Optimal Objective Function Value Research Articles

Optimal Scheduling of Battery Energy Storage System Operations under Load Uncertainty

This paper investigates the optimal scheduling of battery energy storage system operations considering energy load uncertainty. We develop a novel two-stage distributionally robust optimization model to determine an optimal battery usage schedule that minimizes the worst-case energy costs considering peak load costs. The model leverages deep-learning based probabilistic forecasting in the construction of the ambiguity set. Specifically, we develop a Deep Autoregressive Recurrent Networks model to generate a probabilistic forecast of energy loads over a time horizon. The output of the forecasting model is then used to construct a marginal-moment ambiguity set for the distributionally robust optimization model. To solve the proposed model, we establish a closed-form characterization of the optimal second-stage objective function value. Leveraging this closed-form expression and using second-order conic duality, we derive an exact single-level mixed integer second-order conic reformulation of the problem. Extensive computational experiments, conducted on a real dataset, demonstrate the value of our proposed model and the resulting battery schedule. The results demonstrate that the proposed model outperforms several benchmarks, including two-stage stochastic programming. Furthermore, the results show that the accuracy of the load forecast significantly impacts the effectiveness of the optimal battery schedule in eliminating peak loads by achieving up to 18% reduction in the maximum energy load.

Label Deconvolution for Node Representation Learning on Large-scale Attributed Graphs against Learning Bias.

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

Parallel fractional dominance MOEAs for feature subset selection in big data

In this paper, we solve the feature subset selection (FSS) problem with three objective functions namely, cardinality, area under receiver operating characteristic curve (AUC) and Matthews correlation coefficient (MCC) using novel multi-objective evolutionary algorithms (MOEAs). MOEAs often encounter poor convergence due to the increase in non-dominated solutions and getting entrapped in the local optima. This situation worsens when dealing with large, voluminous big and high-dimensional datasets. To address these challenges, we propose parallel, fractional dominance-based MOEAs for FSS under Spark. Further, to improve the exploitation of MOEAs, we introduce a novel batch opposition-based learning (BOP) along with a cardinality constraint on the opposite solution. Accordingly, we propose two variants, namely, BOP1 and BOP2. In BOP1, a single neighbour is randomly chosen in the opposite solution space, whereas in BOP2, a group of randomly chosen neighbours in the opposite solution space. In either case, the opposite solutions are evaluated to improve the exploitation capability of the underlying MOEAs. We observe that in terms of mean optimal objective function values and across all datasets, the proposed BOP2 variant of parallel fractional dominance-based algorithms emerges as the top performer in obtaining efficient solutions. Further, we introduce a novel metric, namely the ratio of hypervolume (HV) and inverted generated distance (IGD), HV/IGD, that combines both diversity and convergence. With respect to the mean HV/IGD computed over 20 runs and Formula 1 racing, the BOP1 variants of fractional dominance-based MOEAs outperformed other algorithms.

Multi-objective Optimization-Based Algorithm for Selecting the Optimal Path of Rural Multi-temperature Zone Cold Chain Dynamic Logistics Intermodal Transportation

The road network in rural areas is complex and the infrastructure is relatively backward. The multi-temperature zone cold chain logistics involves agricultural products with different temperature requirements, which requires considering the transportation cost, carbon emission cost, refrigeration cost, and time cost of different temperature zones during path planning, thereby increasing the difficulty of path planning. Therefore, a multi-objective optimization-based algorithm for selecting the optimal path of rural multi-temperature zone cold chain dynamic logistics intermodal transportation is proposed. Based on the analysis of the multi-temperature cold chain collection and distribution model based on multimodal transportation, a multi-objective optimization model is constructed. This model aims to minimize transportation costs, carbon emission costs, refrigeration costs, time costs, and maximize logistics quality, while satisfying constraints such as transfer schedule times, the number of transport mode conversions, transport mode selection, and time continuity. To solve this model, an improved NSGA-II algorithm is adopted, which combines an improved mutation operator, congestion distance calculation, and the C-W saving algorithm to achieve the optimal transport path solution. Additionally, ArcGIS software is used to implement the shortest path planning based on real road networks. The experimental results show that by selecting the road-rail combined transport mode and adopting the D1–D6–D10 transport path, it is possible to transport fresh agricultural products from location A to the distribution center at location B, with the lowest Pareto fitness value. Furthermore, the algorithm's effectiveness is further verified by completing the end-of-life fresh agricultural product distribution task with four multi-temperature refrigerated vehicles. The study also finds that extending or shortening the latest service time window for customers, although it leads to a decrease or increase in the optimal value of the algorithm's objective function, has little impact on the average distribution time and transport vehicles. These findings provide new theoretical and practical guidance for the path selection of multimodal transportation in multi-temperature cold chain logistics, with significant theoretical and application value.

Zero gradient sum algorithm of arbitrary initial value with constraints and communication delay based on directed graph

The distributed convex optimisation issue with inequality constraints and box constraints on the directed communication topology is examined in this paper. In the case of the communication delay between agents, we propose a piecewise zero-gradient-sum triggered control algorithm that allows arbitrary initial values. Using the log-barrier penalty method, we only need to study an unconstrained approximation problem of the original problem. Firstly, each agent's state converges to the optimal value of the related local objective function in a fixed time. Simultaneously, the upper bound of fixed time in this paper is smaller than some existing results. Then, in the case of communication delay, time-triggered and event-triggered methods with non-uniform sampling interval are proposed in this paper, which make the communication cost lower and the application broader. Using the Lyapunov function method, the sufficient conditions for each agent's state to converge to the optimal point are given, and the Zeno behaviour is excluded. Finally, to confirm the algorithm's effectiveness, we provide two numerical examples and one machine learning example as demonstrations.

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.

Optimization of coal chemical process parameters and energy saving and emission reduction based on genetic algorithm

Abstract Coal is an important energy resource. How to utilize it efficiently and cleanly is a hot topic nowadays. In the coal gasification process, the process parameter indexes have a significant impact, and the uncertainty of these factors will lead to a decrease in the quality of gas production. Therefore, in this paper, the uncertainty of process parameters is considered, and Aspen plus software with the Monte Carlo method is used to simulate the coal chemical process and measure the effect of uncertainty of process parameters on the yield of the coal gasification process. On this basis, in addition, coal flow rate, pressure, and steam/oxygen are taken as the process parameters and optimized, and three sets of multi-objective optimization models are established with gas calorific value, gasification efficiency, and gas yield, respectively, which are solved by improved multi-objective genetic algorithm based on crossover operator and variational operator to obtain Pareto curves, so as to adjust the parameter values according to the actual needs. The results show that the fluctuation of pressure has a big influence on the carbon conversion rate and gasification efficiency, and the carbon conversion rate and gasification efficiency can be made more stable by controlling the change of pressure. The improved genetic algorithm NSGA-II can reach the actual optimal objective function value in both high and low iteration times, providing the required parameters for the decision maker, and the optimal program results in TEC of 402,758 kW and CO2 content of 0.12%, which is effective in energy saving and emission reduction.

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