer Coefficients for Non-Darcy Flow in Conglomerate-Confined Aquifer

A conglomerate-confined aquifer (CCA) plays an important role in affecting the safety and environmental protection during energy mining. In this study, the Forchheimer coefficients and associated seepage characteristics of the CCA were studied for different hydrogeological conditions via integrating theoretical analysis, hydromechanical experiment, and field investigation. Empirical models related to the intrinsic permeability (k) and inertial resistance (β) were developed based on theoretical and experimental solutions, governed by the parameters of particle size, initial porosity, and stress. The non-Darcy flow was obtained through experiments conducted with different ratios of the aggregate particle subjected to stress ranging from 1.43 MPa to 4.38 MPa, and a discharge model associated with k and β was proposed. The aggregate particle and filling material of the CCA presented positive and negative effects on the interconnected pores, respectively, accompanied by wedging and wall effects. Distribution state of the aggregate particle and the filling material was affected by the stress, resulting in the reduction of the hydraulic conductivity and the weakening of the wedging and wall effects in the CCA. In addition, the transportation effect and broken effect occurred for the lower and higher stress situations and contributed to the shrinkage of the interconnected pores. Finally, the models of the CCA were validated using a normalized objective function (NOF), a linear slope γ function, and field measurements.

A solar pressurizable liquid piston stirling engine: Part 2, optimization and development

This investigation is devoted to the optimizing a novel pressurizable liquid piston Stirling engine (PLPSE) using particle swarm optimization (PSO) algorithm. The influences of design parameters including pressure intensifier coefficient, pressure intensifier mass, spring stiffness of the intensifier part of the system, the height of the hot and cold liquid columns and the power piston cross-sectional area on the hydraulic output power of the proposed system are studied. Through sensitivity analysis, it is found that some of the parameters have significant effects on the performance of the proposed PLPSE. Based on maximizing the hydraulic output power and stability of the system's steady-state dynamic behavior, some normalized objective functions are defined, and they are converted into a single objective function via weighting summation method. Then, the optimal values of the decision variables are found via an optimization scheme using PSO algorithm with the purpose of minimizing the objective function. Next, the success of the proposed design approach is examined through simulation results. Finally, the designed PFPSE is fabricated and principally tested. It is shown that the mathematical model based results are in a good accordance with the experimental results through which validity and reliability of the presented design method are attained.

PPCOF: A Robust Proportion-Preserving Composite Objective Function for Scale-Invariant Multi-Objective Optimization

This paper aims at introducing a proportion-preserving composite ob-jective function for multi-objective optimization, namely, PPCOF, and validating its eciency through demonstrating its applicability to opti- mization of the kinetostatic performance of planar parallel mechanisms. It exempts the user from both specifying preference factors and conduct- ing decision-making. It consists of two terms. The rst one adds the normalized objective functions up, where the extrema are resulted from single-objective optimization. To making the composite objective func- tion steer the variations of the objective functions while preserving ra- tional proportions between them, as the main contribution of the paper, it is sought that the normalized objective functions take closely similar values, to which end, they are juxtaposed inside a vector, which is then scaled such that its Euclidean norm-2 is equal to that of the vector of all ones with the same dimensions, and then the second term is constructed as the addition of penalty factors standing for the absolute value of the di erence between each element of the foregoing vector from 1. Based on the experimental results, with a considerably smaller computational cost, the PPCOF obtains an optimal solution that is not dominated by any point from a set of Pareto-optimal solutions o ered by NSGA-II.

An elastodynamic computational time-reversal method for shape reconstruction of traction-free scatterers

This study proposes an elastodynamic time-reversal imaging method for the shape reconstruction of flaws with the traction-free boundary. The proposed method is a generalization of the synthetic aperture focusing technique (SAFT) implemented with the aid of time-reversal back-propagation computation. The reconstruction formula is derived from the boundary condition applied on the flaw boundary without using a diffraction theory yielding an inherently normalized objective function. No restriction is imposed on the wave source or the material properties as long as the wave medium is linearly elastic and lossless. There are two major advantages with the proposed method. First, it is free from ray tracing. The method can thus work with an arbitrary source and the wave modes including inhomogeneous waves. Second, signal conditioning is not required to focus a scattered field to the correct location in the reconstructed image. Numerical examples are presented to demonstrate the performance and benefits of the proposed method. In the numerical examples, the shape of cavities and cracks in an elastic layer is reconstructed from synthetic data. The results show that the method works well with the reverberating incident fields in which inhomogeneous and body waves coexist. Also demonstrated is that the curvature of the cavities is resolved well at the scale of the incident wave length. Through the numerical examples, the method is shown to be a versatile imaging method potentially useful for ultrasonic nondestructive characterization of small flaws.

Optimal direction Gibbs sampler for truncated multivariate normal distributions

ABSTRACTGeneralized Gibbs samplers simulate from any direction, not necessarily limited to the coordinate directions of the parameters of the objective function. We study how to optimally choose such directions in a random scan Gibbs sampler setting. We consider that optimal directions will be those that minimize the Kullback–Leibler divergence of two Markov chain Monte Carlo steps. Two distributions over direction are proposed for the multivariate Normal objective function. The resulting algorithms are used to simulate from a truncated multivariate Normal distribution, and the performance of our algorithms is compared with the performance of two algorithms based on the Gibbs sampler.

Reconfiguration of Distribution Networks with Presence of DGs to improving the Reliability

In this paper, the network reconfiguration in the presence of distributed generation units with the aim of improving the reliability of the network is studied. For this purpose four reliability parameters in the objective function are considered, which is average energy not supplied system average interruption frequency index, system average interruption duration index and momentary average interruption frequency index. The new method will be normalized objective function. Another suggestion of this paper are considering the different fault rates, locating time of faults type and prioritization of customers based on their importance. This nonlinear problem has optimized by particle swarm optimization (PSO) algorithm.

Reconfiguration of Distribution Networks with Presence of DGs to improving the Reliability

In this paper, the network reconfiguration in the presence of distributed generation units with the aim of improving the reliability of the network is studied. For this purpose four reliability parameters in the objective function are considered, which is average energy not supplied system average interruption frequency index, system average interruption duration index and momentary average interruption frequency index. The new method will be normalized objective function. Another suggestion of this paper are considering the different fault rates, locating time of faults type and prioritization of customers based on their importance. This nonlinear problem has optimized by particle swarm optimization (PSO) algorithm.

APPFPA based Best Compromised Solution for Dynamic Economic Emission Dispatch

In this paper a methodology is developed a to obtain Best Compromised Schedule (BCS) of Dynamic Economic Emission Dispatch (DEED) Problem. The DEED Problem is formulated to minimize both the fuel cost and Emission. The traditional weight method may not offer equal significance to both the Fuel Cost and Emission. The proposed methodology was a normalized objective function with a view of providing equal significance to both the objectives there by obtaining BCS. The solution methodology uses the recently suggested Adaptive Predator Prey Flower Pollination Algorithm (APPFPA) and is tested on various test system. The results on two tests system have clearly illustrated that the proposed method is better then weight method. The performance can be improved by combining the algorithms with out involving pareto-optimal solution set for the DEED problem.

Experimental Investigation on Non-Darcian Flow in Unbound Graded Aggregate Material of Highway Pavement

The unbound graded aggregate base (UGAB) has been widely used in drainage layers of highway pavements. This kind of material is of high permeability and can thus drain efficiently the water infiltrated through cracks in the pavement and reduce the associated water damage. The hydraulic conductivity of UGAB is a key factor describing the water flow behavior in UGAB and thus be considered primarily in the design of highway drainage engineering. In this study, the flow behavior of UGAB material was investigated through constant head permeability experiments. Based on the Reynolds number analysis, it was found that the flow in UGAB material was non-Darcian even though under relatively low hydraulic gradient. Therefore, the Darcy law cannot be directly applied to determine the hydraulic conductivity of UGAB. Furthermore, the empirical expression of coefficients in Forchheimer equation, which can be available to evaluate hydraulic conductivity of UGAB material approximately, is presented incorporating the representative particle size and porosity based on the Ergun equation. Then, it was validated against the aid of normalized objective function analysis. Through comparison analysis, the sequencing of hydraulic conductivity of UGAB material was sorted quantitatively in terms of different gradation and representative particle size (\(d_{50}\) and \(\overline{d}\)). The results also showed that the \(d_{50}\)\((\overline{d})\) and the content of fine particles (<0.075 mm) are appropriate indexes for the gradation design of UGAB material in highway pavement engineering.

Best Compromised Schedule for Multi-Objective Unit Commitment Problems

The paper attempts to develop a methodology to obtain Best Compromised Schedule (BCS) of Multi-Objective Unit Commitment (UC) Problem. The UC Problem is formulated to minimize both the fuel cost and Emission. The traditional weight method may not offer equal significance to both the Fuel Cost and Emission. The proposed methodology was a normalized objective function with a view of providing equal significance to both the objectives there by obtaining BCS. The solution methodology use the recently suggested Teaching Learning Based Optimization Algorithms (TLBO) and is tested on various test system ranging upto 100 units. The results on six tests system have clearly illustrated that the proposed method is better than weight method. The performance can be improved by combining the algorithms with Classical Legrangian Relaxations Method.

Mathematical Model for Sediment Wash-Off from Urban Impervious Surfaces

AbstractMathematical models are significant tools for urban runoff management. A rational account of sediment-limited and energy-limited situations in developing a mathematical model may facilitate the improved simulation of total suspended solid (TSS) wash-off in urban impervious surfaces. In this study, a differential equation called the P/r model is proposed to improve the simulation of the sediment discharge process. In this equation, rainfall intensity and the ratio of sediment mass per unit catchment area to rainfall intensity are considered the main variables. The rationality behind the P/r model is analyzed. TSS wash-off from six rainfall events is investigated using the P/r model. Uncertainty analyses are performed to determine the best-fit parameters for the model, with the maximum Nash–Sutcliffe efficiency (NSE) criterion being 0.53 and the minimum normalized objective function being 0.40. The observation percentage within prediction bands is 75%, and the average relative interval length is 1.0...

Thermo-economic modeling and optimization of an irreversible solar-driven heat engine

The present paper illustrates a new thermo-economic performance analysis of an irreversible solar-driven heat engine. Moreover, aforementioned irreversible solar-driven heat engine is optimized by employing thermo-economic functions. With the help of the first and second laws of thermodynamics, an equivalent system is initially specified. To assess this goal, three objective functions that the normalized objective function associated to the power output (FP) and Normalized ecological function (FE) and thermal efficiency (ηth) are involved in optimization process simultaneously. Three objective functions are maximized at the same time. A multi objective evolutionary approaches (MOEAs) on the basis of NSGA-II method is employed in this work.

Membrane-inspired quantum bee colony optimization and its applications for decision engine

In order to effectively solve combinatorial optimization problems, a membrane-inspired quantum bee colony optimization (MQBCO) is proposed for scientific computing and engineering applications. The proposed MQBCO algorithm applies the membrane computing theory to quantum bee colony optimization (QBCO), which is an effective discrete optimization algorithm. The global convergence performance of MQBCO is proved by Markov theory, and the validity of MQBCO is verified by testing the classical benchmark functions. Then the proposed MQBCO algorithm is used to solve decision engine problems of cognitive radio system. By hybridizing the QBCO and membrane computing theory, the quantum state and observation state of the quantum bees can be well evolved within the membrane structure. Simulation results for cognitive radio system show that the proposed decision engine method is superior to the traditional intelligent decision engine algorithms in terms of convergence, precision and stability. Simulation experiments under different communication scenarios illustrate that the balance between three objective functions and the adapted parameter configuration is consistent with the weights of three normalized objective functions.