Optimal Objective Function Value Research Articles

Extending oscars-ii to generally constrained global optimization

AbstractA derivative free method for generally constrained global optimization is described. A non-smooth merit function with one parameter is used. When this parameter equals the optimal objective function value $$f^*$$ f ∗ , the merit function becomes an exact penalty function. The method estimates $$f^*$$ f ∗ , avoiding the need for it to be supplied. The method randomly samples the region satisfying the simple bounds from time to time, ensuring convergence almost surely. Other samples are drawn randomly from smaller regions considered promising. Numerical testing is done using a variety of bound constrained problems and generally constrained problems from the G-suite and elsewhere. Results show the method is competitive in practice. They also show that the method performs better when it estimates the optimal objective function value than when the actual value is used.

Solving the Green Economic Load Dispatch by Applying the Novel Meta-heuristic Algorithm

This study focuses on solving the green economic load dispatch problem by considering the presence of green energy sources, including wind energy and solar power plants. The main objective function of the whole study is to minimize the total fuel cost (TFC) of all the thermal generating sources (TGSs) in the system. Moreover, the multiple selection of all TGSs is also evaluated. Fire hawk optimization (FHO) and the Zebra optimization algorithm (ZOA) are applied to solve the problem of achieving the best TFC value and satisfying all the constraints involved. The results indicated that ZOA can achieve a better optimal solution compared to FHO. Particularly, the results obtained by ZOA are completely superior to FHO in all comparison criteria at two load demand levels, such as Best TFC value (Best.Cost), Average TFC value (Aver.Cost), and Maximum TFC value (Max.Cost). On top of that, ZOA is the only algorithm of two applied ones providing the fast convergence capability to the optimal value of the main objective functions in two cases of load demand levels. Therefore, ZOA is an efficient search method to deal with such GELD problems.

A data-driven digital transformation approach for reverse logistics optimization in a medical waste management system

COVID-19's aftereffects have had a significant impact on our daily lives. The recent pandemic caused by the new coronavirus epidemic has increased the production of infectious medical waste (IMW) and demand for medical care and protective equipment. Although national and local initiatives are primarily concerned with saving lives and bolstering local economies, hazardous waste management is essential for reducing long-term human and environmental health threats. In this situation, establishing a dependable and efficient reverse logistics network of IMW can prevent the spread of viruses. Few studies have been conducted on this topic and those that have rarely considered how to operate a network of multiple medical waste generation centres (MWGCs) cost-effectively and risk-averse. This study proposes a framework for reducing the accumulation of IMW products using reverse logistics in the context of medical waste management. The optimal values of the multiple objective functions were determined using a multi-objective optimization model. Our proposed framework considers four objective functions and their respective constraints while using data-driven digital transformation in reverse logistics energy optimization for managing single-use medical waste.

A new cutting plane method for lexicographic multi-objective integer linear programming

This work presents a new cutting plane method for lexicographic multi-objective integer linear programming (LMOILP). The method uses Grossone Methodology to reformulate a LMOILP problem into one having a single scalar objective function involving Grossone, as done in Cococcioni et al. (2018) (but in that case in the absence of the integer constraints). The problem, without the integer constraints, is solved using the GrossSimplex algorithm presented in Cococcioni et al. (2018) to find a candidate optimal solution. Here a novel cutting plane is introduced, named Gross-based Objective Function Cutting Plane whenever the optimal value of the Gross-scalar objective function is Gross-fractional. When it happens to be not Gross-fractional, cutting planes are generated using the Fractional Cutting Plane, derived from fractional components of the optimal solution. Moreover, by combining them, we proposed an algorithm that we called Gross-based Cutting Plane (GCP) method. It has been proved that it finds the optimal solution of a LMOILP problem and terminates after a finite number of iterations. To speed-up the GCP, at each iteration subsequent the first one, we re-use the optimal basis of the last continuous relaxation, by running the GrossDualSimplex algorithm. This is the well-known warm-start technique, which, however, needs specific attention due to the need to solve a linear problem having a right-hand side involving Grossone-based numbers. In the experimental part, we show the efficacy of the proposed approach.

Designing soil contamination monitoring network in petroleum refineries by XGBoost weighting and geostatistical facility allocation methods.

Petroleum refineries are deemed strategic industrial sectors that can release toxic materials to the environment and cause potential hazards. In this regard, designing and installation of soil contamination monitoring networks at petroleum refineries is a necessity. In this research, we designed an optimal monitoring network with maximum coverage and minimum number of monitoring boreholes. The main regarded parameters are the groundwater contamination history, the location of effective structures, the location of flare stacks and the soil texture. In addition, the soil contamination was calculated based on previous contamination of the soil at the sampling points by the Entropy Weighting Model. It was employed with other parameters to estimate the soil contamination across the site. The Machine Learning method of XGBoost was implemented for estimating and assigning priority for every point of the site. To achieve the optimal network in the optimization program, four parameters were regarded including (a) the optimal value of the optimization program's objective function, (b) the number of Advance Zero-half cuts of the Cut Generation algorithm, (c) the consumed time, and (d) the optimal boreholes number of the network corresponding with different effective contamination detection radius. The network was designed by generalized Maximal Covering Location Problem and for optimizing it, the advantages of Mixed-Integer Linear Programming method were used. To evaluate the applicability of the method, it has been developed and implemented in a refinery in the south of Iran. 92.84% of XGBoost estimation accuracy, the optimal number of 113 and the effective contamination detection radius of 160 m were obtained for boreholes of the network. To investigate the efficiency of the model, a new Regret function has been defined. Furthermore, sensitivity analysis of the parameters and feature importance analysis of XGBoost both showed that the main parameter of the model was the location of effective structures.

Comparative analysis of supercritical CO2–ORC combined cycle for gas turbine waste heat recovery based on multi-objective optimization

To efficiently recover the waste heat of the gas turbine, this study introduces six innovative types of compound combined cycles, and proposes a multidimensional optimization method for the optimal cycle. In the combined cycle, the supercritical carbon dioxide cycle is used in the top cycle and the organic Rankine cycle is used in the bottom cycle. The working medium used in the organic Rankine cycle is the innovative mixture cyclopentane/R365mfc. Firstly, a parametric study is carried out for the proposed combined cycle to investigate the effects of system operating parameters on exergy efficiency, area per unit power output (APR) of the heat exchanger, and the levelized energy cost (LEC). The results show that the optimal values of objective function correspond to different systematic operating parameters. Secondly, the multi-objective optimization based on the genetic algorithm is used to obtain the optimal systematic parameters, and the six proposed composite combined cycles are optimized respectively. The comparison results show that the composite supercritical carbon dioxide regenerative cycle-organic Rankine simple cycle has the optimal performance parameters, and its exergy efficiency, APR and LEC are 55.68 %, 0.115 m2/kW and 4.23 cent/(kW·h), respectively. The layout of the composite cycle is that the supercritical carbon dioxide regenerative cycle and the organic Rankine simple cycle are used to recover the high temperature and low temperature of the gas turbine exhaust gas, while the organic Rankine simple cycle recovers the cooling heat of the supercritical carbon dioxide regenerative cycle. Finally, the superiority relative of the proposed combined system to the other cycles is also verified. This study has determined that the proposed combined system is appropriate for the waste heat recovery of gas turbines, with the advantages of deep utilization of waste heat, high efficiency, high compactness, and low cost.

Exact solution approaches for the discrete α-neighbor p-center problem.

The discrete -neighbor -center problem (d--CP) is an emerging variant of the classical -center problem which recently got attention in literature. In this problem, we are given a discrete set of points and we need to locate facilities on these points in such a way that the maximum distance between each point where no facility is located and its -closest facility is minimized. The only existing algorithms in literature for solving the d--CP are approximation algorithms and two recently proposed heuristics. In this work, we present two integer programming formulations for the d--CP, together with lifting of inequalities, valid inequalities, inequalities that do not change the optimal objective function value and variable fixing procedures. We provide theoretical results on the strength of the formulations and convergence results for the lower bounds obtained after applying the lifting procedures or the variable fixing procedures in an iterative fashion. Based on our formulations and theoretical results, we develop branch-and-cut (B&C) algorithms, which are further enhanced with a starting heuristic and a primal heuristic. We evaluate the effectiveness of our B&Calgorithms using instances from literature. Our algorithms are able to solve 116 out of 194 instances from literature to proven optimality, with a runtime of under a minute for most of them. By doing so, we also provide improved solution values for 116 instances.

Genetic algorithm introducing the estimation of optimal objective function values in subproblems by pre-training

Genetic algorithm introducing the estimation of optimal objective function values in subproblems by pre-training

Micro-damage analysis and numerical simulation of composite solid propellant based on in situ tensile test

Abstract In order to quantitatively analyze the mesoscopic damage process of hydroxyl-terminated polybutadiene composite solid propellant under external load, periodic boundary conditions were applied to the representative volume element model based on sample composition and morphology, the mixed matrix containing aluminum powder was homogenized, and the hyperelastic matrix damage and bilinear/exponential particle–matrix interface cohesive model with initial damage were compiled through the secondary development of Abaqus. At the same time, a data interaction platform was constructed by means of Python and MATLAB, matrix and cohesion parameters were inverted according to the optimization algorithm and experimental data, and the whole process of propellant damage and fracture was simulated from the mesoscopic perspective. The results show that combining the adaptive particle swarm optimization algorithm and the Hooke–Jeeves algorithm can achieve the global optimal parameter inversion in 102 calculations, compared with the single local search algorithm, which can cut about 11% of the objective function values. Considering the matrix damage and the exponential cohesion model with initial damage, the optimal objective function value is 0.01635, which can more accurately simulate the propellant damage and fracture process compared with 0.02136 of a bilinear cohesion model.

Macro and micro damage analysis and parameter inversion of HTPB adhesive Interface based on DIC and FEMU

ABSTRACT In order to realize the quantitative analysis of the structural integrity and damage evolution of hydroxyl-terminated polybutadiene (HTPB) composite solid propellant under external load, the loading failure experiments were carried out on the macro rectangular specimen and the micro specimen, and the numerical analysis of the strain evolution process in the region of interest (ROI) of the specimen was carried out using digital image correlation (DIC). At the same time, with the help of finite element model updating (FEMU) method, the mechanical and cohesion parameters of the specimen were inversed using the combination of adaptive particle swarm optimization (APSO), back propagation (BP) and Hooke-Jeeves algorithm, and the simulation of the whole process of propellant damage and fracture was realized from the microscopic point of view. The results show that inhibiting the debonding of propellant/liner interface is the key to maintain the structural integrity. It starts with the damage and fracture of the propellant side. A scanning electron microscope (SEM) in-situ dynamic tensile test shows that the initial damage occurs at the strain of 27.368%, and the through-type crack propagates along the interface when the strain reaches 43.276%. In addition, the use of combinatorial optimization algorithm can realize the global optimal inversion of 16 parameters divided into three types in 100 complete calculations, reduce the optimal objective function value to 0.0251, and assist the finite element calculation to realize the quantitative analysis and accurate simulation of the experimental process.

Power Flow Optimization Strategy of Distribution Network with Source and Load Storage Considering Period Clustering

The large-scale grid connection of new energy will affect the optimization of power flow. In order to solve this problem, this paper proposes a power flow optimization strategy model of a distribution network with non-fixed weighting factors of source, load and storage. The objective function is the lowest cost, the smallest voltage deviation and the smallest power loss, and many constraints, such as power flow constraint, climbing constraint and energy storage operation constraint, are also considered. Firstly, the equivalent load curve is obtained by superimposing the output of wind and solar turbines with the initial load, and the best k value is obtained by the elbow rule. The k-means algorithm is used to cluster the equivalent load curve in different periods, and then the fuzzy comprehensive evaluation method is used to determine the weighting factor of the optimization model in each period. Then, the particle swarm optimization algorithm is used to solve the multi-objective power flow optimization model, and the optimal strategy and objective function values of each unit output in the operation period are obtained. Finally, IEEE33 is used as an example to verify the effectiveness of the proposed model through two cases: a fixed proportion method to determine the weighting factor, and this method to determine the weighting factor. The proposed method can improve the economy and reliability of distribution networks.

Approximate Condorcet Partitioning: Solving large-scale rank aggregation problems

Rank aggregation has ubiquitous applications in computer science, operations research, and various other fields. Most attention on this problem has focused on an NP-hard variant known as Kemeny aggregation, for which solution approaches with provable guarantees that can handle difficult high-dimensional instances remain elusive. This work introduces exact and approximate methodologies inspired by the social choice foundations of the problem, namely the Condorcet Criterion. We formalize the concept of the finest-Condorcet partition for rankings that may contain ties and specify its required conditions. We prove that this partition is unique and devise an efficient algorithm to obtain it. To deal with instances where it does not yield many subsets, we propose Approximate Condorcet Partitioning (ACP), with which larger subsets can be further broken down and more easily solved. ACP is a scalable solution technique capable of handling large instances while still providing provable guarantees. Although ACP approximation factors are instance-specific, their values were lower than those offered by all known constant-factor approximation schemes — inexact algorithms whose resulting objective values are guaranteed to be within a specified fixed percent of the optimal objective value — for all 113 instances tested herein (containing up to 2,820 items). What is more, ACP obtained solutions that deviated by at most two percent from the optimal objective function values for a large majority of these instances.

Research on Wireless Sensor Network Localization based on An Improved Whale Optimization Algorithm

<p>DV-HOP algorithm for wireless sensor network (WSN) has the disadvantage of large node positioning error and low accuracy. Firstly, the node localization model is elaborated, secondly, Fuch chaotic opposition learning is used in the initialization of the whale optimization algorithm population to improve the initial position diversity, an adaptive strategy is used for the parameters in the encircling predation behavior to avoid the algorithm falling into local optimum prematurely, Gaussian perturbation is used to update the individual positions during the iterative search to improve the global search capability, and finally IWOA is solved for the optimal value of the node localization objective function. The performance of IWOA algorithm is verified in simulation experiments, and the solution accuracy and solution quality are improved in different degrees. The IWOA algorithm demonstrates good localization results in terms of comparative data results of node localization unknown nodes, reference nodes, node density, communication radius aspects and area of the region.</p> <p> </p>

Supply chain management and optimization in transportation logistics

Supply chain management and optimization in transportation logistics

Fixed-Time Distributed Optimization for Multi-Agent Systems with Input Delays and External Disturbances

This study concentrates on a fixed-time distributed optimization problem for multi-agent systems (MASs) with input delay and external disturbances. First, by adopting the Artstein model reduction technique, the time-delay system is first transformed into a delay-free one, and external disturbances are then effectively eliminated by using an integral sliding mode control strategy. Second, a new centralized optimization mechanism is developed that allows all agents to reach the same state in a fixed time and then converge to the optimal value of the global objective function. Meanwhile, the optimization problem is extended to switching topologies. Moreover, as the gradient information of the global objective function is difficult to obtain in advance, we construct a decentralized optimization protocol that enables all agents to acquire the same state in a certain amount of time while also optimizing the global optimization problem. Finally, two numerical simulations are presented to validate the effectiveness and reliability of the developed control strategy.

A Precise Stator Ground Fault Location Method for Large Generators Based on Potential Analysis of Slot Conductors

The stator ground fault location of large generators can guide rapid maintenance. In this paper, a location criterion without fault transition resistance is constructed by using the fundamental potential and the third harmonic potential of the faulty winding simultaneously. The above potentials of the faulty winding are corresponding to the fault position. To precisely locate the grounding fault, it is necessary to clarify the analytical relationship between the faulty winding potential and the fault position. However, the existing methods often take the coil potential as the unit to analyze the winding potential, which has theoretical errors for the generators with short-pitch winding. Aiming at this problem, a more precise analysis method for winding potential is established by taking the slot conductor potential as the unit. To solve the location criterion, the optimization model for each slot conductor of the faulty phase is constructed. The slot conductor with the smallest optimal objective function value is judged as the faulty slot conductor, and the corresponding decision variable is judged as the fault position. Simulation and experiments verify the effectiveness of the proposed method, which can still meet the needs of engineering applications under multiple adverse conditions.

Improving real-time energy decision-making model with an actor-critic agent in modern microgrids with energy storage devices

The hereby study combines a reinforcement learning machine and a myopic optimization model to improve the real-time energy decisions in microgrids with renewable sources and energy storage devices. The reinforcement learning-based agent is built as an actor-critic agent making the aggregated near-optimal charging/discharging energy decisions of the microgrid energy storage devices from a discrete action space relying on a reward related to the microgrid online optimal objective function value. The next step time energy levels of storage devices are then computed and provided to the myopic optimization-based decision-making model as parameters which optimally find the incurred power flow within the microgrid minimizing the real-time microgrid energy cost. The real-time measurement of stochastic parameters of the microgrid coupled with the current energy levels of electrical and heat storage are input to the artificially intelligent machine as observations states. The actor-critic agent approximators are modeled as deep neural networks optimized using the Adam gradient descent algorithm with a gradient threshold. Although the proposed model with a 2-kWh increment of the charging/discharging energy training is time-consuming, it has been able at 100% to optimally make microgrid energy decisions and improve online energy decisions by 90.98% compared to the myopic model alone.

BUILDING MATHEMATICS MODELING FOR SOLVED TRANSPORTATION PROBLEMS AND OPTIMIZING WITH MORE FOR FEWER ALGORITHMS IN THE BUSINESS COMMUNITY

Mathematical modeling supports the development of the business world and the industrial world, especially in transportation (Widana, 2020). Many emerging algorithms are combined with the adoption of changes in the form of real problems modeled into mathematical problems. The modeling aims to optimize to produce the most optimal objective function value based on the formed constraints. Optimization of the mathematical model can be assisted by several optimization algorithms, such as the More for Less Algorithm. The algorithm, as a form of looping, is based on the constraint function with the specified parameters until it reaches the final objective function, namely optimization related to time and cost(Muftikhali et al., 2018). In general, it is hoped that supply and demand will be balanced in transportation. However, in reality, often in field conditions, mixed transportation problems result in non-optimal costs. The study results show that the More for Less Algorithm can provide the most optimal solution according to the allocation of factory requests to shops with the minimum cost. The dual variable matrix index is positive, so the solution to the transportation problem with mixed constraints is called optimal. The solutions obtained in the transportation case study with mixed constraint functions in the field of the Amarta Bakery industry community business are as follows:with a total cost of 580 (in units of money). Combinations - factory-to-store combinations for companies are interpreted as first factory at the first store with an allocation of 90 product units, first factory at the second shop with an allocation of 110 product units, second factory at the second shop with an allocation of 0 product units, factory the second factory at the third store with an allocation of 70 units of product, and the third factory at the third store with an allocation of 0 units of product. The number zero means that to carry out efficiency and optimization according to mixed constraints, it is necessary to make conditions where factories do not distribute to shops.

A sampling-based multi-objective iterative robust optimization method for Bandwidth Packing Problem

This paper proposes a new paradigm for solving robust optimization problems using sampling within a multi-objective framework to solve the Bandwidth Packing Problem, the Sampling-based Robust Optimization Method (SIROM). The key feature of this new approach is that it performs robust optimization without having to specify a priori an uncertainty budget. The new method thus provides the decision-maker a Pareto frontier composed by the best solutions (objective function value versus uncertainty protection) found by exploring the topology of the uncertain parameter set. A general framework based on unsupervised learning is built for the method, which can be used to find solutions for linear, non-linear, and integer programming problems under parametric uncertainty. The general idea is to sample possible realizations of a given uncertain parameter vector and solve each problem associated with all those parameters. After that, we cluster the realizations based on optimal constraint and objective function values. All “similar” cases are grouped together to form problem sets with few “representative” realizations that we can solve and, in analyzing the quality of the optimal solution, use to compose a Pareto frontier. The framework is applied to solve the Bandwidth Packing Problem under uncertain demand and we compare results to a methodology based on Bertsimas and Sim robust optimization approach. The results demonstrate that the proposed method performs better than previously existing ones. The code and instances used to perform the computational experiment are available in https://github.com/butkeraites/sirom_bpp.

Study of solution diversity in multi-objective optimization of storage ring lattice

Evolutionary algorithms, including multi-objective genetic algorithm (MOGA) and multi-objective particle swarm optimization (MOPSO), have been widely used for storage ring lattice designs, showing good performance in searching the optimal objective function values (i.e. Pareto front). Mathematically, different variable values can have the same objective function value, which is called many-to-one mapping. Different from focusing on the convergence of Pareto front, in this paper we study the diversity of variables in the optimization of storage ring lattice and make a comparison between MOGA and MOPSO. Two different lattices are taken as study examples. The study shows that the lattice solutions with almost the same objectives and different variables can show difference in some storage ring properties, which is beneficial for lattice selection. Besides, compared to MOPSO, MOGA gives a wider distribution of optimal lattice solutions in the variable space, though both algorithms can obtain almost the same Pareto front.