Single-objective Optimization Problem Research Articles

Outer approximation algorithms for convex vector optimization problems

In this study, we present a general framework of outer approximation algorithms to solve convex vector optimization problems, in which the Pascoletti-Serafini (PS) scalarization is solved iteratively. This scalarization finds the minimum ‘distance’ from a reference point, which is usually taken as a vertex of the current outer approximation, to the upper image through a given direction. We propose efficient methods to select the parameters (the reference point and direction vector) of the PS scalarization and analyse the effects of these on the overall performance of the algorithm. Different from the existing vertex selection rules from the literature, the proposed methods do not require solving additional single-objective optimization problems. Using some test problems, we conduct an extensive computational study where three different measures are set as the stopping criteria: the approximation error, the runtime, and the cardinality of the solution set. We observe that the proposed variants have satisfactory results, especially in terms of runtime compared to the existing variants from the literature.

Nash Equilibria Strategies and Equivalent Single-Objective Optimization Problems. The Case of Linear Partial Differential Equations

In this paper we study the existence and uniqueness of Nash equilibria (solution to competition-wise problems, with several controls trying to reach possibly different goals) associated to linear partial differential equations and show that, in some cases, they are also the solution of suitable single-objective optimization problems (i.e. cooperative-wise problems, where all the controls cooperate to reach a common goal). We use cost functions associated with a particular linear parabolic partial differential equation and distributed controls, but the results are also valid for more general linear differential equations (including elliptic and hyperbolic cases) and controls (e.g. boundary controls, initial value controls,...).

Study on Properties of Intercalated Melt-blown Nonwovens

Based on the intercalating melt-blown non-woven material performance control principle, through the single factor analysis of variance, two-factor variance analysis and typical correlation analysis, partial least-squares regression model is established, a multi-objective optimization model, structure parameters and performance parameters of the respectively as sample, using the typical correlation analysis between the two sample data, the paper analyses the inner link, The results show that product thickness has a strong positive correlation with filtration resistance.Then the Pearson correlation coefficients between structural variables and product performance were calculated respectively, and the correlation size was judged by the value of the correlation coefficient. It was concluded that the product thickness and porosity had a strong positive correlation.Finally to filter products of the highest efficiency as objective function and combined with multiple constraints, single objective optimization model is set up, using simulated annealing algorithm to optimization, then the product of the highest filter efficiency and minimum drag as the objective function, combination of conditions such as receiving distance and speed of hot air to multi-objective optimization model is established.Then, according to the priority order of constraints, the multi-objective optimization problem is transformed into two single-objective optimization problems, and the rationality of the results is tested according to the factors such as the initial gas flow rate and the number of superimposed layers. It is concluded that the filtration efficiency and filtration resistance solved in this paper are the optimal solutions.

Dynamic Candidate Solution Boosted Beluga Whale Optimization Algorithm for Biomedical Classification

In many fields, complicated issues can now be solved with the help of Artificial Intelligence (AI) and Machine Learning (ML). One of the more modern Metaheuristic (MH) algorithms used to tackle numerous issues in various fields is the Beluga Whale Optimization (BWO) method. However, BWO has a lack of diversity, which could lead to being trapped in local optimaand premature convergence. This study presents two stages for enhancing the fundamental BWO algorithm. The initial stage of BWO’s Opposition-Based Learning (OBL), also known as OBWO, helps to expedite the search process and enhance the learning methodology to choose a better generation of candidate solutions for the fundamental BWO. The second step, referred to as OBWOD, combines the Dynamic Candidate Solution (DCS) and OBWO based on the k-Nearest Neighbor (kNN) classifier to boost variety and improve the consistency of the selected solution by giving potential candidates a chance to solve the given problem with a high fitness value. A comparison study with present optimization algorithms for single-objective bound-constraint optimization problems was conducted to evaluate the performance of the OBWOD algorithm on issues from the 2022 IEEE Congress on Evolutionary Computation (CEC’22) benchmark test suite with a range of dimension sizes. The results of the statistical significance test confirmed that the proposed algorithm is competitive with the optimization algorithms. In addition, the OBWOD algorithm surpassed the performance of seven other algorithms with an overall classification accuracy of 85.17% for classifying 10 medical datasets with different dimension sizes according to the performance evaluation matrix.

An initialization-free distributed algorithm for dynamic economic dispatch problems in microgrid: Modeling, optimization and analysis

In this paper, a distributed optimization algorithm is designed for a hybrid microgrid network to minimize the total generation cost in a dynamic economic dispatch problem (DEDP). The hybrid microgrid model is constructed with different types of traditional power resources, renewable energy and energy storage batteries, which are subject to the supply–demand balance, capacity, and ramp-rate constraints of the generation facilities. Meantime, from the perspective of environment protection, the pollutant emissions from traditional generators are considered to reduce its impact on environment. Firstly, we transform the multi-objective optimization problem to a single objective optimization problem through the weight-sum method. Then, compared to the most existing centralized algorithms, we propose a fully distributed algorithm that does not depend on the initialization process to solve the dynamic dispatch problem. Moreover, we assume that the optimization objective functions are convex functions rather than a strictly standard quadratic function, and the convergence of the proposed algorithm is analyzed through convex analysis and a Lyapunov function method. Finally, some experiments with quadratic or non-quadratic cost functions and comparison examples are simulated, the experimental results verify that the optimal solution satisfies the constraints of the supply–demand constraints and capacity inequalities in each time slot.

Redefining teaching-and-learning-process in TLBO and its application in cloud

Teaching-Learning-Based Optimization (TLBO) algorithm was developed to solve single-objective optimization problems. TLBO is inspired by the theory of teaching-learning mechanism. Basic TLBO works better for unimodal problems but poorly for multi-model problems because of its poor exploration. To provide a fair exploration for solving complex optimization problems, we redefined the learning strategy to the basic TLBO. This newly redefined variant is called Multi-Teacher Teaching-Learning Based Optimization (MT-TLBO). The performance of MT-TLBO was tested on the latest optimization benchmark functions, CEC-C06, 2019. It is observed that the performance of MT-TLBO is superb comparatively. After that, it is simulated to solve workflow scheduling problems by minimizing the execution cost of the standard workflow and maximizing the workload on computing resources in a cloud environment. Finally, it is found that MT-TLBO produces minimal execution cost and a fair workload distribution on resources on standard benchmark workflow, comparatively.

Optimization of injection molding process parameters for the lining of IV hydrogen storage cylinder

The hydrogen storage cylinder lining was taken as the research object. The injection model of the cylinder liner was developed employing 3D software, a two-cavity injection molding system was built, and Moldflow was utilized for analysis to determine the best combination of injection molding process parameters. The effects of injection process parameters (melt temperature, mold temperature, holding pressure, holding time and cooling time) on the evaluation index were analyzed by orthogonal experiment L16(45). The prediction data of IV hydrogen storage cylinder lining under different parameters were obtained by the range analysis method. The multi-objective optimization problem of injection molding process was transformed into a single-objective optimization problem by using the grey correlation analysis method. The optimal parameters such as melt temperature 270 °C, mold temperature 80 °C, packing pressure 55 MPa, packing time 20 s and cooling time 13 s were obtained. Taguchi method was adopted to obtain SNR (signal-to-noise ratio), while range and variance methods were used for analysis. The results showed that warpage was 0.4892 mm, the volume shrinkage was 12.31%, the residual stress in the first direction was 98.13 MPa, and the residual stress in the second direction was 108.1 MPa. The comprehensive index was simultaneously most impacted by the melt temperature.

Determination of the Optimum Operating Conditions and Geometrical Dimensions of the Plate Fin Heat Sinks Using Teaching-Learning-Based-Optimization Algorithm

Abstract Electronic devices must be effectively cooled for long-term reliability and safe operation. It is essential to determine operating conditions and optimum dimensions of cooling devices in terms of device weight, space, cost, and sound limits. Plate fin heat sinks (PFHSs) are frequently used for cooling electronic devices. Optimum thermal designs of PFHSs are explored in this study using a teaching-learning-based-optimization (TLBO) algorithm where entropy generation (S˙gen) minimization, profit factor (J) maximization, base plate temperature excess (θb) minimization, total mass (mass) minimization, and total volume (volume) minimization are the objective functions of the constrained single-objective optimization problems. For further investigations of the entropy generation minimization method, three different optimization problems are also studied: minimization of thermal resistance (Rth), minimization of pressure drop (ΔP), and minimization of pumping power (W˙pump). Each optimization problem is subjected to a constraint, namely, temperature excess of base plate temperature (θb) should be lower than 10 K. Four optimization variables are considered which are the number of plate fins (N), freestream velocity (Vf), the thickness of the fin (tfin), and height of the fin (Hfin). Optimum configurations belonging to the different optimization problems are compared, and the effect of each optimization variable on the objective functions is discussed in detail. It is found that one can obtain optimum operating conditions and geometrical dimensions of the PFHSs according to the design objective, i.e., minimum mass requirement, space limitation, minimum base plate requirement, etc. As a result, the optimum designs of the studied cases are different which are superior to each other in terms of design targets.

Optimization of Selective Laser Sintering/Melting Operations by Using a Virus-Evolutionary Genetic Algorithm

This work presents the multi-objective optimization results of three experimental cases involving the laser sintering/melting operation and obtained by a virus evolutionary genetic algorithm. From these three experimental cases, the first one is formulated as a single-objective optimization problem aimed at maximizing the density of Ti6Al4V specimens, with layer thickness, linear energy density, hatching space and scanning strategy as the independent process parameters. The second one refers to the formulation of a two-objective optimization problem aimed at maximizing both the hardness and tensile strength of Ti6Al4V samples, with laser power, scanning speed, hatch spacing, scan pattern angle and heat treatment temperature as the independent process parameters. Finally, the third case deals with the formulation of a three-objective optimization problem aimed at minimizing mean surface roughness, while maximizing the density and hardness of laser-melted L316 stainless steel powder. The results obtained by the proposed algorithm are statistically compared to those obtained by the Greywolf (GWO), Multi-verse (MVO), Antlion (ALO), and dragonfly (DA) algorithms. Algorithm-specific parameters for all the algorithms including those of the virus-evolutionary genetic algorithm were examined by performing systematic response surface experiments to find the beneficial settings and perform comparisons under equal terms. The results have shown that the virus-evolutionary genetic algorithm is superior to the heuristics that were tested, at least on the basis of evaluating regression models as fitness functions.

Optimal Operation of Energy Hub Systems under Resiliency Response Options

The economic and resilient operation of power systems has always been one of the main priorities of energy systems. In spite of improvements in various fields of energy systems, especially power systems, the issue of resilience has become more important. For this purpose, this paper proposes a multiobjective optimization model to improve the economic performance of energy hub systems and improve the resilience of electrical consumers. Also, consumer welfare, which is a function of the energy not supplied index, is maximized over a 24-hour period by considering extreme weather conditions. The ε-constraint method is applied to solve the proposed model by transforming the multiobjective optimization problem into several single-objective optimization problems. The max-min fuzzy method is also used to select the optimal solution among the Pareto solutions. A sample hub system is made up of electrical, thermal, and gas loads, electrical and thermal energy sources, and storage systems employed as a test system. A group of actions is applied to improve the resilience of the system, which may be affected by outages caused by storms under the resilience response program (RRP). The results proved the efficiency of the proposed RRP in improving economics and resilience.

A generality analysis of multiobjective hyper-heuristics

Selection hyper-heuristics have emerged as high level general-purpose search methodologies that mix and control a set of low-level (meta) heuristics. Previous empirical studies over a range of single objective optimisation problems have shown that the number and type of low-level (meta) heuristics used are influential to the performance of selection hyper-heuristics. In addition, move acceptance strategies play an important role and can significantly affect the overall performance of a hyper-heuristic. In this paper, we introduce an adapted variant of an existing learning automata based multiobjective hyper-heuristic from the literature. We investigate the performance and generality level of the proposed method, and another learning automata based selection hyper-heuristic, operating over a search space of multiobjective evolutionary algorithms (MOEAs) across two well-known multiobjective optimisation benchmarks. The experimental results demonstrate that, regardless of the number and type of low-level metaheuristics available, the learning automata based hyper-heuristics outperform each constituent MOEA individually, and an online learning and random choice selection hyper-heuristic from the literature. This performance and generality is shown to be consistent across a number of different move acceptance strategies.

Population-based discrete state transition algorithm with decomposition and knowledge guidance applied to electrolytic cell maintenance decision

With continuous scale expansion and higher safety requirements in modern aluminum electrolysis, it is more and more necessary to realize an intelligent decision-making for shutting-down and running of aluminum reduction cells (SRARC). However, this realization needs to solve a special single-objective constrained integer optimization problem (SCIOP), where the key challenge is a high requirement for the constraint-handling ability. In this paper, based on a high-scalability intelligent optimization algorithm called discrete state transition algorithm (DSTA), a population-based DSTA with decomposition and knowledge guidance (PDSTA/D-S) is proposed. This PDSTA/D-S improves the constraint-handling ability of DSTA from three aspects. Firstly, a hybrid framework combining DSTA with genetic algorithm is proposed. Secondly, a decomposition-based multi-objective optimization for constrained problems with uniformly-angled weighted sum vector is proposed. Thirdly, the manual decision-making is transferred to a knowledge-based transformation operator of DSTA. Therefore, a high-level performance of decision-making for SRARC can be obtained. The related experiments on a SRARC which is built from the practical production have demonstrated that the proposed PDSTA/D-S not only makes an effective improvement of DSTA from three aspects, but also has a more advanced performance compared with other existing high-performance intelligent optimization algorithms.

A non-dominated sorting based multi-objective neural network algorithm

Neural Network Algorithm (NNA) is a recently proposed Metaheuristic that is inspired by the idea of artificial neural networks. The performance of NNA on single-objective optimization problems is very promising and effective. In this article, a maiden attempt is made to restructure NNA for its possible use to address multi-objective optimization problems. To make NNA suitable for MOPs several fundamental changes in the original NNA are proposed. A novel concept is proposed to initialize the candidate solution, position update, and selection of target solution. To examine the optimization ability of the proposed scheme, it is tested on several benchmark problems and the results are compared with eight state-of-the-art multi-objective optimization algorithms. Inverse generational distance(IGD) and hypervolume (HV) metrics are also calculated to understand the optimization ability of the proposed scheme. The results are statistically validated using Wilcoxon signed rank test. It is observed that the overall optimization ability of the proposed scheme to solve MOPs is very good.•This paper proposes a method to solve multi-objective optimization problems.•A multi-objective Neural Network Algorithm method is proposed.•The proposed method solves difficult multi-objective optimization problems.

Mission Planning for Energy-Efficient Passive UAV Radar Imaging System Based on Substage Division Collaborative Search.

In our earlier study, an energy-efficient passive UAV radar imaging system was formulated, which comprehensively analyzed the system performance. In this article, based on the evaluator set, a mission planning framework for the underlying energy-efficient passive UAV radar imaging system is proposed to achieve optimized mission performance for a given remote sensing task. First, the mission planning problem is defined in the context of the proposed synthetic aperture radar (SAR) system and a general framework is outlined, including mission specification, illuminator selection, and path planning. It is found that the performance of the system is highly dependent upon the flight path adopted by the UAV platform in a 3-D terrain environment, which offers the potential of optimizing the mission performance by adjusting the UAV path. Then, the path planning problem is modeled as a single-objective optimization problem with multiple constraints. Path planning can be divided into two substages based on different mission orientations and low mutual correlation. Based on this property, a path planning method, called substage division collaborative search (Sub-DiCoS), is proposed. The problem is divided into two subproblems with the corresponding decision space and subpopulation, which significantly relax the constraints for each subproblem and facilitates the search for feasible solutions. Then, differential evolution and the whole-stage best guidance technique are devised to cooperatively lead the subpopulations to search for the best solution. Finally, simulations are presented to demonstrate the effectiveness of the proposed Sub-DiCoS method. The result of the mission planning method can be used to guide the UAV platform to safely travel through a 3-D rough terrain in an energy-efficient manner and achieve optimized SAR imaging and communication performance during the flight.

Solving a New Test Set of Nonlinear Equation Systems by Evolutionary Algorithm.

During the past two decades, many evolutionary algorithms have been proposed to solve nonlinear equation systems (NESs). However, the benchmark test sets have not received enough attention. Some features of NESs (e.g., high dimension, large search range, the connectivity of the feasible region) are rarely considered in the original benchmark test sets, which results in that they cannot represent the real-world problems well. Thus, a general toolkit is proposed to generate artificial test problems and 18 test instances with diverse characteristics are constructed in this article, which is the first attempt to design NESs. The experimental results indicate that the current algorithms perform poorly on this new benchmark test set. Furthermore, we develop a transformation method that transforms a NES into a new single-objective optimization problem and design a two-phase method to solve this transformed multimodal optimization problem. Compared to other algorithms, the proposed method has a superior or at least competitive performance.

Optimal Trading in Local Electricity Market Based on an Enhanced Evolutionary Algorithm with Distribution Estimation

The evolution from passive to active distribution network, the ability to actively control distributed energy resources and to perform bilateral energy exchange has significantly complicated the market transactions in recent years due to activities among consumers and prosumers. Local electricity market (LEM) is challenged to optimize welfare as well as reduction of emissions by involving participants in energy transactions. In this paper, the trading strategy is modeled as a single-objective optimization problem to determine each agent's optimal energy trading. Modern heuristic optimization techniques have proven their efficiency and robustness in large optimization problems and thus, an enhanced artificial bee colony (EABC) incorporating a distribution estimation algorithm is proposed, which guides the search for optimum by building and sampling explicit probabilistic models of promising candidate solutions. With the help of a distribution estimation algorithm, the EABC eliminates many tuning parameters in the original ABC and increases its exploitation to obtain more robust and competitive performance. A comparative study is conducted with the basic ABC, differential evolution, and particle swarm optimization, and the EABC demonstrates its efficiency on the case study where nine agents are involved in trading energy in the day-ahead LEM.

Wireless edge device intelligent task offloading in mobile edge computing using hyper-heuristics

To overcome with the computation limitation of resource-constrained wireless IoT edge devices, providing an efficient task computation offloading and resource allocation in distributed mobile edge computing environment is consider as a challenging and promising solution. Hyper-heuristic in recent times is gaining popularity due to its general applicability of same solution to solve different types of problems. Hyper-heuristic is generally a heuristic method or framework which iteratively evaluates and chooses the best low-level heuristic, to solve different types of problems. In this paper, we try to solve wireless device task offloading in mobile edge computing, which is a non-convex and NP-Hard problem by using a proposed novel Hyper-Heuristic Framework using Stochastic Heuristic Selection (HHFSHS) using Contextual Multi-Armed Bandit (CMAB) with Epsilon-Decreasing strategy, considering two key Quality of Service (QoS) objectives computation time and energy consumption. These multiobjective criteria are modeled as single-objective optimization problem with the goal to minimize latency and energy consumption of wireless devices without losing the pareto optimality. Finally, evaluate its performance by comparing with other individual meta-heuristic algorithms.

Optimal operation and stochastic scheduling of renewable energy of a microgrid with optimal sizing of battery energy storage considering cost reduction

In order to alleviate worldwide worries about environmental issues, power system operators and planning entities are looking for new energy sources that will produce fewer emissions than conventional fossil-fuel power plants. When it comes to powering their systems, utilities are increasingly choosing renewable energy sources (RESs). Here, microgrids (MG) would furnish the ideal conditions for incorporating RESs. Thus, this study presents an seasonal optimization framework for the short-term operation of an MG, including energy storage and solar photovoltaic (PV) systems, while thoroughly exploring the effects of varying climatic factors on the optimal scheduling of resources. The day-ahead MG scheduling is addressed in this model, taking into account the impact of varying irradiances across a year. The resulting single-objective optimization problem is then tackled with the help of the converged barnacles mating optimizer (CBMO), as a robust and effective optimization method. The simulation findings show that the total operating cost of the grid-integrated microgrid is alleviated when a PV model is used in a real-world setting to raise the accuracy of the energy management system. In case 1, the CBMO reduces the operating cost of the MG by 262.784 €ct/day, which is less than the results obtained by some other algorithms. Using the hybrid CBMO, the reported costs for Case 2 is 298.8513 €ct/day. The CBMO approach yielded the best results of 352.1964 €ct on a warm sunny day, 285.2851 €ct on a cold sunny day, 257.7912 €ct on a warm cloudy day, and 252.135 €ct on a cold cloudy day. After running the simulations, it has been found out that the suggested CBMO has the shortest mean simulation time by 114.217 s in Case 3, while other algorithms need longer simulation time such that the GA needs 120.364 s, the PSO needs 118.487 s, the DE needs 118.039 s and the ICA needs 116.287 s. Therefore, the CBMO takes significantly less time than other methods.

Multi-Objective Multi-Scale Optimization of Composite Structures, Application to an Aircraft Overhead Locker Made with Bio-Composites

The use of composite materials has grown exponentially in transport structures due to their weight reduction advantages, added to their capability to adapt the material properties and internal micro-structure to the requirements of the application. This flexibility allows the design of highly efficient composite structures that can reduce the environmental impact of transport, especially if the used composites are bio-based. In order to design highly efficient structures, the numerical models and tools used to predict the structural and material performance are of great importance. In the present paper, the authors propose a multi-objective, multi-scale optimization procedure aimed to obtain the best possible structure and material design for a given application. The procedure developed is applied to an aircraft secondary structure, an overhead locker, made with a sandwich laminate in which both, the skins and the core, are bio-materials. The structural multi-scale numerical model has been coupled with a Genetic Algorithm to perform the optimization of the structure design. Two optimization cases are presented. The first one consists of a single-objective optimization problem of the fibre alignment to improve the structural stiffness of the structure. The second optimization shows the advantages of using a multi-objective and multi-scale optimization approach. In this last case, the first objective function corresponds to the shelf stiffness, and the second objective function consists of minimizing the number of fibres placed in one of the woven directions, looking for a reduction in the material cost and weight. The obtained results with both optimization cases have proved the capability of the software developed to obtain an optimal design of composite structures, and the need to consider both, the macro-structural and the micro-structural configuration of the composite, in order to obtain the best possible solution. The presented approach allows to perform the optimisation of both the macro-structural and the micro-structural configurations.

An improved marine predator algorithm based on epsilon dominance and Pareto archive for multi-objective optimization

Solving multi-objective optimization problems plays an important role in several applications. Recently, the Marine Predator Algorithm (MPA) was introduced for solving single objective optimization problems inspired by the behaviour of marine predator in their search for a prey. This paper proposes a modified MPA based framework called Guided Multi-objective Marine Predator Algorithm (GMOMPA) to solve multi-objective optimization problems. The proposed GMOMPA incorporates an external archive to help store the optimal Pareto set solution and guide the particles during the exploitation of the search space. For obtaining non-dominated solutions, the Pareto dominance concept is utilized while the epsilon dominance is considered to update the archive’s sorted solutions. In this context, the epsilon dominance concept extends the diversity and exploration of the solutions. Further, a fast non-dominated solution and crowding distance are introduced to update the particle’s position, while maintaining the diversity and ensuring a fast convergence towards the Pareto optimal. The proposed GMOMPA is evaluated on several different benchmark test functions including multi-objective ZDT, DTLZ, UF, and WFG test functions as well as the recent multi-objective multimodal CEC 2020 test functions. Moreover, the performance of the proposed GMOMPA is compared with well-known multi-objective optimization algorithms. The obtained results show that the proposed GMOMPA is a good tool for multi-objective optimization and has significant advantages over several state-of-the-art algorithms in almost all of the test functions.