Complex Multi-objective Optimization Problems Research Articles

Multiobjective Optimization of Papermaking Wastewater Treatment Processes under Economic, Energy, and Environmental Goals.

Due to the heterogeneity of recycled paper materials and the production conditions, pollutants in papermaking wastewater fluctuate sharply over time. Quality control of the papermaking wastewater treatment process (PWTP) is challenging and costly. As regulations are also growing about the environmental effects of the PWTP on greenhouse gas (GHG) emission, energy consumption, etc., the PWTP formulates a complex multiobjective optimization problem. This research established a multiagent deep reinforcement learning framework to simultaneously optimize process cost, energy consumption, and GHG emission in the PWTP, subjected to the effluent quality, to realize economic, energy, and environmental (3E) goals. The biological treatment process of wastewater in paper mills was simulated using benchmark simulation model no. 1 (BSM1). The data generated based on the BSM manual was utilized for model training, and real data acquired from a local papermaking factory was used to estimate the model performance. The results show that the proposed method outperforms conventional techniques in identifying the best control strategies for multiple targets.

Adaptive Sampling Offspring Generation Strategy for Multi-objective Optimization

A covariance adaptive sampling offspring generation strategy (CASS) based on fuzzy clustering is proposed, and a multi-objective distribution estimation algorithm (MEDCA) based on this strategy is introduced. The GK-FCM clustering partitioning strategy is designed to build a Gaussian model for each individual, collectively approximating the manifold of the Pareto solution set and generating offspring through sampling. The introduction of an individual’s survival generation adapts the individual’s preference for exploration and exploitation. This is achieved by incorporating it as a scaling factor of the covariance matrix in the sampling model, in order to satisfy the individual’s preferences for development and exploration in different evolutionary stages. This method significantly improves the performance of MEDCA in solving complex multi-objective optimization problems through covariance matrix adaptation sampling strategy and scaling factor adaptation strategy. The experimental results demonstrate the advantages of MEDCA in the application of offspring generation strategies during model sampling.

A resilient and intelligent multi-objective energy management for a hydrogen-battery hybrid energy storage system based on MFO technique

In this paper, a new design and flexible energy management strategy are presented for microgrids. The proposed intelligent energy management system (IEMS) achieves effective integration between the resilient microcontroller, chosen for its rapid response speed and its capability to perform multiple operations simultaneously, and the optimization techniques to enhance the power quality. The IEMS is designed using the FPGA board, chosen for its flexibility and capability to handle multiple and complex operations simultaneously. The experimental testing of the IEMS demonstrates a significant level of effectiveness in managing energy. To enhance system performance and ensure cost-effective reliability, advanced optimization techniques are employed. This study deals with a complex multi-objective optimization problem involving the limitations of energy generation, load demand, and a hydrogen-battery hybrid energy storage system. The moth-flame optimization (MFO) algorithm is chosen to solve this optimization problem due to its rapid convergence rate and accuracy. The effectiveness of the MFO algorithm is assessed by comparing it with several new algorithms. The obtained results show the robust performance of the IEMS and its high responsiveness to dynamic operational scenarios. It can observe, gather, and analyze data in real-time. It achieves a remarkable 1.287 % reduction in operating costs within a short timeframe.

Comfort, carbon emissions, and cost of building envelope and photovoltaic arrangement optimization through a two-stage model

The design of a high-performance building necessitates tradeoffs among multiple performance objectives, and many simulation-based optimization tools have been developed for this purpose. In practice, these tools are often constrained by excessive computational load and tight project deadlines. This study aimed to develop a holistic approach to rapidly identify optimal building design schemes. A novel two-stage model was developed as a surrogate to conventional physics-based models, which were then linked to multi-objective optimization algorithms, namely, NSGA-II, NSGA-III, and C-TAEA, in search of the Pareto optimal and best design schemes. The performance of the two-stage model was further enhanced by applying the least absolute shrinkage and selection operator (LASSO) and Neural Architecture Search methods and learning from the statistical layer. The above approach was tested in the design of an apartment building for seniors in Northern China such as thermal comfort, carbon, and cost. The optimal design achieved through the compromise optimum can significantly reduce thermal discomfort, life-cycle carbon emissions, and high levels of daylighting conditions. The design scheme was visualized using a geometrical remodel module. This study contributes methodologically to complex multi-objective building optimization problems with practical implications for design.

Enhancing the performance of radial distribution systems via optimal integration of electric vehicles

<span lang="EN-US">Electric vehicles (EVs) and their associated charging stations (CSs) are a promising avenue for greenhouse gas reduction and energy security. However, improper location and size of the EV charging station (CSs/EVs) negatively affect the power system. It results in some technical challenges such as increased real power-loss, decreased voltage stability and increased voltage deviation. This paper suggests optimum planning of CSs/EVs locations to conserve voltage, improve power-loss and reduce the effect of CSs/</span><span lang="EN-US">EVs in electrical distribution systems. The multi objective genetic algorithm method (MOGA) is utilized to solve the optimization problem and reduce the impact of the random location of CSs/EVs. <span>The simulations are</span> performed on IEEE 33-bus and IEEE 69-bus radial distribution systems (RDS). In addition, the optimal EV allocation is carried out with two fixed levels of loading from 100% to 150% of the candidate EV load. A comparison between the proposed MOGA technique and other optimization techniques is carried out. The results demonstrated the capability of the proposed technique for optimal placement of CSs/EVs in RDS. </span><span lang="EN-US">Moreover, it is providing an objective value to solve a complex multi-objective nonlinear optimization problem to reduce the total power-loss, improve the voltage profile and extend the voltage stability.</span>

Multi‐objective optimization method for control parameters of flexible direct current transmission converters based on intelligent algorithms

AbstractIn order to meet the current needs of power transmission, people have turned their attention to direct current (DC) transmission. When the alternating current(AC) power grid (PG) fails, it is easy to cause commutation failure in the DC system, thereby increasing the fault scope of the system. Therefore, this article adopts a flexible DC transmission system. Flexible DC converters have many control parameters, and there are mutual influences and conflicts between these parameters. By applying intelligent algorithms to multi‐objective optimization (MOP), these complex MOP problems can be effectively solved and an optimal set of control parameter combinations can be found. This method has an important contribution and novelty for optimizing the converter control parameters of flexible DC transmission systems. This article achieves fast and accurate MOP of the control parameters of flexible DC transmission converters by continuously detecting the similarities between antibodies and maintaining the diversity of the population. The research results show that the average DC side current is about 405A in the first 20 seconds, and the DC side current fluctuates regularly after 20 seconds. This article lays the foundation for establishing a real‐time simulation model of flexible DC transmission systems suitable for real‐time simulation systems.

On the adaptation of reference sets using niching and pair-potential energy functions for multi-objective optimization

Multi-objective evolutionary algorithms (MOEAs) have shown a good capability to approximate the Pareto front (PF) of complex multi-objective optimization problems (MOPs). Recently, several decomposition-based, indicator-based, and reference set-based MOEAs have been proposed to tackle MOPs with four or more objective functions, known as many-objective optimization problems (MaOPs). Some well-known MOEAs from these design strategies use a predefined reference set generated with uniformly distributed weight vectors on a unit simplex. These MOEAs have demonstrated good convergence, coverage, and uniformity of solutions on MOPs with regular PF shapes, i.e., simplex-like shapes. However, it has been shown that their performance degrades on MOPs with irregular PF shapes. In this paper, we proposed a pluggable reference set adaptation method based on niching and pair-potential energy functions (PPFs), called AdaK, to enhance the performance of these MOEAs on MOPs with irregular PF shapes while maintaining their good behavior on MOPs with regular PF shapes. Our adaptation method was validated by plugging it into three well-known MOEAs that use a predefined weight vector-based reference set. We perform an empirical study using different PPFs for our adaptation method on the DTLZ, WFG, Minus-DTLZ, Minus-WFG, IMOP, and VNT test suites. Our experimental results show the capability of our adaptation method to promote an invariant performance regardless of the PF shape. Additionally, we show that MOEAs with our adaptation method have a competitive performance against state-of-the-art MOEAs.

An effective surrogate model assisted algorithm for multi-objective optimization: application to wind farm layout design

Due to the intricate and diverse nature of industrial systems, traditional optimization algorithms require a significant amount of time to search for the optimal solution throughout the entire design space, making them unsuitable for meeting practical industrial demands. To address this issue, we propose a novel approach that combines surrogate models with optimization algorithms. Firstly, we introduce the Sparse Gaussian Process regression (SGP) into the surrogate model, proposing the SGP surrogate-assisted optimization method. This approach effectively overcomes the computational expense caused by the large amount of data required in Gaussian Process model. Secondly, we use grid partitioning to divide the optimization problem into multiple regions, and utilize the multi-objective particle swarm optimization algorithm to optimize particles in each region. By combining the advantages of grid partitioning and particle swarm optimization, which overcome the limitations of traditional optimization algorithms in handling multi-objective problems. Lastly, the effectiveness and robustness of the proposed method are verified through three types of 12 test functions and a wind farm layout optimization case study. The results show that the combination of meshing and SGP surrogate enables more accurate identification of optimal solutions, thereby improving the accuracy and speed of the optimization results. Additionally, the method demonstrates its applicability to a variety of complex multi-objective optimization problems.

Improved multi-objective grasshopper optimization algorithm and application in capacity configuration of urban rail hybrid energy storage systems

Aiming at addressing problems of poor diversity and ergodicity of initial population, slow convergence speed, and susceptibility to local optima in conventional multi-objective grasshopper optimization algorithm (MOGOA), an improved MOGOA is proposed in this paper. The proposed algorithm is based on Sobol sequence, adaptive social force, cosine parameter c, as well as Levy flight mechanism (SACLMOGOA), where Sobol sequence is adopted to initialize the population, thereby improving the diversity and ergodicity of the initial population. The adaptive social force is proposed to enhance the global exploration ability in the early stage of iteration and the local development ability in the late stage of iteration. A cosine type parameter c is used to ensure sufficient exploration time and rapid convergence of the algorithm during position update process and Levy flight is used to guide some grasshoppers to mutate, enhancing the ability to escape from the local optima and improving the performance and efficiency of the algorithm. The proposed algorithm is tested with ZDT and DTLZ series benchmark test functions to validate its effectiveness, and it is also compared with conventional MOGOA, multi-objective particle swarm optimization, multi-objective gray Wolf, and multi-objective jellyfish algorithms. The simulation results demonstrate that the proposed algorithm outperforms other algorithms in terms of inverse generational distance (IGD), spread (SP), maximum spread (MS), run time and Wilcoxon rank sum test. Furthermore, the proposed algorithm is successfully applied to the capacity configuration of the urban rail hybrid energy storage systems (HESS) of Changsha Metro Line 1 in China, reducing the traction network voltage fluctuations by 3.3 % and 2.2 % compared to no HESS capacity configuration optimization, and by 14 % and 5.7 % compared to no HESS during train starting and breaking, respectively. While achieving the goal of energy-saving and voltage stabilization, the cost of the hybrid energy storage systems is minimized as well. All of these have demonstrated SACLMOGOA is an effective tool for solving complex multi-objective optimization problems in engineering.

Improving Multi-Objective Optimization Methods of Water Distribution Networks

Water distribution network design is a complex multi-objective optimization problem and multi-objective evolutionary algorithms (MOEAs) such as NSGA II have been widely used to solve this optimization problem. However, as networks get larger, NSGA II struggles to find the diverse and uniform solutions that are critical in multi-objective optimization. This research proposes an improved version of NSGA II that uses three new-generation methods to target different regions of the Pareto front and thus increase the number of solutions in critical regions. These methods include saving an archive, local search around extreme and uncrowded Pareto front, and local search around the knee area of the Pareto front. The improved NSGA II is tested on benchmark networks of different sizes and compared to the best-known Pareto front of the networks determined by MOEAs. The results show that the proposed algorithm outperforms the original NSGA II in terms of broadening the Pareto front solution range, increasing solution density, and discovering more non-dominated solutions. The improved NSGA II can find solutions that cover all parts of the Pareto front using a single algorithm without increasing computational effort.

A State-of-the-Art Review of Task Scheduling for Edge Computing: A Delay-Sensitive Application Perspective

The edge computing paradigm enables mobile devices with limited memory and processing power to execute delay-sensitive, compute-intensive, and bandwidth-intensive applications on the network by bringing the computational power and storage capacity closer to end users. Edge computing comprises heterogeneous computing platforms with resource constraints that are geographically distributed all over the network. As users are mobile and applications change over time, identifying an optimal task scheduling method is a complex multi-objective optimization problem that is NP-hard, meaning the exhaustive search with a time complexity that grows exponentially can solve the problem. Therefore, various approaches are utilized to discover a good solution for scheduling the tasks within a reasonable time complexity, while achieving the most optimal solution takes exponential time. This study reviews task scheduling algorithms based on centralized and distributed methods in a three-layer computing architecture to identify their strengths and limitations in scheduling tasks to edge service nodes.

Improved multi-objective artificial bee colony algorithm-based path planning for mobile robots.

Mobile robots are widely used in various fields, including cosmic exploration, logistics delivery, and emergency rescue and so on. Path planning of mobile robots is essential for completing their tasks. Therefore, Path planning algorithms capable of finding their best path are needed. To address this challenge, we thus develop improved multi-objective artificial bee colony algorithm (IMOABC), a Bio-inspired algorithm-based approach for path planning. The IMOABC algorithm is based on multi-objective artificial bee colony algorithm (MOABC) with four strategies, including external archive pruning strategy, non-dominated ranking strategy, crowding distance strategy, and search strategy. IMOABC is tested on six standard test functions. Results show that IMOABC algorithm outperforms the other algorithms in solving complex multi-objective optimization problems. We then apply the IMOABC algorithm to path planning in the simulation experiment of mobile robots. IMOABC algorithm consistently outperforms existing algorithms (the MOABC algorithm and the ABC algorithm). IMOABC algorithm should be broadly useful for path planning of mobile robots.

An improved multi-objective brainstorming algorithm with the application of rapeseed germination characteristics optimization

As one of the most important raw materials for daily edible oil, the annual production and quality of oilseed rape have a great impact on the daily lives of people and the development of the country. The germination quality of rapeseed directly affects the future yield and quality of oilseed rape, and seed germination vigor (SGV) and chlorophyll content (CC) are important factors affecting the quality of rapeseed germination. It is very necessary to make the rapeseeds have optimal germination characteristics and seed germination vigor at the early stage of germination by controlling the combination of each decision variable at the segmented harvest. The two objectives are coupled with each other to form a complex multi-objective optimization problem, which is important in the current research field of the rapeseed problem. To solve this problem, a modified brainstorming optimization algorithm based on OPTICS clustering, named MOPCBSO, is proposed in this study. The algorithm uses optics clustering as a new clustering method, chaotic mutation as a new updating method for individuals, and introduces an elite strategy and a tracking strategy. 19 benchmark test functions and nonparametric tests are adopted to examine the performance of the MOPCBSO compared with other optimization algorithms. The results show that the proposed algorithm has significant advantages over other algorithms in terms of convergence and comprehensiveness, demonstrating the effectiveness of the algorithm improvement. To optimize rapeseed germination characteristics, mathematical models are built, in which, cut-down time, after-ripening time and stubble height are selected as decision variables, while chlorophyll concentration and seed germination vigor in seeds as the target characteristics. The data of oliseed rape field trials were collected from 2020 to 2021 in Huanggang City, Hubei Province. Finally, the optimal solution for the germination characteristics of rapeseeds was obtained by the MOPCBSO, which provided an effective basis for the subsequent rapeseed production experiments.

Optimal Allocation and Assessment of Distributed Generation Units with Multi-Objective Planning in Unbalanced Distribution Networks

—Real-world distribution networks are generally unbalanced due to unbalanced loads and asymmetric line parameters. Proper allocation of distributed generation (DG) units in unbalanced radial distribution networks to extract their maximum potential benefits is still quite difficult. Converter-coupled DG units have individual phase real and reactive power regulating ability and provide voltage unbalance compensation. This article proposes a new technique for the suitable allocation and capacity of converter-based multiple DG units considering the unbalanced operation of distribution networks. The objective function contains power loss minimization, multiphase voltage stability augmentation, and reduction of voltage unbalances among different phases in the system. A complex multi-objective optimization problem has been synthesized with the help of a Fast and Flexible Radial Power Flow (FFRPF) and solved by employing a Weighted aggregation (WA) based particle swarm optimization (PSO) approach. The performance of the proposed technique is validated on 19-bus, 25-bus, and 34-bus unbalanced radial distribution networks that consider various power factor modes of the converter-coupled DG units. The analysis of the simulation results indicates a significant enhancement in the power delivery efficiency in all the unbalanced test systems

A two-archive multi-objective multi-verse optimizer for truss design

Multi-objective structure optimization is a complex design issue that involves dealing with multiple conflicting objectives and various constraints. Although metaheuristics have been successful in resolving such issues, their stochastic nature and limitations can make implementation challenging. To address this challenge, an efficient and powerful optimizer called the multi-objective multi-verse optimizer (MOMVO) has been proposed in this study. The MOMVO algorithm is based on a two-archive concept focused on convergence and diversity, respectively, and is termed MOMVO2arc. The effectiveness of MOMVO2arc was evaluated by applying it to five conventional planar and spatial real-world structural optimization problems. These problems had conflicting objectives, such as minimizing structural mass and minimizing maximum nodal deflection, while imposing safety and size constraints related to stress on components and discrete cross-sectional areas. The results were then compared with those of seven advanced optimization techniques, including MOEA/D and NSGA-II, using four globally accepted performance indicators, including Hypervolume, Inverted Generational Difference, Spacing to Extent matrices, and the qualitative behavior of the best Pareto-front plots that each algorithm can produce. The comparative analysis and average Friedman rank test revealed that MOMVO2arc was more effective in solving large structure optimization problems with less computation time. The suggested approach not only found and maintained more Pareto-optimal sets but also achieved good diversity and convergence in both the decision and objective spaces. Therefore, MOMVO2arc can be a promising tool for resolving complex multi-objective structure optimization problems.

Multi-objective deep reinforcement learning for optimal design of wind turbine blade

The design of a wind turbine blade is a typical complex multi-objective optimization problem, mostly solved by evolutionary algorithms. However, these methods are not effective due to limitations such as inaccurate solutions on Pareto fronts for high-dimensional problems, numerous iterations and low adaptability to problems with similar conditions. To address these issues, two multi-objective deep reinforcement learning models are introduced in this paper from an entirely different perspective. The first model, namely the multi-objective deep deterministic policy gradient (MO-DDPG), extends the existing popular reinforcement learning algorithm DDPG to multi-objective optimization problems by integrating various techniques including modeling of constraints on high-dimensional spaces and generation of Pareto solutions. The second model, namely the multi-objective deep stochastic policy gradient (MO-DSPG), further improves the MO-DDPG by incorporating a random neural network called restricted Boltzmann machine (RBM). An adaptive random agent is trained to transform multiple deterministic policies into an optimal stochastic policy. In addition, neighborhood-based parameter transfer strategy is applied to MO-DSPG in the model training phase to reduce the computation time. Experiments showed that the aerodynamic performance of the blades is improved by both the MO-DDPG and the MO-DSPG models with the hypervolume increasing an average of 6.67% and 9.25% respectively, compared with the state-of-art models. The computational efficiency of MO-DSPG is improved by using the parameter transfer strategy, with its runtime reduced to 72.52% compared with state-of-art models.

MOJMA: A novel multi-objective optimization algorithm based Java Macaque Behavior Model

<abstract> <p>We introduce the Multi-objective Java Macaque Algorithm for tackling complex multi-objective optimization (MOP) problems. Inspired by the natural behavior of Java Macaque monkeys, the algorithm employs a unique selection strategy based on social hierarchy, with multiple search agents organized into multi-group populations. It includes male replacement strategies and a learning process to balance intensification and diversification. Multiple decision-making parameters manage trade-offs between potential solutions. Experimental results on real-time MOP problems, including discrete and continuous optimization, demonstrate the algorithm's effectiveness with a 0.9% convergence rate, outperforming the MEDA/D algorithm's 0.98%. This novel approach shows promise for addressing MOP complexities in practical applications.</p> </abstract>

A multi-objective lion swarm optimization based on multi-agent

<p style='text-indent:20px;'>This paper proposes a multi-objective lion swarm optimization based on multi-agent (MOMALSO) for solving the increasingly complex multi-objective optimization problem in engineering practice. First, the Multi-agent system is introduced into the lion swarm optimization (LSO) algorithm. The optimization mechanism of LSO and the information exchange between the agents are integrated to enhance the local search and global search ability of the algorithm, and the self-learning operation can accelerate the approximate Pareto front obtained by the algorithm near to real front. Besides, the external archive is introduced for extending the LSO into a multi-objective algorithm. Finally, the simulations compared with other three algorithms are performed, and the results show that MOMALSO has significant advantages in both convergence and coverage, which verifies the superiority and effectiveness of the algorithm in multi-objective optimization.</p>

An improved multi-objective firefly algorithm for energy-efficient hybrid flowshop rescheduling problem

Hybrid flowshop scheduling problem is a hot research topic, and is widely applied for production shop or line in chemical industry, metallurgical industry, semiconductor manufacturing and other industries. However, on the one hand, the uncertain events are inevitable in actual production, which will disrupt the production plan. On the other hand, nowadays the energy problem becomes more and more serious, and attracts much attention in the manufacturing industry. Therefore, an energy-efficient hybrid flowshop rescheduling problem under the machine breakdown is addressed in this paper. Firstly, the mathematical model for the problem is established, and an energy saving strategy based on problem model is designed, which can ensure the reduction of energy consumption without affecting the production efficiency. Then, an improved multi-objective firefly algorithm is proposed to optimize the production efficiency, energy consumption and production stability. To express the problem characteristics, a two-level encoding mechanism is used to describe the individual, and a corresponding decoding mechanism is presented to generate the scheduling scheme. By simulating the location updating law of the fireflies, the population updating rule is designed, in which the variable neighborhood search is employed to avoid the local optimal. To ensure the quality of the solution set, the fast non-dominated sorting method and elite individual reserving strategy are introduced to the population evolution. Finally, the numerical experimental results indicate that the designed energy saving strategy is effective, and the proposed algorithm obtains better Pareto frontier and performs the better convergence and diversity comparing with MOEA/D and NSGA-Ⅱ, the common algorithms to solve complex multi-objective optimization problem.

Multi-objective train speed profile determination for automatic train operation with conscious search: A new optimization algorithm, a comprehensive study

Train speed profile is one of the most fundamental optimization issues in rail transportation. The speed profile has several indices, such as travel time and energy consumption. These indices mostly have opposite natures, which leads to a non-linear, complex multi-objective optimization problem. This paper introduces a new heuristic algorithm called Conscious Search (CS) to determine the optimal speed profile. For this purpose, after modeling the train dynamics, we initially analyze the validated heuristic optimization algorithms, including Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), Bees Algorithm (BA), and Teaching–learning Based Optimization (TLBO) statistically using sensitivity analysis. Then, using new criteria called the Impact Factor, we show that a trade-off prevails in the global and local search for algorithms. In general, the stronger the algorithm in one domain, the weaker in the other. Subsequently, no algorithm is superior to another. In this regard, CS is proposed as a hybrid algorithm that performs the optimization in two separate global and local phases to address this problem and achieve the ideal optimization. CS steps are designed to dominate other algorithms in both local and global phases. In the evaluation, we obtained the train speed profile using the proposed method and the proven latest versions of the mentioned algorithms. Based on the simulation results, CS outperforms the considered algorithms by a palpable margin, and its solutions dominate others. These results indicate on effectiveness and excellence of the proposed method.