Multi-objective Optimization on Dynamic Performance for a Planar Parallel Mechanism with NSGA-II Algorithm

This study compared the performances of three state-of-theart evolutionary multi-objective optimization algorithms: the Non-Dominated Sorted Genetic Algorithm II (NSGA-II), the Epsilon-Dominance Non-Dominated Sorted Genetic Algorithm II (e -NSGA-II) and the Epsilon-Dominance Multi-Objective Evolutionary Algorithm ( e MOEA), on a constrained biobjective crop-mix planning problem (BCP). The BCP test case objectives were to: (i) maximize crop production and (ii) minimize planting area. The BCP problem was enumerated to provide the true Pareto-optimal solution set to facilitate rigorous testing of the evolutionary multi-objective optimization algorithms. The performances of the three algorithms were assessed and compared using three performance metrics (additive epsilon indicator, inverted generational distance and spacing). For the comparative study, a graphical comparison with respect to true Pareto front of optimal crop planning problem was provided. Results of the analyses indicated that the e MOEA greatly outperforms the NSGAII and the e -NSGA-II.

Determining the contribution of an agent to a system-level objective function (credit assignment) is a key area of research in cooperative multiagent systems. Multi-objective optimization is a growing area of research, though mostly focused on single agent settings. Many real-world problems are multiagent and multi-objective, (e.g., air traffic management, scheduling observations across multiple exploration robots) yet there is little work on their intersection. In this work, we leverage recent advances in single-objective multiagent learning to address multi-objective domains. We focus on the impact of difference evaluation functions (which extracts an agent's contribution to the team objective) on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II), a state-of-the-art multi-objective evolutionary algorithm. We derive multiple methods for incorporating difference evaluations into the NSGA-II framework, and test each in a multiagent rover exploration domain, which is a good surrogate for a wide variety of distributed scheduling and resource gathering problems. We show that how and where difference evaluations are incorporated in the NSGA-II algorithm is critical, and can either provide significant benefits or destroy system performance, depending on how it is used. Median performance of the correctly used difference evaluations dominates best-case performance of NSGA-II in a multiagent multi-objective problem.

In order to obtain higher quality silicon single crystal, a hybrid strategy for modeling of Czochralski silicon crystal growth and optimizing of process parameters is presented in the paper. The hybrid strategy includes the computational fluid dynamics (CFD) method, neural network of group method of data handing (GMDH), and improved nondominated sorting genetic algorithm II (NSGA‐II). The shape variable of solid‐liquid interface h and the defect evaluation criteria V/G are set to objective functions according to engineering experience and process requirement. The polynomial of the objective functions is produced by GMDH and CFD. Ultimately, an improved elitist strategy and crowding distance NSGA‐II is proposed in the paper to obtain the Pareto optimum solution by the objective functions identified by the GMDH. Compared with other optimization algorithms, the improved NSGA‐II can increase the lateral diversity and the uniform distribution of the nondominated solutions. Engineering validation proved that the proposed hybrid strategy can effectively solve the complex uncertain multiobjective optimization problem of system and provides a new method for obtaining high‐quality crystal growth process parameters.

Almost all real-world and engineering problems involve multi-objective optimization of some sort that is often constrained. To solve these constrained multi-objective optimization problems, constrained multi-objective optimization evolutionary algorithms (CMOEAs) are enlisted. These CMOEAs require specific constraint handling techniques. This study aims to address and test the most successful constraint handling techniques, seven different penalty constraint techniques, as applied to the Non-dominated Sorting Genetic Algorithm II (NSGA-II). In this paper, NSGA-II is chosen because of its high popularity amongst evolutionary algorithms. Inverted Generational Distance and Hypervolume are the main metrics that are discussed to compare the constraint handling techniques. NSGA-II is applied on 13 constrained multi-objective problems known as CF1-CF10, C1-DTLZ1, C2-DTLZ2, and C3-DTLZ4. The result of IGD and HV values are compared and the feasibility proportions of each combination on each problem are shown. The results of simulation present interesting findings that have been presented at the end of paper as discussion and conclusion.

The non-dominated sorting genetic algorithm II (NSGA-II) is applied to the concurrent generation scheduling and load management of the isolated microgrid: the joint generation — voyage scheduling of an all-electric ship (AES). The AES uses integrated power generators and an energy storage system (ESS) to match its propulsion and service loads, thus forming an isolated microgrid. The propulsion load is the variable load that determines th ship voyage; hence, the schedulings of the generator, the propulsion load and the ESS have to be processed concurrently, for the optimal operation of the AES. NSGA-II outperforms the existing methods for the AES scheduling problem by modelling the schedulings in a one-stage optimisation. Another advantage of NSGA-II applied here is its multi-objective optimisation. Existing work on ship scheduling has hitherto set the minimisation of the AES operational cost as the single optimisation objective, with the reduction of the greenhouse gas (GHG) emission merely treated as a constraint of the optimisation. The proposed work emphasises the environmental concerns and makes GHG mitigation a separate objective, thus expanding the optimisation into multi-objective. The simulation demonstrate that optimising the ship voyage jointly with the generation scheduling results in the reduction of both operational cost and GHG emission, compared to the fixed-voyage generation scheduling. Integrating the ESS dispatch into the generation scheduling further enhances the benefits.

Minimizing carbon emissions in power system operations has become a critical challenge as the energy sector transitions toward sustainability. This paper presents a high-fidelity simulation framework for CO<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>-optimized energy dispatch, employing an enhanced Non-Dominated Sorting Genetic Algorithm II (NSGA-II) tailored for emission-oriented optimization. Unlike traditional economic dispatch approaches that primarily focus on cost, the proposed framework explicitly minimizes total CO<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> emissions while ensuring demand–supply balance, operational limits, and ramp-rate feasibility. Key enhancements to the baseline NSGA-II include adaptive crossover–mutation operators, hybrid population initialization, and constraint-repair mechanisms, which improve convergence speed, robustness, and solution diversity. The framework is validated through multiple case studies incorporating stochastic load demand and renewable variability. Results show that the enhanced NSGA-II achieves nearly 20% emission reduction compared to baseline economic dispatch, with faster convergence and a broader Pareto-optimal solution set than standard NSGA-II. Furthermore, dispatch outcomes demonstrate increased reliance on renewable and storage units, reducing the share of coal and gas generation. These findings highlight the potential of the proposed approach to support low-carbon, policy-aligned energy system operations and provide a foundation for future extensions in multi-objective optimization, real-time scheduling, and carbon pricing integration.

Multi- objective modeling and optimization of dissimilar laser welding by integrating an artificial intelligence predictive model with NSGA-II algorithm

Multi-objective Cascade Control of Regulatory Process with Two Conflicting Objectives

A new approach for assessing the assembled vulnerability of coastal aquifers based on optimization models

Corn was frozen at harvest time in high-latitude areas, when corn kernel is wetter and more easily broken. When frozen corn was threshed and separated by the longitudinal axial threshing cylinder of a combine harvester, it caused a significantly high kernel damage rate and loss rate. The process parameters of threshing cylinder were optimized using RSM (response surface method) and NSGA-II (Non-Dominated Sorted Genetic Algorithm-II). The drum speed (Ds), feed rate (Fr) and concave clearance (Cc) were determined as the optimized process parameters. The loss rate (Lr) and damage rate (Dr) were indicators of operational performance. The RSM was used to establish a mathematical model between process parameters and indicators. With an elite strategy, NSGA-II was used for multi-objective optimization to obtain the optimal operational performance of the threshing cylinder. Overall, when the drum speed was selected as 384.1 rpm, the feed rate as 8.6 kg/s and the concave clearance as 40.5 mm, according to the requirement of corn harvest, the best operational performance of the longitudinal axial threshing cylinder on frozen corn was obtained. The Lr was 1.98% and the Dr was 3.49%. This result indicated that the applicability of the optimal process parameters and the optimization method of combining NSGA-II and RSM was effective for determining the optimal process parameters. This will provide an optimization method for synchronously reducing the loss rate and damage rate of grain harvesters.

Water distribution networks (WDN) model optimization is an important part of smart water systems to achieve optimal strategies. WDN optimization focuses on the nonlinearity of the discharge head loss equation, the availability of discrete properties of pipe sizes, and the conservation of constraints. Multi-objective evolutionary algorithms (MOEAs) have been proposed and successfully applied in the field of WDN design optimization. Previous studies have focused on comparing the optimization effects of algorithms in water distribution networks, ignoring the problems of unbalanced pressure distribution and water hammer at the nodes of the pipe network caused by the complex terrain in mountainous areas. In this paper, a multi-objective water supply optimization model that integrated cost, reliability, and water quality was established for a mountainous WDN in real engineering. The method of traversing the nodes to solve the water age was introduced to find a more scientific and practical water age solution model, with setting the weight function to evaluate the water age of the water supply model comprehensively. Strength Pareto Evolutionary Algorithm II (SPEA-II) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) were adopted to optimize the WDN design model in the mountainous complex terrain. The significance levels of the number of Pareto solutions (NOPS) and running time are 0.029 and 0.001, respectively, indicating that the two algorithms have significant differences. Compared to NSGA-II, SPEA-II has a better convergence rate and running time in multi-objective water supply optimization design. The solution set distribution of SPEA-II is more concentrated than that of NSGA-II, also the numerical value is better. The number of SPEA-II optimization schemes is larger and the scheme is more effective. Among them, the Pareto solution set of SPEA-II can obtain more desirable optimization results on cost, reliability index (RI) and water age. In summary, the study provides valuable information for decision makers in WDN with complex terrain.

Heuristic-based multi-objective optimization design for viscous dampers in RC frame structures considering soil-structure interaction

The process planning decisions on detailed steps of machining a part including selection of operations, machines, tools and operation sequences are crucial, directly impacting the carbon emissions associated with machining. Operation sequencing generates the optimal order of operations by reducing production time and cost. A need is felt to explore operation sequence optimization by balancing economic and environmental considerations that very few studies have so far addressed. Our study proposes an approach for multiobjective operation sequence optimization by simultaneously minimizing carbon emission and total production cost in machining. Firstly, machining operations are selected and carbon emissions are quantified for individual operations. Secondly, the proposed multiobjective optimization model for operation sequencing is applied. Due to NP-hard nature of this problem due to the exponential growth of potential solution sequences as the number of operations increases, making it computationally challenging to find an optimal sequence, it is often challenging and very time-consuming to solve using exact mathematical models. However, metaheuristic approaches can potentially offer near-optimal solutions in a more reasonable time frame. We implemented Non-dominant Sorting Genetic Algorithm-II(NSGA-II), Multiobjective Particle Swarm Optimization (MOPSO) and Multiobjective Ant colony Optimization (MOACO). Finally, a case study is used to validate and compare their effectiveness in providing low-carbon emissions with cost-effective sequences. NSGA-II is found to have higher computational time but a superior Pareto tradeoff between reducing carbon emissions and production costs.

An optimization model that may be applied to analyze building retrofit strategies is presented in this research. The aim of this research paper is to identify the optimal thermal envelope configuration that will assure the minimum energy requirement for heating in the case of a residential building, while also considering price restrictions obtained through a specific market survey. To achieve this, several values for the following parameters are considered: thermal insulation materials’ conductivities and thicknesses, windows’ overall heat transfer coefficients and total solar energy transmittance and doors’ thermal proprieties. Additionally, this paper presents a method used to find the best option from among the available heat pumps that could cover most of the energy requirements for heating and domestic hot water systems, also considering the products’ prices. The proposed method is based on a Non-dominated Sorting Genetic Algorithm II (NSGA-II) model developed in the Pymoo (Multi-Objective Optimization in Python) library. The result shows that the energy requirement for heating can be reduced by up to approximately 75% compared to that obtained in the case of a non-insulated building by using suitable insulation materials and doors and windows with superior thermal proprieties chosen by the NSGA-II.

Proton exchange membrane fuel cell (PEMFC) is one of the most promising energy conversion devices in the world. Performance, durability, and cost are the key issues currently limiting its large-scale commercial application. This paper proposes a non-dominated sorting genetic algorithm II (NSGA-II) for optimizing operating parameters of the start process to improve the output performance of a PEMFC stack. First, a Simulink model of the PEMFC stack including the anode module, cathode module, water transfer module, output voltage module, and output net power module is established, and the accuracy of the stack model is verified through experiments. The three performances are then optimized simultaneously based on NSGA-II. The results show that the optimized operating parameters for the start process results in a PEMFC stack that outperforms the base case in steady-state voltage, percentage of undershoot, and net power these three indicators with the same response time, demonstrating the success of the method in solving multiple optimization problems. This study presents an effective approach for the multi-objective optimization of the PEMFC stack, which is of guidance for engineering practice.