Multi-objective Meta-heuristic Algorithms Research Articles

A novel technique for multi-objective sustainable decisions for pavement maintenance and rehabilitation

To maintain pavement in good condition while considering financial costs and sustainability, it is necessary to develop a comprehensive pavement management plan. Pavement Maintenance and Rehabilitation (M&R) consists of two essential components: firstly, predicting the pavement condition within a specified timeframe, and secondly, employing an appropriate optimization algorithm. This study utilized three ensemble learning techniques including extreme gradient boosting, categorical boosting, and light gradient boosting machine to develop accurate predictions about the pavement condition. Subsequently, the most accurate prediction technique, which was extreme gradient boosting, was combined with non-dominated sorting genetic algorithm III which is a multi-objective metaheuristic optimization algorithm, resulting in a hybrid technique that offers highly accurate multi-objective maintenance and rehabilitation planning. Although previous studies neglected important criteria such as road closure in the optimization process, this study takes into account four objective functions including greenhouse gas emission, M&R cost, pavement condition, and road closure to be minimized over a 5-year program. This process generated 52 non-dominated optimal solutions known as the Pareto front. To compare and rank various optimal maintenance and rehabilitation plans, grey relational analysis was employed. The results suggested that there is a direct correlation between M&R costs and GHG emissions. Minimizing only pavement conditions in the planning can significantly increase GHG emissions, M&R costs, and road closure. Implementing preventive M&R actions can reduce M&R costs and overall road closure while light and medium rehabilitation actions are recommended to optimize the condition of pavements.

A combined interval prediction system based on fuzzy strategy and neural network for wind speed

Wind energy exhibits strong fluctuations and intermittencies. The accurate prediction of wind speed is of considerable significance for the operation and maintenance of wind farms and the safety of the power grid. However, previous studies have often ignored the impact of data noise on trend prediction, and lacked effective data pre-processing methods and adaptive interval prediction schemes, resulting in poor prediction results. To improve the accuracy of prediction, this paper proposes a wind-speed combination interval prediction system based on a fuzzy strategy and neural network. This study used a fuzzy strategy to pre-process the data and proposed a joint optimization algorithm that uses multiple multi-objective metaheuristic algorithms to optimize the neural network jointly. An improved prediction hybrid algorithm was used to reconstruct the predicted results. Finally, based on the fuzzy theory and neural network, interval prediction schemes that can adapt to different situations were proposed. Wind-speed data from the Penglai Wind Farm in China were used for verification. The mean absolute percentage error of the wind-speed point prediction was 3.75%, and the prediction interval coverage probability of the wind-speed interval prediction was 97.92%. The experimental results showed that the proposed model not only outperforms other comparable models but also improves the prediction interval coverage probability by 176.4% compared with the baseline model. This proves that the integrated hybrid model can improve the accuracy and effectiveness of wind-speed prediction. The accurate interval prediction of wind speed can result in the complementary scheduling of renewable energy generation and the sustainable development of the energy field, and support intelligent upgrades.

A multi-objective optimization model of truck scheduling problem using cross-dock in supply chain management: NSGA-II and NRGA

PurposeThis paper aims to develop a multi-objective problem for scheduling the operations of trucks entering and exiting cross-docks where the number of unloaded or loaded products by trucks is fuzzy logistic. The first objective function minimizes the maximum time to receive the products. The second objective function minimizes the emission cost of trucks. Finally, the third objective function minimizes the number of trucks assigned to the entrance and exit doors.Design/methodology/approachTwo steps are implemented to validate and modify the proposed model. In the first step, two random numerical examples in small dimensions were solved by GAMS software with min-max objective function as well as genetic algorithms (GA) and particle swarm optimization. In the second step, due to the increasing dimensions of the problem and computational complexity, the problem in question is part of the NP-Hard problem, and therefore multi-objective meta-heuristic algorithms are used along with validation and parameter adjustment.FindingsTherefore, non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are used to solve 30 random problems in high dimensions. Then, the algorithms were ranked using the TOPSIS method for each problem according to the results obtained from the evaluation criteria. The analysis of the results confirms the applicability of the proposed model and solution methods.Originality/valueThis paper proposes mathematical model of truck scheduling for a real problem, including cross-docks that play an essential role in supply chains, as they could reduce order delivery time, inventory holding costs and shipping costs. To solve the proposed multi-objective mathematical model, as the problem is NP-hard, multi-objective meta-heuristic algorithms are used along with validation and parameter adjustment. Therefore, NSGA-II and NRGA are used to solve 30 random problems in high dimensions.

Using common redundancy components for suppliers in a supply chain network design problem considering energy costs and environmental effects

Improving the reliability of factories and suppliers through appropriate allocation of redundancy components is crucial in responding to customer demand. However, if individual factories independently buy and allocate redundancy components, huge investments will be required. To optimize the reliability level and costs of the supply chain network, the present study allocates these components to suppliers based on customer demand. While allocating redundancy components to factories improves the chain's reliability, it increases energy consumption and greenhouse gas emissions. Therefore, a balance between cost, reliability, and pollution needs to be established. The study considers a three-level supply chain, including the supplier (factories), distributor, and retailer, with stochastic and normally distributed demand assumed for each retailer. To address demand fluctuations, the risk pooling effect is implemented. As the problem belongs to the class of NP-hard problems, the study develops three multi-objective meta-heuristic algorithms, namely Non-dominated Sorting Genetic Algorithm II (NSGAII), Archived Multi-Objective Simulated Annealing (AMOSA), and Multi-Objective Artificial Bee Colony (MOABC) to solve it. The performance of these algorithms is evaluated using the results of the complete enumeration method. The comparison results based on six multi-objective performance metrics show that the MOABC algorithm has better performance in finding high-quality solutions in less time, while the NSGAII algorithm provides more diverse Pareto optimal solutions.

Addressing a Collaborative Maintenance Planning Using Multiple Operators by a Multi-Objective Metaheuristic Algorithm

Selective maintenance has a significant impact on the sustainable management of maintenance operations. The collaboration of multiple maintenance teams/operators is helpful to achieve sustainability for selective maintenance sequence planning. For products with a large number of components, a single maintenance team/operator is inefficient due to a long completion time which is not acceptable for emergency planning. Providing specific and efficient maintenance sequence planning is critical to effectively handle different types of emergencies (e.g., wartime) while avoiding vague task assignments to multiple maintenance teams/operators. For scheduling many maintenance jobs while improving the efficiency and quality of maintenance operations, this study proposes a collaborative maintenance planning based on the concept of imperfect maintenance. In this regard, this study develops a multi-objective optimization model to optimize parallel maintenance sequences considering maintenance profit, maintenance cost, maintenance team, and resource limitations. We show the feasibility of the proposed multi-objective optimization model through a real case of maintenance practice for the components of an assistor device. For analyzing the complexity of the proposed maintenance sequence planning problem, this study introduces a new multi-objective metaheuristic algorithm which is an enhanced multi-objective gravitational search algorithm (EMOGSA) to find high-quality Pareto solutions for the proposed problem. Different multi-objective evaluation metrics are used to study the performance of the proposed algorithm. From the results, the proposed model and developed solution algorithm can help maintenance decision-makers to determine complex maintenance planning. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper deals product with a maintenance and proposes gravitational search algorithm based on only maintenance task, which maintenance task. The goal of this paper is to analyze the maintenance problem from the perspective of collaboration of multiple maintenance teams/operators.

Multi-objective metaheuristic optimization algorithms for wrapper-based feature selection: a literature survey

In the data mining and machine learning (ML) discipline, feature selection problem is considered among many researchers in the recent times. Feature selection process targets to minimize feature set number and maximize performance accuracy by identifying optimal features. Multiple objectives are considered while identifying the optimal feature hence multi-objective metaheuristic optimization algorithms (MOMOAs) are applied. In this study, literature review is performed MOMOAs-for solving wrapper feature selection problem (WFS). The literature review for solving WFS problem and discuss the challenges faced by the researchers in solving the feature selection problem. The literature review is performed on all relevant studies published in the last 12 years [2009-2022]. A detailed overview of the feature selection preliminaries, MOMOAs-WFS, role of the classifier in feature selection problem are presented. The outcome of this literature review is to highlight the existing works related to WFS problem using MOMOAs. Finally, the research areas for improvement are identified and emphasized for the scientists to survey in the field of MOMOAs.

Enhancing Urban Surface Runoff Conveying System Dimensions through Optimization Using the Non-Dominated Sorting Differential Evolution (NSDE) Metaheuristic Algorithm

Rapid urban development and increase in construction have significantly altered the surface coverage of cities, resulting in a rise in impervious surfaces such as roofs, streets, and pavements. These changes act as barriers against rainwater infiltration into the soil, leading to a substantial increase in surface runoff. Managing surface runoff has become a critical task in civil engineering and urban planning, as it can mitigate damage and provide opportunities for utilizing excess water. However, traditional flood control and guidance systems tend to be extensive and expensive, prompting researchers to explore cost-effective alternatives that consider all design parameters and variables. In this research, we propose an innovative approach that combines the NSDE (non-dominated sorting differential evolution) metaheuristic algorithm as an optimizer with the SWMM (storm water management model) as a simulator. The objective is to design efficient surface runoff collection networks by thoroughly investigating their hydraulic behaviors. This study focuses on the Chitgar watershed in Tehran, Iran, utilizing the SWMM model and NSDE multi-objective metaheuristic algorithm to determine the optimal dimensions of the channel and its intersecting structures. The aim is to minimize costs and reduce water leakage from the network. A comparison is made between the optimized design results and the existing network plan (without any design modifications). The analysis reveals substantial reductions in water leakage for all three design scenarios: a 7.66% reduction when considering only bridges, a 7.35% reduction with only the canal, and an impressive 95.26% reduction when both the canal and bridges are incorporated. These findings demonstrate the superiority of the optimized designs in terms of cost-effectiveness and the efficient management of surface runoff.

Application of state-of-the-art multiobjective metaheuristic algorithms in reliability-based design optimization: a comparative study

Application of state-of-the-art multiobjective metaheuristic algorithms in reliability-based design optimization: a comparative study

A metaheuristic-driven physical asset risk management framework for manufacturing system considering continuity measures

To ensure the uninterrupted operation of physical assets, the effective implementation of risk mitigation plans (RMPs) and business continuity plans (BCPs) for critical assets is required. However, manufacturing decision-makers face the challenge of allocating limited resources between RMPs and BCPs while prioritizing sustained success. To address this challenge, a novel approach proposes integrating a metaheuristic algorithm into a risk management framework that considers interconnected risks. The framework utilizes a Bayesian Network (BN) to model interdependencies among critical physical asset risks. It determines the optimal combination of BCPs and RMPs, considering continuity measures and resource limitations. A physical asset risk assessment process evaluates operational and disruption risks based on expected loss and probabilities within the risk network. Given the complexity, the proposed framework incorporates hybrid multi-objective metaheuristic algorithms (e.g., Nondominated Sorting Genetic Algorithm II (NSGA-II), Strength Pareto Evolutionary Algorithm 2 (SPEA2), Multi-Objective Particle Swarm Optimization (MOPSO), and Pareto Envelope-based Selection Algorithm II (PESA-II)) combined with a reinforcement learning approach. A case study of a manufacturing company demonstrates the framework’s applicability and discusses the results. The findings show a significant reduction in the expected loss within the risk network and migration of most physical asset risks from high-risk to acceptable areas. Additionally, a sensitivity analysis examines the available budget, aiding decision-makers in determining the necessary compromise between asset availability and network risk level. In conclusion, the proposed framework empowers decision-makers to allocate resources effectively, prioritize RMPs and BCPs, and ensure continuity for critical physical assets, thereby fostering sustained success in manufacturing systems.

Optimal Exploitation of Urban Water Supply Networks Based on Pressure Management with the Nondominated Sorting Differential Evolution (NSDE) Algorithm

Urban water distribution networks are crucial infrastructures for providing essential services to society, but their exorbitant costs and limited water resources make their optimization a critical research area. Optimal management and design of these networks can help to reduce costs and enhance their efficiency while meeting technical, economic, and quality standards. In particular, the management of network pressure is critical for reducing leakage in water distribution systems. Thus, this study aimed to investigate two objective functions for optimizing the water distribution network: (i) minimizing costs while considering the number of pressure-relief valves, and (ii) minimizing network pressure by observing the optimal pressure range. To achieve this, the Nondominated Sorting Differential Evolution (NSDE) multi-objective metaheuristic algorithm was employed as the optimization tool, and a computer program was written in MATLAB software for solving the optimization models. EPANET software was also used for hydraulic simulation of the water distribution network. The efficiency and capabilities of these models were tested on the case study of the third district of Mashhad in Iran. The results indicated that the installation and adjustment of pressure-relief valves in accordance with the positions and optimal settings of the output of the proposed models significantly improved the desired goals, particularly the average pressure of the network. As an example of optimization, the study achieved a 56.12% reduction in pressure compared to the case without a plan, considering five pressure-relief valves.

Efficient multi-objective metaheuristic algorithm for sustainable harvest planning problem

The shift towards sustainable and regenerative agriculture is being propelled by global farmers due to increasing awareness of social inequalities and climate change. To make this transition a reality, farmers should consider various sustainability factors including all economic, environmental, and social factors, and tackle the complexity of the harvest planning. This study introduces a new multi-objective optimization approach that employs fuzzy logic and multiple objectives to facilitate sustainable harvest planning in the face of various sources of uncertainties such as changes in commodity prices, weather conditions, crop ripening patterns, and productivity fluctuations. The model seeks to optimize profit while minimizing greenhouse gas emissions and wastes generated by harvesting machines as the economic and environmental dimensions. To incorporate social sustainability, we define the farmer's working days on each block as a constraint set in our model. To address the complexity of this optimization model in large-scale networks, this paper proposes a revised version of the non-dominated sorting genetic algorithm (NSGA-II) using the genetic engineering concept, called the non-dominated sorting genetic engineering algorithm (NSGEA). This article showcases the outcomes of a case study that employed the blueberry industry in Canada. The findings indicate that the NSGEA algorithm, which was proposed in the study, is effective in addressing our multi-objective optimization model in comparison to other metaheuristic algorithms and the epsilon constraint method. This paper concludes by discussing theoretical contributions and managerial insights that emphasize the advantages of the proposed multi-objective harvest planning problem for achieving sustainable blueberry agriculture in Canada.

Elderly people evacuation planning in response to extreme flood events using optimisation-based decision-making systems: A case study in western Sydney, Australia

Climate change is causing an increase in the frequency and severity of floods in various regions globally, raising concerns about the efficacy of evacuation planning strategies that were created under different climate scenarios, particularly for vulnerable individuals. Urban areas are at high risk of flooding, making the evacuation of elderly people to safer locations a potential necessity in many future flooding situations. However, despite the significance of transportation planning in the evacuation of the elderly, there has been little research considering the impact of disasters on the areas undergoing evacuation. This paper aims to address this research gap by presenting an integrated evacuation approach for elderly people under flooding conditions. The proposed model combines a flood simulator with multi-objective metaheuristic algorithms to minimise the expected evacuation time for all evacuees and reduce the number of rescue vehicles used. To improve the performance of the optimisation algorithms, dominant properties are established, which are used to create a local search. The proposed approach is tested and validated using a case study in Sydney, Australia, and the findings suggest that the proposed method can generate effective evacuation plans for the elderly in a reasonable amount of time under realistic emergency scenarios brought on by extreme flood events. The study adds to the body of knowledge on disaster risk reduction strategies both theoretically and practically, and has crucial policy implications for emergency managers, planners, and decision-makers in countries where urban areas are becoming increasingly vulnerable to climate change.

Ship traffic optimization method for solving the approach channel and lock co-scheduling problem of the Three Gorges Dam on the Yangzi River

Since the demands of waterway transport on the Yangzi River have been growing in recent years, traffic congestion at Three Gorges Dam (TGD) has become a very serious issue, which leads to long waiting time as well as environmental pollution. To improve the efficiency of the ship traffic scheduling, this paper investigates an approach channel and lock co-scheduling problem of the TGD on the Yangzi River. A new mathematical model is presented to optimize the lock chamber utilization rate, average waiting time and total energy consumption of ships, simultaneously. To solve this problem, a multi-objective metaheuristic algorithm (MOMA) based on fuzzy correlation entropy is proposed. In the algorithm, with a ship sequence encoding scheme, a pre-grouping panning approach is firstly designed for decoding. Then, a fitness evaluation mechanism using fuzzy correlation entropy is adopted to assess the solutions. Finally, an adaptive local reinforcement search strategy is introduced to improve local intensification ability. Various simulation experiments are carried out based on the real historical data at TGD. Computational results demonstrate the applicability and effectiveness of proposed MOMA. The result of this study is very useful for TGD to improve the ship traffic efficiency and save energy.

Multi-objective SHADE with manta ray foraging optimizer for structural design problems

This paper presents a hybrid multi-objective success history-based parameter adaptive differential evolution (SHADE) with manta ray foraging optimizer (MRFO) for structural design problems, called MO-SHADE-MRFO. In the proposed algorithm, the updating rules of SHADE, a variant of differential evolution with great performance, are combined with the operators from MRFO, a recent swarm-based metaheuristic algorithm inspired from the manta ray with cyclone, chain and somersault foraging behaviors, which can balance the exploration and exploitation of the algorithm for structural design problems. Furthermore, MO-SHADE-MRFO utilizes the external archive to save and update the obtained Pareto fronts during the optimization process. The proposed algorithm is verified by multi-objective truss optimization problems with two objectives of minimizing the structural weight and the compliance, including 10-bar, 25-bar, 37-bar, 120-bar, 200-bar and 942-bar truss problems. Moreover, 9 different multi-objective metaheuristic algorithms are implemented to compare with the proposed algorithm, where three metrics are used to measure the performance of the algorithms, including hypervolume (HV), inverted generational distance (IGD), and spacing-to-extent (STE). According to the experimental results, MO-SHADE-MRFO can provide the best statistical values of HV, IGD and STE in most cases, ranking the first among the compared algorithms. Besides, the proposed algorithm also gives well-distributed Pareto solutions for the tested problems, illustrating the effectiveness of the hybrid updating rules of SHADE and MRFO.

Optimized prediction models for faulting failure of Jointed Plain concrete pavement using the metaheuristic optimization algorithms

This study aims to predict faulting failure of jointed plain concrete pavement (JPCP) using different variables. For this purpose, four feature selection methods were developed by combining the artificial neural networks (ANN) and four multi-objective metaheuristic optimization algorithms, namely, the Pareto envelope-based selection algorithm II (PESA-2), the strength Pareto evolutionary algorithm 2 (SPEA-2), multi-objective particle swarm optimization (MPSO), and multi-objective evolutionary algorithm based on decomposition (MOEA/D). The MOEA/D showed better performance compared to the other models, which identified 17 input variables affecting faulting failure. In the next step, the classic back-propagation (BP), Biogeography-based optimization (BBO), invasive weed optimization (IWO), and simulated annealing algorithm (SAA) were combined with the ANN to develop three prediction models for faulting failure. Modeling with metaheuristic optimization algorithms showed better performance than the ordinary ANN. The pavement age, cumulative average precipitation, and elasticity modulus of the concrete slab have the most significant impact on the formation and increase of faulting.

Efficient multi-objective meta-heuristic algorithms for energy-aware non-permutation flow-shop scheduling problem

This study investigates the optimization of non-permutation flow-shop scheduling problems and lot-sizing simultaneously. Contrary to previous works, we first study the energy awareness of non-permutation flow-shop scheduling and lot-sizing using modified novel meta-heuristic algorithms. In this regard, first, a mixed-integer linear mathematical model is proposed. This model aimed to determine the size of each sub-category and determine each machine's speed within each sub-category to minimize makespan and total consumed energy simultaneously. In order to optimize this model, Multi-objective Ant Lion Optimizer (MOALO), Multi-objective Keshtel Algorithm (MOKA), and Multi-objective Keshtel and Social Engineering Optimizer (MOKSEA) are proposed. First, the validation of the mathematical model is evaluated by implementing it in a real case of the food industry using GAMS software. Next, the Taguchi design of the experiment is applied to adjust the meta-heuristic algorithms' parameters. Then the efficiency of these meta-heuristic algorithms is evaluated by comparing with Epsilon-constraint (EPC), Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Particle Swarm Optimization (MOPSO) using several test problems. The results demonstrated that the MOALO, MOKA, and MOKSEO algorithms could find optimal solutions that can be viewed as a set of Pareto solutions, which means the used algorithm has the necessary validity. Moreover, the proposed hybrid algorithm can provide Pareto solutions in a shorter time than EPC and higher quality than NSGA-II and MOPSO. Finally, the model's key parameters were the subject of sensitivity analysis; the results showed a linear relationship between the processing time and the first and second objective functions.

Performance Analysis of Current Multi-Objective Metaheuristic Optimization Algorithms for Unconstrained Problems

Multi-objective optimization is a method used to produce suitable solutions for problems with more than one Objective. Various multi-objective optimization algorithms have been developed to apply this method to problems. In multi-objective optimization algorithms, the pareto optimal method is used to find the appropriate solution set over the problems. In the Pareto optimal method, the Pareto optimal set, which consists of the solutions reached by the multi-objective optimization, includes all the best solutions of the problems in certain intervals. For this reason, the Pareto optimal method is a very effective method to find the closest value to the optimum. In this study, the Multi-Objective Golden Sine Algorithm we developed (MOGoldSA), the recently published Multi-Objective Artificial Hummingbird Algorithm (MOAHA), and the Non-Dominant Sequencing Genetic Algorithm II (NSGA-II), which has an important place among the multi-objective optimization algorithms in the literature, are discussed. In order to see the performance of the algorithms on unconstrained comparison functions and engineering problems, performance comparisons were made on performance metrics

A Performance-Oriented Optimization Framework Combining Meta-Heuristics and Entropy-Weighted TOPSIS for Multi-Objective Sustainable Supply Chain Network Design

The decision-making of sustainable supply chain network (SSCN) design is a strategy capacity for configuring network facility and product flow. When optimizing conflicting economic, environmental, and social performance objectives, it is difficult to select the optimal scheme from obtained feasible decision schemes. In this article, according to the triple bottom line of sustainability, a multi-objective sustainable supply chain network optimization model is developed, and a novel performance-oriented optimization framework is proposed. This framework, referred to as performance-oriented optimization framework, integrates multi-objective meta-heuristic algorithms and entropy-weighted technique for order preference by similarity to an ideal solution (EW-TOPSIS). The optimization framework can comprehensively evaluate the performance of overall SSCN by EW-TOPSIS and guide the evolution process of algorithms. In this framework, decision-makers can obtain the feasible schemes calculated by meta-heuristics and determine the optimal one according to the performance value evaluated by EW-TOPSIS. This article combines three performance evaluation strategies with four meta-heuristic algorithms, namely, non-dominated Sorting Genetic Algorithm-II (NSGA-2), multi-objective differential evolutionary (MODE), multi-objective particle swarm optimization (MOPSO), and multi-objective gray wolr optimization (MOGWO), for verifying the effectiveness of the performance-oriented optimization framework. The results validate that the proposed framework has much better sustainability performance than the traditional optimization algorithms and evaluation methods. Furthermore, the proposed performance-oriented optimization framework can provide managers with a special optimal scheme with the best sustainability performance. Finally, some research prospects are presented such as more multi-criteria decision making methods.

Comprehensive assessment of 20 state-of-the-art multi-objective meta-heuristic algorithms for multi-reservoir system operation

Optimal operation of multi-purpose multi-reservoir dams is a challenging problem for dams’ stakeholders and decision-makers. Optimization algorithms are able to present reliable solutions for such complex problems. This study compared the capability of 20 state-of-the-art robust meta-heuristic algorithms for determining the optimal operating policy of Halilrood multi-reservoir system under the three competing operational objectives of water supply, flood control, and hydropower generation. Before that, the performance of the algorithms in solving two benchmark problems (the Schaffer problem and the MMF1 problem from the CEC suite) was evaluated. Four metrics of generational distance (GD), spacing (S), spread (Δ), and maximum spread (MS) were used to compare the algorithms’ performance in solving the benchmark problems. In addition, four reservoirs performance evaluation indicators of reliability (Rel), resiliency (Res), vulnerability (Vul), and sustainability index (SI) were used to ass the algorithms’ performance in solving the real-case Halilrood problem. The results showed that although the solving capability of each algorithm depends on the nature of the problem, some algorithms were always superior in solving all three problems (2 benchmark problems and one real case). For the Schaffer benchmark problem, the MOAHA algorithm with the performance metrics of (GD = 0.00095, S = 0.58155, Δ = 0.20375, MS = 4.0002) had the best Pareto front in terms of coverage and diversity, and so it was placed at the first rank. In this problem, the MOCryStAl algorithm with (GD = 0.00141, S = 0.48395, Δ = 1.49467, MS = 3.94799) placed at the lowest rank. For the MMF1 problem, the MOMA (GD = 0.00751, S = 0.07516, Δ = 0.29519, MS = 0.99826) followed by the MOAHA (GD = 0.00833, S = 0.07660, Δ = 0.17832, MS = 1.00) had the best performance, respectively, and the MOFA algorithms was the worst. For the Halilrood real-case problem, the MOGWO algorithm (with Rel = 83.41, Res = 67.57, Vul = 22.07 and SI = 76.01) followed by the MOAHA algorithm (Rel = 84.57, Res = 64.71, Vul = 33.60, and SI = 71.41) and the MOMA algorithm (Rel = 79.82, Res = 66.67, Vul = 21.65, and SI = 74.70) obtained the best ranks in terms of reservoir's performance evaluation indicators. They could successfully minimize all three objectives of the total deficit, the flood control and electricity generation indicating the highest performance of these algorithms in the optimization problem. The Pareto front obtained by these algorithms had better distribution and was closer to the origin of coordinates compared to the other utilized algorithms. They could favorably supply the total water demand in the Halilrood basin while increasing the hydropower energy generation up to the power plant capacity at the Jiroft dam. The results of this study can be applied to the optimal operation of any other multi-reservoir system with conflict in water demands.

Optimal Operation of a Distributed Generation Microgrid based on the Multi-Objective Genetic Algorithms

This document describes the application of multiobjective genetic algorithms as techniques and tools to optimize generation and distribution in small microgrids. In this way, genetic algorithms have been used for the allocation of distributed generation to reduce losses and improve the voltage profile. The IEEE14 network has been taken as a study and analysis model. This smart grid has 14 nodes and integrates several generation units, both conventional and renewable, transformers, and multiple loads. In this way, a multi-objective metaheuristic algorithm is proposed with the purpose of planning the power distribution grid based on a series of conditions such as the optimal generation configuration, the minimization of power losses in the lines, power transfer capacity, the reduction of CO2 emissions, and the optimization of the benefits obtained in renewable generation. The overall purpose is the development of an intelligent microgrid management system that is capable of determining the optimal configuration, by estimating demand, energy costs, and operating costs.