Multi-objective Method Research Articles

Multi-objective scheduling of cloud-edge cooperation in distributed manufacturing via multi-agent deep reinforcement learning

ABSTRACT Due to the limited computational power of edge devices in distributed manufacturing systems, the challenge of meeting real-time computing requirements for industrial big data arises. Additionally, the significant number of computational tasks results in considerable energy expenses. Therefore, it is crucial to effectively tackle the multi-objective cloud-edge collaborative task offloading problem (MOCECTOP). This paper focuses on two optimisation objectives: total computation time delay and computational energy consumption, which are related to promoting work efficiency and lowering carbon emissions. The weights of these two objectives are hard to determine at different production stages. The challenge is to get multiple models with various possible weight pairs of multiple objectives within a single training session and to achieve high-quality schedules for MOCECTOP in real-time production line control. We address this challenge by proposing a hierarchical parameter sharing (HPS) multi-objective optimisation framework based on multi-agent deep reinforcement learning. The network model comprises a task selection agent and a computing node selection agent. The task selection agent prioritises tasks for computation based on their state features, while the computing node selection agent allocates available computing devices to a selected task. Parameter sharing and collaborative training are employed to obtain a solution for the multi-objective problem when considering the variations in computational capabilities between the cloud and the edge. The HPS optimisation framework effectively fulfills the near real-time requirements for task computation in distributed manufacturing. Numerical experiments demonstrate that our HPS-based strategy quickly produces better schedules superior to those of existing multi-objective solution methods.

Multimodal multi-objective hierarchical distributed consensus method for multimodal multi-objective economic dispatch of hierarchical distributed power systems

As the scale of power systems increases, the multi-layer distributed multi-objective consensus algorithm (MLDMOCA) can speed up computation and enhance privacy. However, the MLDMOCA needs to face: (1) the problems of error enlargement of hierarchy bringing deteriorating results; (2) over-dependence of certain weights on the choice of power balance adjustment factors. Moreover, multimodal multi-objective economic dispatch has not been performed for either small or large systems, resulting in poor diversity of economic scheduling solutions. Therefore, this study proposes a multimodal multi-objective hierarchical distributed consensus approach. The multimodal multi-objective hierarchical distributed consensus approach contains multimodal increments, and the proposed multimodal search method can obtain multimodal results. By changing the multimodal factor and multimodal critical threshold, the multimodal results and multimodal decision solutions of the proposed method are adjusted. In this study, the multimodal multi-objective hierarchical distributed consensus approach is simulated in IEEE 118-bus and IEEE 3059-bus cases. The simulation results show that the multimodal multi-objective hierarchical distributed consensus approach can achieve multiple multimodal solutions quickly and can adapt the power balance adjustment factor to almost all weights. Moreover, multiple linear-weighted multimodal objective values of the proposed approach are smaller than the objective value of the existing hierarchical distributed method.

Cost and thermodynamic analysis of wind-hydrogen production via multi-energy systems

With rising temperatures, extreme weather events, and environmental challenges, there is a strong push towards decarbonization and an emphasis on renewable energy, with wind energy emerging as a key player. The concept of multi-energy systems offers an innovative approach to decarbonization, with the potential to produce hydrogen as one of the output streams, creating another avenue for clean energy production. Hydrogen has significant potential for decarbonizing multiple sectors across buildings, transport, and industries. This paper explores the integration of wind energy and hydrogen production, particularly in areas where clean energy solutions are crucial, such as impoverished villages in Africa. It models three systems: distinct configurations of micro-multi-energy systems that generate electricity, space cooling, hot water, and hydrogen using the thermodynamics and cost approach. System 1 combines a wind turbine, a hydrogen-producing electrolyzer, and a heat pump for cooling and hot water. System 2 integrates this with a biomass-fired reheat-regenerative power cycle to balance out the intermittency of wind power. System 3 incorporates hydrogen production, a solid oxide fuel cell for continuous electricity production, an absorption cooling system for refrigeration, and a heat exchanger for hot water production. These systems are modeled with Engineering Equation Solver, and analyzed based on energy and exergy efficiencies, and on economic metrics like levelized cost of electricity (LCOE), cooling (LCOC), refrigeration (LCOR), and hydrogen (LCOH) under steady-state conditions. A sensitivity analysis of various parameters is presented to assess the change in performance. Systems were optimized using a multi-objective method, with maximizing exergy efficiency and minimizing total product unit cost used as objective functions. The results show that System 1 achieves 79.78 % energy efficiency and 53.94 % exergy efficiency. System 2 achieves efficiencies of 55.26 % and 27.05 % respectively, while System 3 attains 78.73 % and 58.51 % respectively. The levelized costs for micro-multi-energy System 1 are LCOE = 0.04993 $/kWh, LCOC = 0.004722 $/kWh, and LCOH = 0.03328 $/kWh. For System 2, these values are 0.03653 $/kWh, 0.003743 $/kWh, and 0.03328 $/kWh. In the case of System 3, they are 0.03736 $/kWh, 0.004726 $/kWh, and 0.03335 $/kWh, and LCOR = 0.03309 $/kWh. The results show that the systems modeled here have competitive performance with existing multi-energy systems, powered by other renewables. Integrating these systems will further the sustainable and net zero energy system transition, especially in rural communities.

Enhancing the performance of hybrid wave-wind energy systems through a fast and adaptive chaotic multi-objective swarm optimisation method

Hybrid offshore renewable energy platforms have been proposed to optimise power production and reduce the levelised cost of energy by integrating or co-locating several renewable technologies. One example is a hybrid wave-wind energy system that combines offshore wind turbines with wave energy converters (WECs) on a single floating foundation. The design of such systems involves multiple parameters and performance measures, making it a complex, multi-modal, and expensive optimisation problem. This paper proposes a novel, robust and effective multi-objective swarm optimisation method (DMOGWA) to provide a design solution that best compromises between maximising WEC power output and minimising the effect on wind turbine nacelle acceleration. The proposed method uses a chaotic adaptive search strategy with a dynamic archive of non-dominated solutions based on diversity to speed up the convergence rate and enhance the Pareto front quality. Furthermore, a modified exploitation technique (Discretisation Strategy) is proposed to handle the large damping and spring coefficient of the Power Take-off (PTO) search space. To evaluate the efficiency of the proposed method, we compare the DMOGWA with four well-known multi-objective swarm intelligence methods (MOPSO, MALO, MODA, and MOGWA) and four popular evolutionary multi-objective algorithms (NSGA-II, MOEA/D, SPEA-II, and PESA-II) based on four potential deployment sites on the South Coast of Australia. The optimisation results demonstrate the dominance of the DMOGWA compared with the other eight methods in terms of convergence speed and quality of solutions proposed. Furthermore, adjusting the hybrid wave-wind model’s parameters (WEC design and PTO parameters) using the proposed method (DMOGWA) leads to a considerably improved power output (average proximate boost of 138.5%) and a notable decline in wind turbine nacelle acceleration (41%) throughout the entire operational spectrum compared with the other methods. This improvement could lead to millions of dollars in additional income per year over the lifespan of hybrid offshore renewable energy platforms.

Multi-objective optimization of Fe-based SCR catalyst on the NOx conversion efficiency for a diesel engine based on FGRA-ANN/RF

With the development of industrial level and the increasingly strict emission regulations, selective catalytic reduction (SCR) system is one of the important ways to control NOx emissions from diesel engines. In this study, the effects of intake pressure on pressure and NOx conversion efficiency before and after catalyst were investigated at different loads. In order to improve the SCR efficiency, a multi-objective prediction method based on FGRA-ANN/RF was developed for SCR systems, where the predicted output parameters (the front and back section temperatures of the catalyst, the pressure difference, and the instantaneous catalytic efficiency) and the decision variables (the engine operating parameters). Firstly, the sensitivity analysis of the multi-objective inputs obtained from the ETC condition experiments is performed by the fuzzy grey relation method (FGRA) to select the high sensitivity parameters. Then, the prediction was carried out by artificial neural network (ANN) as well as the improved random forest (RF). The experimental results showed that the evaluation index R2 of RF was generally greater than 0.92 and the improved random forest method had high accuracy and robustness. It is valuable for solving SCR industrial simulation and reducing the hysteresis of ammonia injection response.

Performance analysis of the lisflood hydrological model in a flood event in the madeira river basin

The largest recorded flood of the Madeira River (largest tributary of the Amazon River) occurred in 2014, remaining above the flood level for 90 days, reaching the maximum level on March 30, at 19.69 m. Among the various tools capable of assisting in monitoring and forecasting floods are hydrological models, such as LisFlood, a distributed hydrological model of the rainfall-runoff type. Thus, the objective of this research was to evaluate the performance of the LisFlood model for maximum flows in the Madeira River basin. There were a total of 7 river gauge stations calibrated and subsequently validated, distributed across 5 sub-basins. The calibration process was carried out using a multi-objective method, applying the NSGA II as an optimization algorithm, with the model's performance being evaluated by the NSE and KGE metrics. The calibration and validation results demonstrated, in general, that the LisFlood model performed well between the simulated and observed flow values for the Madeira River basin. The average of the 07 stations analyzed was 0.81 for KGE and 0.69 for NSE, for the calibration process. In validation, the average metrics were 0.78 in KGE and 0.67 in NSE. In relation to the historic flood event that occurred in 2014, it can be seen that the model followed the maximum flow peak observed at the Porto Velho station, with a difference in the simulated flow of 17% lower than the observed flow, for the year 2014, demonstrating good efficiency of LisFlood in simulating maximum flow. Thus, the study demonstrated that the application of the LisFlood model in large basins is effective in simulating maximum flows, satisfactorily simulating extreme flood peaks.

A Multi-objective Feature Selection Method Considering the Interaction Between Features

A Multi-objective Feature Selection Method Considering the Interaction Between Features

Mix proportion and microscopic characterization of coal-based solid waste backfill material based on response surface methodology and multi-objective decision-making

The mix proportion of multi-source coal-based solid waste (CSW) for underground backfilling affects transportation and support performance of backfill materials, and even the backfilling cost. In this study, the optimal mix proportion of desulfurization gypsum (DG), furnace bottom slag (FBS) and gasification fine slag (GFS) is determined by the Response Surface Methodology–Box Behnken Design (RSM-BBD). Then the fluidity, bleeding rate, 3-day strength, 7-day strength and preparation cost are evaluation indicators, the optimal mix proportion of backfill materials is determined by the multi-objective decision-making method (MDM). Finally, the microstructure of the backfill material with optimal mix proportion was studied by TGA, MIP, SEM–EDS and XRD. The results show that the mix proportion of CSW with the optimal comprehensive index is coal gangue (CG): coal fly ash (CFA): DG: FBS: GFS = 1:1.5:0.2:0.1:0.1, the mass concentration is 78%, and ordinary Portland cement (OPC)/CSW = 7.5%. The weight loss phenomenon of the backfill material with the optimal mix proportion occurs continuously during the heating process, mainly due to the evaporation of crystal water, structural water and hydroxyl water. There are dense narrow-necked pores in the backfill material, and the pore connectivity is poor. There is no hydration reaction occurs between CSW particles, and the strength increase of the backfill material mainly depends on the hydration reaction of cement. In ettringite, part of Al2O3 is replaced by SiO2, and part of CaSO4 is replaced by CaCO3. This study provides a reference for the engineering application of underground backfilling with multi-source CSW.

Routing Control Optimization for Autonomous Vehicles in Mixed Traffic Flow Based on Deep Reinforcement Learning

With recent technological advancements, the commercialization of autonomous vehicles (AVs) is expected to be realized soon. However, it is anticipated that a mixed traffic of AVs and human-driven vehicles (HVs) will persist for a considerable period until the Market Penetration Rate reaches 100%. During this phase, AVs and HVs will interact and coexist on the roads. Such an environment can cause unpredictable and dynamic traffic conditions due to HVs, which results in traffic problems including traffic congestion. Therefore, the routes of AVs must be controlled in a mixed traffic environment. This study proposes a multi-objective vehicle routing control method using a deep Q-network to control the driving direction at intersections in a mixed traffic environment. The objective is to distribute the traffic flow and control the routes safely and efficiently to their destination. Simulation results showed that the proposed method outperformed existing methods in terms of the driving distance, time, and waiting time of AVs, particularly in more dynamic traffic environments. Consequently, the traffic became smooth as it moved along optimal routes.

A multi-objective stacked regression method for distance based colour measuring device

Identifying colour from a distance is challenging due to the external noise associated with the measurement process. The present study focuses on developing a colour measuring system and a novel Multi-target Regression (MTR) model for accurate colour measurement from distance. Herein, a novel MTR method, referred as Multi-Objective Stacked Regression (MOSR) is proposed. The core idea behind MOSR is based on stacking as an ensemble approach with multi-objective evolutionary learning using NSGA-II. A multi-objective optimization approach is used for selecting base learners that maximises prediction accuracy while minimising ensemble complexity, which is further compared with six state-of-the-art methods over the colour dataset. Classification and regression tree (CART), Random Forest (RF) and Support Vector Machine (SVM) were used as regressor algorithms. MOSR outperformed all compared methods with the highest coefficient of determination values for all three targets of the colour dataset. Rigorous comparison with state-of-the-art methods over 18 benchmarked datasets showed MOSR outperformed in 15 datasets when CART was used as a regressor algorithm and 11 datasets when RF and SVM were used as regressor algorithms. The MOSR method was statistically superior to compared methods and can be effectively used to measure accurate colour values in the distance-based colour measuring device.

Multiobject Real-Time Automatic Detection Method for Production Quality Control of Prefabricated Laminated Slabs

Multiobject Real-Time Automatic Detection Method for Production Quality Control of Prefabricated Laminated Slabs

Path Planning for Autonomous Mobile Robots Using the RFO-GWO Optimization Algorithm

Path planning is a challenging navigation problem that can be handled using multi-objective methods. This paper, present a thre Path planning is a challenging navigation problem that can be handled using multi-objective methods. This paper presents a three-stage multi-objective path-planning method. The first stage is to locate the best or near-best solution path and avoid detected obstacles using a hybrid of the red fox–gray wolf optimizer (RFO–GWO), which finds a route from the start position to the target position. In the second step, a mutation operation using an evolutionary algorithm is utilized to enhance the length, integrity, and smoothness of the route generated by the RFO–GWO algorithm. The final step of the suggested method is refined further using a multiphase technique. By integrating the real sizes of the mobile robots and the size of the barriers and phrasing the issue as a traveling object in the available area, the suggested path-planning method resembles the actual world. The simulation results indicate that this strategy creates the most viable path even in complicated surroundings, overcoming the disadvantages of traditional approaches. Furthermore, when compared to prior path-planning methods, the simulation’s outcomes indicate that the suggested RFO–GWO method is effective in terms of the route, and the strategy is extremely competitive. The results showed a significant improvement, where the total percentage convergence time (in seconds) for RFO–GWO for the three maps was 15%, 12%, and 10%, respectively, whereas it was 35%, 41%, and 43% seconds in GWO and 34%, 35%, and 37% seconds in RFO. There was also a significant improvement in the number of nodes for RFO-GWO (2%, 3%, and 2%) compared to GWO nodes (64%, 65%, and 62%), and RFO nodes (32%, 30%, and 35%) for the same three maps. Subsequently, the smoothness of the path formed by the recommended approach was enhanced using the evolutionary algorithm (EA), where the total percentage length of the path in the worst scenario for GWO was 28% and for RFO was 26% in units, but after improvement with the RFO-GWO with EA, it became 22% in units. stages multi-objective path planning method: The first stage is to locate the best or near-best solution path and avoid the detected obstacles using a hybrid of the Red Fox-Grey Wolf optimizer (RFO-GWO) method, which finds a rout from the start position to the target position. In the second step, a mutation operation by evolutionary, are utilized to enhance the length, integrity, and smooth of the rout generated by the RFO-GWO method. the final step the suggested method is refined further by using the multiphase technique. By integrating both the real sizes of the mobile robots and the size of the barriers and phrasing the issue as a traveling object in the available area, the suggested path planning method resembles the actual world. The simulation results indicate that this strategy creates the best viable path even in complicated surroundings, overcoming the disadvantages of traditional approaches. Furthermore, when contrasted with prior path-planning methods, simulation outcomes indicate that the suggested RFO-GWO in terms of route effectivity, the strategy is extremely competitive.

Improvement of signal communication for a foraging task using evolutionary robotics

Communication systems represent an evolutionary advantage for a group of robots solving coordinated tasks. In the field of evolutionary robotics, the emergence and establishment of communication are regulated by different variables. These systems are a tool produced by artificial evolution for the exchange of personal and environmental information. Since evolutionary processes involve multi-objective evolutionary methods, it is important to study all the mechanisms that affect the emergence and establishment of communication systems. One of these variables is the evolutionary advantage of emerging signals. In this article it is assumed that the signals appear because they are evolutionarily useful in solving a task. Emitter and receiver generate a process of conceptualization, which makes the signals associated with a meaning for the community. In this way an experiment is adapted to the FARSA simulator and the MARXBOT robot. This experiment consists of a group of robots that spend as much time as possible in a food zone and avoid a poisoned zone. Under normal conditions, robots tend to point to the food zone to attract the rest of the population. When the evolutionary importance of pointing out the food zone is reduced, the signals arise in different situations such as the presence of nearby objects and the poisoned zone. Communication is configured with the LED rings and linear cameras of the robots. In addition, an ethological method is adapted to quantify the behavioral effects of experimental manipulation.

Enhancing multi-objective evolutionary algorithms with machine learning for scheduling problems: recent advances and survey

Multi-objective scheduling problems in workshops are commonly encountered challenges in the increasingly competitive market economy. These scheduling problems require a trade-off among multiple objectives such as time, energy consumption, and product quality. The importance of each optimization objective typically varies in different time periods or contexts, necessitating decision-makers to devise optimal scheduling plans accordingly. In actual production, decision-makers confront intricate multi-objective scheduling problems that demand balancing clients’ requirements and corporate interests while concurrently striving to reduce production cycles and costs. In solving various problems, multi-objective evolutionary algorithms have attracted the attention of researchers and gradually become one of the mainstream methods to solve these problems. In recent years, research combining multi-objective evolutionary algorithms with machine learning technology has shown great potential, opening up new prospects for improving the performance of multi-objective evolutionary methods. This article comprehensively reviews the latest application progress of machine learning in multi-objective evolutionary algorithms for scheduling problems. We review various machine learning techniques employed for enhancing multi-objective evolutionary algorithms, particularly focusing on different types of reinforcement learning methods. Different categories of scheduling problems addressed using these methods were also discussed, including flow-shop scheduling issues, job-shop scheduling challenges, and more. Finally, we highlighted the challenges faced by the field and outlined future research directions.

Parametric design of photovoltaic louver integrated shading devices for west facade windows of office buildings in central China

ABSTRACT In order to improve the shading performance and power generation effect of Photovoltaic shading integrated devices (PVSDs) on the west facade of buildings in China, a multi-objective optimization design method is proposed in this paper. Taking a west-facing office building in Zhengzhou, Henan Province, as an example, a parametric model of photovoltaic (PV) louvers for windows on the west facade is established, and parametric design research is carried out on the energy-saving potential of PV louver shading systems. Based on the optimization objectives of power generation of PV louvers, indoor thermal discomfort hours, building cooling load and lighting energy consumption, the performance of the west facade office with PVSD under different design strategies was simulated, and the optimal design strategy was determined according to the preference of decision makers. Compared with the basic type without a non-shading model, the indoor lighting energy consumption of the optimized west facade PVSD is slightly increased. However, overall performance is improved, with a 35% reduction in cooling load, a decrease of 804.59 kWh in total energy consumption, and a shortened summer thermal discomfort time of 404 hours. The power generation of PV louvers can replace 46% of the total energy consumption of the room. The results show that the installation of PVSD on the west facade window is important for alleviating the overheating inside the room and improving the energy-saving and power generation potential of the room.

Multi-stage and multi-objective design optimization for improving resilience of base-isolated hospital buildings

The hospital is a critical infrastructure for treating the injured after the earthquake. The hospital is a complex system composed of structure, non-structural components, and medical equipment that are located on different floors, have different importance and seismic performance, and need different control objectives, enhancing any component could improve the hospital's functionality. It is imperative to economically and rationally choose enhancement measures to minimize initial functionality losses and improve hospital resilience. This study provides a hospital functional evaluation method that takes into account the physical dimension of the damage to the structure, non-structural components and medical equipment, as well as the organizational dimension of the treatment process of earthquake casualties. Bayesian networks and discrete event simulation methods are used to calculate the availability probability of medical rooms and the functional indicator of the number of earthquake casualties that can be treated. Then, a two-stage and multi-objective functionality improvement method was proposed to improve hospital functionality. The first stage is the design optimization of the isolation system with the objectives of minimizing the functionality loss and displacement of the isolation layer. The second stage optimizing the enhancement strategies for non-structural components and medical equipment aims at minimizing the functionality loss and enhancement budget. The proposed method uses a fast and elitist non-dominated sorting genetic algorithm (NSGA-II) approach to optimize the design of the isolation system and the enhancement of non-structural components and medical equipment. The method is applied to a hypothetical hospital to highlight the proposed method's capability of improving the hospital's functionality.

Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems

We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical system in the multiobjective setting, which trajectories converge weakly to Pareto optimal solutions. Discretization of this system yields an inertial multiobjective algorithm which generates sequences that converge weakly to Pareto optimal solutions. We employ Nesterov acceleration to define an algorithm with an improved convergence rate compared to the plain multiobjective steepest descent method (Algorithm 1). A further improvement in terms of efficiency is achieved by avoiding the solution of a quadratic subproblem to compute a common step direction for all objective functions, which is usually required in first-order methods. Using a different discretization of our inertial gradient-like dynamical system, we obtain an accelerated multiobjective gradient method that does not require the solution of a subproblem in each step (Algorithm 2). While this algorithm does not converge in general, it yields good results on test problems while being faster than standard steepest descent.

Stacked Multiscale Densely Connected Temporal Convolutional Attention Network for Multi-Objective Speech Enhancement in an Airborne Environment

Airborne speech enhancement is always a major challenge for the security of airborne systems. Recently, multi-objective learning technology has become one of the mainstream methods of monaural speech enhancement. In this paper, we propose a novel multi-objective method for airborne speech enhancement, called the stacked multiscale densely connected temporal convolutional attention network (SMDTANet). More specifically, the core of SMDTANet includes three parts, namely a stacked multiscale feature extractor, a triple-attention-based temporal convolutional neural network (TA-TCNN), and a densely connected prediction module. The stacked multiscale feature extractor is leveraged to capture comprehensive feature information from noisy log-power spectra (LPS) inputs. Then, the TA-TCNN adopts a combination of these multiscale features and noisy amplitude modulation spectrogram (AMS) features as inputs to improve its powerful temporal modeling capability. In TA-TCNN, we integrate the advantages of channel attention, spatial attention, and T-F attention to design a novel triple-attention module, which can guide the network to suppress irrelevant information and emphasize informative features of different views. The densely connected prediction module is used to reliably control the flow of the information to provide an accurate estimation of clean LPS and the ideal ratio mask (IRM). Moreover, a new joint-weighted (JW) loss function is constructed to further improve the performance without adding to the model complexity. Extensive experiments on real-world airborne conditions show that our SMDTANet can obtain an on-par or better performance compared to other reference methods in terms of all the objective metrics of speech quality and intelligibility.

A hybrid evolutionary approach for multi-objective unit commitment problem in power systems

The operating strategy of the power system is changing from the minimum cost to the minimum cost with a minimum emission approach as a result of growing worries about global warming and environmental change brought on by the combustion of fossil fuels. The generating scheduling problem becomes a multi-objective one as a result of the economic and emission objectives' inherent conflict. In this study, a multi-objective whale-differential evolution-genetic algorithm (WODEGA) is employed to produce an optimal solution that illustrates a potential trade-off between the unit commitment (UC) problem's emission and cost objectives. The environmental and economic dispatch problem with system and unit constraints is solved using the multi-objective WODEGA method. Main goal of research is to explore the problem of unit commitment and sub-problem of unit commitment i.e. economic dispatch.

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

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