Parameters Of Objective Function Research Articles

A meta-heuristic extension of the Lagrangian heuristic framework

Lagrangian heuristics for discrete optimization work by modifying Lagrangian relaxed solutions into feasible solutions to an original problem. They are designed to identify feasible, and hopefully also near-optimal, solutions and have proven to be highly successful in many applications. Based on a primal-dual global optimality condition for non-convex optimization problems, we develop a meta-heuristic extension of the Lagrangian heuristic framework. The optimality condition characterizes (near-)optimal solutions in terms of near-optimality and near-complementarity measures for Lagrangian relaxed solutions. The meta-heuristic extension amounts to constructing a weighted combination of these measures, thus creating a parametric auxiliary objective function, which is a close relative to a Lagrangian function, and embedding a Lagrangian heuristic in a search procedure in the space of the weight parameters. We illustrate and make a first assessment of this meta-heuristic extension by applying it to the generalized assignment and set covering problems. Our computational experience show that the meta-heuristic extension of a standard Lagrangian heuristic can significantly improve upon solution quality.

Novel hybrid arithmetic-equilibrium optimizer as robust tuner for power system stabilizer (PSS) parameters in interconnected electrical power system

Nowadays, the metaheuristic approaches become popular in the optimal tuning parameters of power system controllers, especially Power System Stabilizers (PSS). Besides the easiness, the stochastic behavior in metaheuristic approaches needs further investigation to increase the quality of the offered optimal parameters. Thus, this paper proposes A Novel Hybrid Arithmetic-Equilibrium Optimizer (HAEO) as a robust tuner for PSS in the interconnected electrical power system. The algorithms are hybridized in unique ways to utilize the features in both Arithmetic Optimizer (AO) and Equilibrium Optimizer (EO). Hybridization is performed to improve the exploration ability by providing the widest optimal parameters possible. In benchmarking by the Friedman Ranking Test, the proposed algorithm shows a significant improvement in consistency and accuracy over the basic AO and EO. A wider-distributed optimal solution and better convergence are also offered by the proposed algorithm. Besides that, the application in the optimal tuning shows that the proposed algorithm can provide the best PSS parameters in different objective functions with better average and standard deviation values. The HAEO-PSS gives a significant overshoot suppression of 35 % to 57 %, while the settling time of the system is also improved by 7 % to 13 %. Overall, the HAEO-PSS is proven to improve the stability response of the interconnected electrical power system both in local and interarea responses.

Hybrid minigrid system comprising energy storage systems with optimal frequency control empowering the new Egypt large optical telescope site

Proposed hybrid minigrid two area system simulation model encompassing Photo Voltaic (PV) system, Wind Turbines (WT), diesel generators and Energy Storage Systems with intelligent based optimal Frequency Controllers (FCs) empowering the new Egypt large optical telescope (ELOT) site is presented in this research. Technical study and specifications for a PV solar system of 1000 Kw is introduced. Intelligent fine optimized Proportional Integral Derivative (PID) and Fuzzy self-tuned PID (FSTPID) controllers are designed through applying Harris Hawk optimizer (HHO). The proposed HHO employed method performance is validated under number of eventualities which include vacillations of load, sun radiation and wind speed. The objective function and control parameters are the integral time summation of absolute deviations and the parameters of controllers, consecutively. The system dynamic response and simulation results show that the proposed HHO based FSTPID type FCs are effective in reducing frequency and tie line power signals’ deviations in a diminutive time for such minigrid hybrid system. For supplemental validations, simulation results obtained are compared with genetic algorithm to get the proposed controllers’ gains.

Development of an Emulgel for the Effective Treatment of Atopic Dermatitis: Biocompatibility and Clinical Investigation.

Atopic dermatitis (AD) is a common dermatological disease affecting both children and adults. No drug-free emulgel has been developed and studied in vitro and in vivo for the treatment of AD. The aim of this study was to develop and assess the efficacy of a topical emulgel containing hyaluronic acid, glycerol, Calendula officinalis, Aloe vera, polyphenols and EGF for the concomitant treatment in patients with AD aged over 14. Objective skin barrier function parameters were included, such as transepidermal water loss (TEWL), skin temperature, pH, stratum corneum hydration, skin elasticity and erythema. The subjective opinion of the patients was determined including acceptability, absorption, comfort of use and tolerability, as well as the degree of improvement in patients' quality of life. We observed an improvement in the subjective parameters studied and statistically significant differences in the objective parameters. Specifically, we found an improvement in TEWL (p = 0.006), erythema (p = 0.008) and hydration (p < 0.001), parameters indicating an improvement in the epidermal barrier. One hundred per cent of patients were satisfied with the product. Therefore, these results suggest that the product may contribute to the treatment of AD.

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

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

Examination of convective heat transfer and entropy generation performance in twisted elliptical tubes using response surface method

In this paper, the convective heat transfer (CHT) and flow properties of twisted elliptical tubes (TETs) are numerically simulated within the range of Reynolds numbers (Re) 710 to 4790. The effects of design parameters such as twist ratio (P/D), aspect ratio (A/B), and Re on the CHT and flow resistance properties of TETs are highlighted. The response surface method (RSM) is used to research the effect of interaction between design parameters on the performance of CHT in TETs and establish the relationship between the objective function, i.e., Nusselt number (Nu), friction factor (f), and design parameters. The objective function fitted by RSM are optimized by the non-dominated sequential genetic algorithm (NSGA-II) to obtain the Pareto optimal solution. Besides, the entropy generation minimization principle explores entropy generation characteristics to reveal the mechanism of CHT enhancement in TETs. The results show that the CHT performance, flow resistance, and total entropy generation in TET increase, decrease, and increase with the growth of Re, respectively. They all increase with the reduction of P/D or the growth of A/B. The maximum values of Nu and pressure drop (ΔP) occur when A/B = 2.16 and P/D = 11.90; the minimum value of total entropy generation is reached when A/B = 1.34 and P/D = 26.33; and the Pareto optimal solution corresponds to the best combination of design parameters of Re = 3980, P/D = 13.32, and A/B = 1.82.

Optimising CH4 simulations from the LPJ-GUESS model v4.1 using an adaptive Markov chain Monte Carlo algorithm

Abstract. The processes responsible for methane (CH4) emissions from boreal wetlands are complex; hence, their model representation is complicated by a large number of parameters and parameter uncertainties. The arctic-enabled dynamic global vegetation model LPJ-GUESS (Lund–Potsdam–Jena General Ecosystem Simulator) is one such model that allows quantification and understanding of the natural wetland CH4 fluxes at various scales, ranging from local to regional and global, but with several uncertainties. The model contains detailed descriptions of the CH4 production, oxidation, and transport controlled by several process parameters. Complexities in the underlying environmental processes, warming-driven alternative paths of meteorological phenomena, and changes in hydrological and vegetation conditions highlight the need for a calibrated and optimised version of LPJ-GUESS. In this study, we formulated the parameter calibration as a Bayesian problem, using knowledge of reasonable parameters values as priors. We then used an adaptive Metropolis–Hastings (MH)-based Markov chain Monte Carlo (MCMC) algorithm to improve predictions of CH4 emission by LPJ-GUESS and to quantify uncertainties. Application of this method on uncertain parameters allows for a greater search of their posterior distribution, leading to a more complete characterisation of the posterior distribution with a reduced risk of the sample impoverishment that can occur when using other optimisation methods. For assimilation, the analysis used flux measurement data gathered during the period from 2005 to 2014 from the Siikaneva wetlands in Southern Finland with an estimation of measurement uncertainties. The data are used to constrain the processes behind the CH4 dynamics, and the posterior covariance structures are used to explain how the parameters and the processes are related. To further support the conclusions, the CH4 flux and the other component fluxes associated with the flux are examined. The results demonstrate the robustness of MCMC methods to quantitatively assess the interrelationship between objective function choices, parameter identifiability, and data support. The experiment using real observations from Siikaneva resulted in a reduction in the root-mean-square error (RMSE), from 0.044 to 0.023 gC m−2 d−1, and a 93.89 % reduction in the cost function value. As a part of this work, knowledge about how CH4 data can constrain the parameters and processes is derived. Although the optimisation is performed based on a single site's flux data from Siikaneva, the algorithm is useful for larger-scale multi-site studies for a more robust calibration of LPJ-GUESS and similar models, and the results can highlight where model improvements are needed.

SDE-based software reliability additive models with masked data using ELS algorithm

The growing complexity of contemporary software systems, with multiple sub-modules, demands innovative modeling approaches, especially in addressing intricate failures and masked data generation. This paper proposed a stochastic differential equation (SDE)-based software reliability additive model tailored for multi-component systems dealing with masked data. However, in the presence of masked data, the challenge of parameter estimation arises due to the inherent complexity of the objective function and numerous parameters. To overcome this, we proposed the Expectation Least Square (ELS) algorithm, providing a strategic solution for the intricate task of parameter estimation with masked data. In order to verify the effectiveness of our proposed model, we conducted a comparative analysis with traditional reliability models using three actual failure data sets. The experimental results emphasize the superior performance of the proposed model and highlight the effectiveness of the ELS algorithm in accurately estimating software reliability.

Multi-objective design method for high-power microwave source devices based on preferred PIC/gNSGA-II

To solve the challenging problem of multi-objective optimization for high-power microwave sources, a specialized preference-based multi-objective optimization method, namely PIC/gNSGA-II, is proposed. Additionally, to achieve the quantitative optimization of the frequency spectrum and power of high-power microwave source devices, objective functions for both the spectrum and power are designed. PIC/gNSGA-II is employed to carry out structural optimization tests on relativistic backward wave oscillators (RBWO). The optimized results produced novel device structures that meet the specified frequency bands: in the X-band, the average output power is 845.85 MW, and the operating frequency is 9.53 GHz; in the Ku-band, the average output power is 167.25 MW, and the operating frequency is 14.73 GHz. This demonstrates that by controlling the parameters of such objective functions, the code can simultaneously optimize the spectrum and power of RBWOs. Comparing the optimization results of PIC/gNSGA-II with those of NSGA-II, PIC/gNSGA-II demonstrates better optimization efficiency and the ability to design device structures that meet various performance criteria.

New Approach to Solving Fuzzy Multiobjective Linear Fractional Optimization Problems

In this paper, an iterative approach based on the use of fuzzy parametric functions is proposed to find the best preferred optimal solution to a fuzzy multiobjective linear fractional optimization problem. From this approach, the decision-maker imposes tolerance values or termination conditions for each parametric objective function. Indeed, the fuzzy parametric values are computed iteratively, and each fuzzy fractional objective is transformed into a fuzzy non-fractional parametric function using these values of parameters. The core value of fuzzy numbers is used to transform the fuzzy multiobjective non-fractional problem into a deterministic multiobjective non-fractional problem, and the ε-constraint approach is employed to obtain a linear single objective optimization problem. Finally, by setting the value of parameter ε, the Dangtzig simplex method is used to obtain an optimal solution. Therefore, the number of solutions is equal to the number of used values, and the optimal solution is chosen according to the preference of the decision-maker. We have provided a didactic example to highlight the step of our approach and its numerical performances.

An optimization approach for assembly job shop order release based on clearing functions

As an integral part of production planning control, order release management is critical to enhance the competitiveness and production efficiency of companies. Previous literature shows limited application of optimization-based models in assembly job shops, primarily due to the intricate nature of product structures and assembly operations. Therefore, based on the idea of the allocated clearing function (ACF) model, we introduce material flow constraints and complex assembly structure constraints during the assembly stage, proposing the assembly job shop allocated clearing function (AACF) model. The performance of the AACF model and the rule-based mechanisms in terms of cost and timing measures are compared through experiments containing 6 factors and 96 scenarios. The results show that the AACF model performs better in terms of cost management, service level and order due date deviation. In addition, a sensitivity analysis of the objective function parameters is performed to confirm the robustness of the AACF model. Finally, a case application in a real assembly shop illustrates the feasibility and validity of the proposed AACF model.

Effectiveness of a cardiac rehabilitation program on biomechanical, imaging, and physiological biomarkers in elderly patients with heart failure with preserved ejection fraction (HFpEF): FUNNEL + study protocol

BackgroundPatients with heart failure with preserved ejection fraction (HFpEF) have a low functional status, which in turn is a risk factor for hospital admission and an important predictor of survival in HFpEF. HFpFE is a heterogeneous syndrome and recent studies have suggested an important role for careful, pathophysiological-based phenotyping to improve patient characterization. Cardiac rehabilitation has proven to be a useful tool in the framework of secondary prevention in patients with HFpEF. Facilitating decision-making and implementing cardiac rehabilitation programs is a challenge in public health systems for HFpEF management. The FUNNEL + study proposes to evaluate the efficacy of an exercise and education-based cardiac rehabilitation program on biomechanical, physiological, and imaging biomarkers in patients with HFpEF.MethodsA randomised crossover clinical trial is presented among people older than 70 years with a diagnosis of HFpEF. The experimental group will receive a cardiac rehabilitation intervention for 12 weeks. Participants in the control group will receive one educational session per week for 12 weeks on HFpEF complications, functional decline, and healthy lifestyle habits. VO2peak is the primary outcome. Biomechanical, imaging and physiological biomarkers will be assessed as secondary outcomes. Outcomes will be assessed at baseline, 12 weeks, and 24 weeks.DiscussionIdentifying objective functional parameters indicative of HFpEF and the subsequent development of functional level stratification based on functional impairment ("biomechanical phenotypes") may help clinicians identify cardiac rehabilitation responders and non-responders and make future clinical decisions. In this way, future pharmacological and non-pharmacological interventions, such as exercise, could be improved and tailored to improve quality of life and prognosis and reducing patients' hospital readmissions, thereby reducing healthcare costs.Trial registrationNCT05393362 (Clinicaltrials.gov).

The Effect of Different Gas Water Ratio on Recovery Factor and CO2 Storage Capacity in Water Alternating Gas Injection. A Case Study: “V” Field Development, North Sea

CO2 injection is one of the Enhanced Oil Recovery (EOR) methods. In this study Water alternating gas (WAG) CO2 injection method was used to obain the maximum sweep efficiency. The purpose of this study was to analyze the effect of gas water ratio (GWR) value on recovery and CO2 storage capacity, and to analyze the best scenario in term of technical objective.&#x0D; This study was carried out using E300 reservoir simulator. The increase in recovery and CO2 storage were observed throught the parameters of recovery factor and CO2 storage capacity, while the determination of the best scenario in term of technical objective was observed using the parameters of objective function. This study was carried out in 3 different scenarios, which were the injection of 100% CO2, 60% CO2and 40% water, and 40% CO2 and 60% water&#x0D; Based on the observation, it was founded that third scenario with the GWR of 40:60 resulted the highest cumulative production and recovery factor with the value reaching 14.1 milliom m3 and 67.4%. Meanwhile the second scenario with the GWR of 60:40 has the highest CO2 storage capacity of 3 billion Sm3 CO2. The second scenario has the best performance in term of technical objective with the value of objective function reaching 0.45.

A study of distributionally robust mixed-integer programming with Wasserstein metric: on the value of incomplete data

This study addresses a class of linear mixed-integer programming (MILP) problems that involve uncertainty in the objective function parameters. The parameters are assumed to form a random vector, whose probability distribution can only be observed through a finite training data set. Unlike most of the related studies in the literature, we also consider uncertainty in the underlying data set. The data uncertainty is described by a set of linear constraints for each random sample, and the uncertainty in the distribution (for a fixed realization of data) is defined using a type-1 Wasserstein ball centered at the empirical distribution of the data. The overall problem is formulated as a three-level distributionally robust optimization (DRO) problem. First, we prove that the three-level problem admits a single-level MILP reformulation, if the class of loss functions is restricted to biaffine functions. Secondly, it turns out that for several particular forms of data uncertainty, the outlined problem can be solved reasonably fast by leveraging the nominal MILP problem. Finally, we conduct a computational study, where the out-of-sample performance of our model and computational complexity of the proposed MILP reformulation are explored numerically for several application domains.

Lifestyle-integrated functional exercise for fall prevention : How and why do walking characteristics change?

The lifestyle-integrated functional exercise (LiFE) program has been shown to increase physical activity. It remains unclear, however, how these changes translate into long vs. short walking episodes. The aim of this work was to investigate changes in short vs. long walking episodes between baseline and 6‑month follow-up and to determine which factors are associated with these changes. This was a two-arm randomized noninferiority study with 309 older adults (mean age 78.7 ± 0.3years; 73.5% female) at risk of falling who exercised either in agroup (gLiFE; n = 153) or individually (LiFE; n = 156). Walking episodes were measured using activPAL 4micro sensors: a distinction was made between walking episodes < 10s, < 20s, and > 60 s. Changes in walking episodes between baseline and 6‑month follow-up were analyzed, including calculation of effect sizes (Cohen'sd). Determinants of changes in the walking episodes were analyzed using multiple regression. The walking episodes < 10s and < 20 s showed a significant increase in both intervention groups but not for > 60 s. The overall daily walking duration and average steps per day had an influence on changes in the walking episodes between baseline and 6months. Parameters of objective and subjective function explained avery small but significant amount of the variance. The LiFE program seems to work on abehavioral rather than on afunctional level. By accumulating short walking episodes, large gains in physical activity can potentially be achieved. This can be of health-promoting benefit especially for persons living in institutional settings or for those who are cautious or even anxious to undertake longer walking episodes (e.g., outdoors).

A Real-World Benchmark Problem for Global Optimization

Abstract The paper presents the statement of the problem of dynamical system „crane-load” optimal control. The acceleration period is under consideration and control must meet the minimum duration condition as well as load oscillations elimination. The objective function, which ensures the final condition satisfaction, is developed and analyzed in terms of its topology features. It includes three arguments and their searching is the essence of the benchmark problem. Two variants of the problem are proposed with varied objective function parameters. Twelve agent-based optimization algorithms have been applied to find solutions to a bunch of problems. A brief analysis of the performance of the algorithms reveals their weaknesses and advantages. Thus, the proposed real-world problem may be exploited to estimate the optimization algorithms’ search performance.

Robust scheduling of EMU first-level maintenance in a stub-end depot under stochastic uncertainties

Frequently occurring and unavoidable perturbations in railway systems cause a reduction in performance and even the infeasibility of the original schedule. In addition, existing related studies assume that the maintenance routes are fixed in a deterministic situation. Therefore, it is necessary to focus on robust scheduling of electric multiple units first-level maintenance with flexible maintenance routes to defend against stochastic uncertainties. Firstly, a mixed-integer linear programming model with uncertain parameters in objective functions and constraints is built for the first time. Multiple constraints are formulated to consider flexible maintenance routes, train shunting conflicts, and track occupation conflicts in a stub-end depot. A robust optimization approach is adopted to obtain a deterministic robust counterpart model with uncertainties in processing/arrival/departure times. In this model, uncertainty and reliability levels are introduced to describe and quantify the disturbance degree of processing/arrival/departure times and the allowable violation degree of resource constraints respectively. Moreover, an adaptive iterative local search is proposed by embedding heuristic rules for the initialization. The proposed algorithm includes problem-specific neighborhood structures to improve the evolutionary ability, a variable neighborhood descent method to guide and drive the search toward promising areas of the search space, and an adaptive perturbation mechanism to enable the algorithm to jump out of local optimum. Numerical results from China’s railway system validate the proposed model and quantitatively demonstrate the merit of the proposed algorithm. Further analysis shows that our approach can achieve an appropriate trade-off between robustness and efficiency for various uncertainty and reliability levels.

RESEARCH OF COMPUTATIONAL MATHEMATICAL MODELS FOR TECHNICAL SYSTEMS

In the theory of analysis and synthesis of technical systems, mathematical modelling and optimization of multilayer systems containing sources of physical fields occupy an important place. This is due to the fact that their state is described by means of boundary value problems with multidimensional differential equations. To solve the boundary value problems and implement the process of optimizing the technical parameters of the modelled systems, it is necessary to conduct interdisciplinary studies of computational and applied optimization mathematical models. Fulfilment of the conditions for the existence of a single solution to boundary value problems by default is possible only when the object of study is a single-layer material under the action of load sources. If it is necessary to calculate and optimize the technical parameters of a multilayer material subjected to load sources, then it is impossible to immediately guarantee the correctness of the calculated and applied optimization mathematical models, since it is necessary to obtain the conditions for the existence and uniqueness of solutions to boundary value problems with systems of differential equations. Maximizing the technical parameters of load sources and averaging the characteristics of material layers will lead to approximate values of the objective function and technical parameters of the modelled system, which leads to irrational consumption of energy and heat resources and uncontrolled losses, and useless losses of the test material in the technological process. The article presents the conditions for the correctness of multipoint boundary value problems with multidimensional differential equations describing the state of a multilayer material under thermal action. It is advisable to use these studies to substantiate the correctness of other technical and biotechnological systems, which will increase the accuracy of the implementation of applied optimization problems of economic and mathematical modelling.

Routing and wavelength assignment with protection: A quadratic unconstrained binary optimization approach enabled by Digital Annealer technology

Routing and wavelength assignment with protection is an important problem in telecommunications. Given an optical network and incoming connection requests, a commonly studied variant of the problem aims to grant a maximum number of requests by assigning lightpaths with minimum network resource usage, while ensuring the provided services remain functional in the case of a single-link failure through dedicated protection paths. We consider a version where alternative lightpaths for requests are assumed to be given as a precomputed set and show that it is NP-hard. We formulate the problem as an Integer Programming (IP) model and also use it as a foundation to develop a Quadratic Unconstrained Binary Optimization (QUBO) model. We present necessary and sufficient conditions on objective function parameters to prioritize request granting objective over wavelength-link usage for both models, and a sufficient condition ensuring the exactness of the QUBO model. Moreover, we implement a problem-specific branch-and-cut algorithm for the IP model and employ a new quantum-inspired technology, Digital Annealer (DA), for the QUBO model. We conduct computational experiments on a large suite of nontrivial instances to assess the efficiency and efficacy of all of these approaches as well as two problem-specific heuristics. Although the objective penalty coefficient values that guarantee the exactness of the QUBO model were outside the acceptable range for DA, it always yielded feasible solutions even with smaller values in practice. The results show that the emerging technology DA outperforms the considered techniques coupled with GUROBI in finding mostly significantly better or as good solutions in two minutes compared to two-hour run time, whereas problem-specific heuristics fail to be competitive.

A Primal-Dual Forward-Backward Splitting Algorithm for Distributed Convex Optimization

Motivated by modern large-scale information processing problems in engineering, this paper concentrates on studying distributed constrained convex optimization problems over a connected undirected network. The problem involves a sum of a differentiable convex function with Lipschitz continuous gradient and two non-smooth convex functions with a linear operator. To solve such a problem, we propose a novel distributed primal-dual forward-backward splitting algorithm, called D-PDFBS. Each agent locally computes the Lipschitz continuous gradient and two proximal operators, and exchanges information with its neighbors. D-PDFBS adopts non-identical stepsizes, and we reveal the relationship between selection of stepsizes and parameters of objective functions. The simulation results verify the feasibility of D-PDFBS and the correctness of theoretical findings.