Modified NSGA-II for day-ahead multi-objective thermal generation scheduling

Cloud computing provides powerful, highly scalable, flexible resources for real world applications. It also reduces the cost and operation expenses. Workflow scheduling is important for getting higher performance, reducing cost and using resources more efficiently in cloud computing. Workflow scheduling in cloud systems assigns tasks to resources available in the system and aims to utilize cloud resources by decreasing makespan of the workflow. In this study, an evolutionary algorithm is proposed to solve workflow scheduling problem. The main objective of this work is to minimize the makespan of the schedule. To achieve this goal, problem specific crossover operator and mutation operators are proposed in the evolutionary algorithm. The crossover operator will combine the problem-specific information stored in both parents to create a new individual. The mutation operators will explore neighbor solutions using some intelligent search mechanisms. This unique design of the operators increases the diversity of the search space and the quality of the solutions. As a result, the workflow schedules obtained from the evolutionary algorithm decreases the makespan of the workflow in the cloud system. The performance of the proposed study is measured using well-known scientific workflows and is compared with the algorithms from the literature. The proposed study outperforms all related algorithms in 67% of the test cases and obtains the same results in the remaining test cases.

Fast Mesh-Sorting in Multi-objective Optimization

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.

Degradation state identification for hydraulic pumps is crucial to ensure system performance. As an important step, feature extraction has always been challenging. The non-stationary and non-Gaussian characteristics of the vibration signal are likely to weaken the performance of traditional features. In this paper, an efficient feature extraction algorithm named multi-scale ternary dynamic analysis (MTDA) is proposed. MTDA reconstructs the phase space based on the given signal and converts each embedding vector into a ternary pattern independently, which enhances its capacity of describing the details of non-stationary signals. State entropy (SE) and state transition entropy (STE) are calculated to estimate the dynamical changes and complexity of each signal sample. The excellent performance of SE and STE in detecting frequency changes, amplitude changes, and the development process of fault is verified with the use of four simulated signals. The proposed multi-scale analysis enables them to provide a more precise estimation of entropy. Furthermore, support vector machine (SVM) and nondominated sorting genetic algorithm II (NSGA-II) are introduced to conduct feature selection and state identification. NSGA-II and SVM can conduct the joint optimization of these two goals. The details of the method proposed in this paper are tested using simulated signals and experimental data, and some studies related to the fault diagnosis of rotating machinery are compared with our method. All the results show that our proposed method has better performance, which obtains higher recognition accuracy and lower feature set dimension.

Mathematical runtime analysis for the non-dominated sorting genetic algorithm II (NSGA-II)

The non-dominated sorting genetic algorithm II (NSGA-II) is the most intensively used multi-objective evolutionary algorithm (MOEA) in real-world applications. However, in contrast to several simple MOEAs analyzed also via mathematical means, no such study exists for the NSGA-II so far. In this work, we show that mathematical runtime analyses are feasible also for the NSGA-II. As particular results, we prove that with a population size larger than the Pareto front size by a constant factor, the NSGA-II with two classic mutation operators and three different ways to select the parents satisfies the same asymptotic runtime guarantees as the SEMO and GSEMO algorithms on the basic OneMinMax and LOTZ benchmark functions. However, if the population size is only equal to the size of the Pareto front, then the NSGA-II cannot efficiently compute the full Pareto front (for an exponential number of iterations, the population will always miss a constant fraction of the Pareto front). Our experiments confirm the above findings.

In recent years, with the rapid development of renewable energy, the penetration rate of renewable energy generation in the active distribution network (ADN) has increased. Because of the instability of renewable energy generation, the operation stability of ADN has decreased. Due to the ability to cut peak load and fill valley load, battery energy storage systems (BESSs) can enhance the stability of the electric system. However, the placement and capacity of BESSs connected to ADN are extremely significant, otherwise, it will lead to a further decline in the stability of ADN. To ensure the effectiveness of the BESSs connected to the grid, this work uses the fuzzy kernel C-means (FKCM) method for scene clustering. Meanwhile, a multi-objective optimization model of BESS configuration is established with the objective of BESS configuration cost, voltage fluctuation, and load fluctuation, and solved by non-dominated sorting genetic algorithm-II (NSGA-II). In this work, the grey target decision method based on the entropy weight method (EWM) is used to obtain the optimal compromise solution from the Pareto non-dominated set. Moreover, the proposed method is tested and verified in the extended IEEE-33 node system and the extended IEEE-69 node system. The results show that the BESSs configuration scheme obtained by NSGA-II can effectively reduce the fluctuation of voltage and load, and improve the stability of ADN operation.

Multi-objective optimization method using an improved NSGA-II algorithm for oil–gas production process

Supply-chain scheduling in modern production systems faces significant challenges due to the complexity of balancing cost efficiency, delivery lead times, and order variability—especially under stochastic demand and uncertain transportation conditions. Conventional metaheuristic approaches, such as the standard Non-dominated Sorting Genetic Algorithm II (NSGA-II), often struggle with premature convergence, limited population diversity, and rigid parameter settings that hinder adaptability in dynamic environments. To address these limitations, this study proposes a novel Hybrid Adaptive NSGA-II (HA-NSGA-II) framework, enhanced by two key innovations: (1) a Global-Intensity Mutation Operator (GIMO) that strengthens population diversity by dynamically adjusting mutation intensity across the entire solution space; and (2) an Adaptive Parameter Self-Tuning (APST) module based on reinforcement learning, which intelligently regulates crossover and mutation rates in response to evolutionary progress and environmental changes. A tri-objective optimization model is formulated to simultaneously minimize total supply chain cost, order quantity variance (mitigating the bullwhip effect), and customer delivery delays. The proposed HA-NSGA-II demonstrates superior convergence and diversity performance compared to traditional NSGA-II, offering a more robust and adaptive solution for complex, real-world supply chain scheduling under uncertainty. The model is tested on a simulated supply chain with 5 factories, 15 warehouses, and 50 customers facing random demand and Gaussian-distributed lead times. The new HA-NSGA-II is compared with traditional NSGA-II, SPEA2, and MOEA/D based on Hypervolume (HV), Inverted Generational Distance (IGD), Spread (Δ), Total Inventory Cost, Bullwhip Index (BI), and Robustness Index (RI). Results of 50 simulation runs demonstrate that HA-NSGA-II surpasses all the baseline algorithms with 12.9% enhancement in HV, 41.1% improvement in IGD, and 13.7% reduction in convergence time. In addition, it delivers a 14.6% supply chain cost reduction, a 20.4% bullwhip effect suppression, and 25% accelerated times of fulfillment. The research concludes that the HA-NSGA-II provides a scalable and effective scheduling approach applicable for real-time Industry 4.0 supply chains. Work in the future involves expanding the framework towards multi-period dynamic environments using IoT and blockchain-based visibility.

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

This study addresses complex multi‐objective optimization challenges in large‐scale, real‐world water distribution networks (WDNs). The primary objectives are to improve a water quality index (water age) and network resilience by optimizing pipe diameters and network topology as decision variables. The proposed approaches leverage the non‐dominated sorting genetic algorithm II (NSGA‐II) producing Pareto optimal alternatives for water utility decision‐makers. To enhance computational convergence runtime and solution quality of optimization, novel techniques are employed. These include advanced NSGA‐II constraint handling, search space reduction, graph theory‐based formulation of decision variables, constraints, and objective functions, as well as multi‐stage and hydraulic‐free optimization strategies. Furthermore, soft constraints are relaxed and integrated into Pareto decision‐making spaces to provide a comprehensive, multi‐criteria decision‐making framework. The approaches are applied to a real case study, and the results demonstrate optimization performance improvements, with efficiency increasing by approximately 20% (in terms of convergence speed). Additionally, water age is reduced by 52% while achieving favorable results in the hydraulic and topological criteria. These findings highlight the effectiveness of the proposed methodologies in addressing WDN optimization challenges.

A two-stage multi-objective optimization method for envelope and energy generation systems of primary and secondary school teaching buildings in China

Slotted WDM, which achieves higher capacity compared with conventional WDM and SDH networks, has been discussed a lot recently. The ring network for this architecture has been demonstrated experimentally. In slotted WDM ring network, each node is equipped with a wavelength-tunable transmitter and a fixed receiver and assigned with a specific wavelength. A node can send data to every other node by tuning wavelength accordingly in a time slot. One of the important issues for it is scheduling. Scheduling of it can be reduced to input queued switch when synchronization and propagation are solved and many schemes have been proposed to solve these two issues. However, it’s proved that scheduling of such a network taking both jitter and throughput into consideration is NP hard. Greedy algorithm has been proposed to solve it before. The main contribution of this paper lies in a novel genetic algorithm to obtain optimal or near optimal value of this specific NP hard problem. We devise problem specific chromosome codes, fitness function, crossover and mutation operations. Experimental results show that our GA provides better performances in terms of throughput and jitter than a greedy heuristic.

This paper presented a parallel hybrid electric vehicle (HEV) equipped with a hybrid energy storage system. To handle complex energy flow in the powertrain system of this HEV, a fuzzy-based energy management strategy was established. A chaotic multi-objective genetic algorithm, which optimizes the parameters of fuzzy membership functions, was also proposed to improve fuel economy and HC, CO, and NOx emissions. The main target of this algorithm is to escape from local optima and obtain high quality trade-off solutions. Chaotic initialization operator, chaotic crossover and mutation operators, chaotic disturbance operator, and chaotic local search operator were integrated into non-dominated sorting genetic algorithm II (NSGA-II) to form this new algorithm named chaotic NSGA-II (C-NSGA-II). Simulation results and comparisons demonstrated that chaotic operators can enhance searching ability for optimal solutions. In conclusion, C-NSGA-II is suitable for solving HEV energy management optimization problem.

Bat Algorithm (BA) is a recently proposed heuristic algorithm based on the echolocation behavior of bats. BA has proven to have better performance than other well-known algorithms like particle swarm optimization (PSO) and genetic algorithm (GA). However, the research on using BA for binary and multi-objective optimization has just begun. In this paper we propose a multi-objective binary bat algorithm (MBBA) for multi-objective optimization in binary search space. The algorithm uses a modified bat position updating strategy which works better with binary problems, a mutation operator is introduced to improve the local search ability and help the diversity of algorithm, a Pareto dominance based approach with external elitist archive to find optimal Pareto solutions, and a flight leader selection approach to help bat ight. An experimental study is done on multiple multi-objective benchmarks to test the performance of the proposed algorithm and compare it to the performance of non-dominated sorting genetic algorithm II (NSGA-II). The experimental results show that the proposed MBBA is a competitive multi-objective algorithm and outperforms NSGA-II.