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• An analysis of lexicographic optimization for feature selection and data classification. • Cooperative co-evolution for feature selection while the classifier hyperparameters are also being optimized. • Optimization of multiple objectives using a simple evolutionary algorithm. • A new lexicographic ranking methodology to compare the results of different feature selection methods. • Quite good results for real high-dimensional datasets. This paper starts with two hypotheses. The first one is that the simultaneous optimization of the hyperparameters regulating the classifier within a wrapper method, while the best subset of features is being determined, should improve the results with respect to those obtained with a pre-parameterized classifier. The second one is that solving these two problems can be formulated as a lexicographic optimization problem, allowing the use of a simple single-objective evolutionary algorithm to solve this multi-objective problem. The fitness function is of key importance for such wrapper methods. It is responsible for guiding the search towards potentially good solutions and it also consumes most of the runtime. Having these issues in mind, this paper also proposes a new lexicographic fitness function, designed to minimize the runtime of the algorithm and also to avoid over-fitting. Furthermore, the execution time and the quality of the results obtained by the wrapper procedure also depend on some algorithmic hyperparameters: the similarity thresholds used when comparing two different solutions lexicographically and the percentage of data samples used for validation during the training process. Thus, an experimental analysis has been carried out to find adequate values for these hyperparameters. Finally, the lexicographic cooperative co-evolutionary wrapper approach, using the new fitness function proposed in this paper, has been tested with several datasets belonging to the University of California, Irvine (UCI) repository and also with some real high-dimensional datasets, obtaining quite good results, compared to other state-of-the-art wrapper methods. The comparison has also been made lexicographically, with a new methodology proposed in this paper. [ABSTRACT FROM AUTHOR]

The number of research works on dynamic constrained optimization problems has been increasing rapidly over the past two decades. In this domain, many real-life decision problems need to be solved repeatedly with changing data and parameters. However, no research on dynamic problems with changes in the coefficients of the constraint functions has been reported. In this paper, to deal with such problems, a new evolutionary framework with multiple novel mechanisms is proposed. The new mechanisms are for (1) dealing with both linear and non-linear components in the constraint functions, (2) identifying the rate of change in the coefficients of the variables and (3) updating the population efficiently after every change occurs in the problem. To evaluate the performance of the proposed algorithm, we designed a new set of 13 dynamic benchmark problems, each of which consists of 20 dynamic changes and 3 different scenarios. The results demonstrate that the proposed algorithm significantly contributes in achieving good quality solutions, high feasibility rates and fast convergence in rapidly changing environments. In addition, the framework shows its capability of using different meta-heuristics to solve dynamic problems. [ABSTRACT FROM AUTHOR]

Decomposition-based multiobjective evolutionary algorithms are widely utilized for solving multiobjective optimization problems (MOPs). These algorithms have a higher degree of diversity due to a uniform distribution of the reference vectors in the objective space. However, these algorithms may struggle to select a suitable candidate set for solving many-objective optimization problems (MaOPs) with irregular Pareto fronts (PFs). To solve this problem, a solution potential-based adaptation reference vector evolutionary algorithm (SPARVEA) is proposed in this paper. In the algorithm, a concept called solution potential is presented to assess whether the direction of convergence of the solution to the ideal solution has potential. The solution potential is obtained with an evaluation function to calculate the potentials of the corresponding solutions. A solution potential-based adaptation strategy is then designed for adapting the reference vector to better guide the direction of convergence of the solution when solving MaOPs with irregular PFs. A modified angle penalty distance (mAPD) is adjusted to improve the convergence rate of the solution set in many-objective optimization problems. The proposed algorithm SPARVEA is compared with state-of-the-art many-objective evolutionary algorithms on four test sets with irregular PFs and four practical problems. Experimental results demonstrate the superior performance of SPARVEA on many-objective optimization problems. This contribution helps to advance the development of efficient algorithms for solving many-objective optimization problems. • SPARVEA is proposed for solving many-objective optimization problems with irregular Pareto fronts. • A concept of solution potential is evaluated to assess the direction of the solution to the ideal point. • A solution potential-based adaptation strategy is presented to adjust the reference vectors to guide the direction of convergence of the solution. • A modified angle penalty distance is adapted to control the convergence rate of the population. • The SPARVEA outperforms other contrasting state-of-the-art many-objective optimization algorithms. [ABSTRACT FROM AUTHOR]

Many engineering optimization problems fall into the category of Mixed-Integer Nonlinear Programming (MINLP) problems, which combine nonlinear relations, constraint conditions, and different types of variables, including continuous, integer, and/or discrete variables. Solving MINLP problems can be a challenging exploration process since their landscape can be composed of many discontinuous feasible parts with different sizes. In this scheme, Evolutionary Algorithms (EAs) often fail to generate enough diversity to explore the discontinuous feasible parts. Consequently, EAs are vulnerable to being attracted to larger discontinuous feasible parts, even if they are not promising regions. In this paper, a new proposal based on two fundamental strategies is presented to improve the performance of the differential evolution algorithm when solving MINLP problems. The first strategy considers a set of "good fitness-infeasible solutions" that contribute to exploring promising regions from infeasible contours. It reduces the vulnerability of the solutions to be attracted to larger discontinuous feasible parts with unpromising objective function values. The second is a composite trial vector generation to improve the combinatorial exploration while ensuring a robust convergence capacity toward the final solution. Sixteen well-known MINLP problems are used in several experiments to evaluate the performance of the proposed algorithm, comparing it to state-of-the-art EAs. The results provided by the proposal show a better performance in terms of quality, robustness, and computational cost. • Solving mixed-integer nonlinear programming problems can be challenging. • Improved differential evolution for mixed-integer nonlinear programming problems. • Good fitness-infeasible solutions contribute to exploring the smaller feasible regions. [ABSTRACT FROM AUTHOR]

The fitness landscape is a theory applied to the evolutionary dynamics of biological evolution to explain the behavior of evolutionary algorithms in the solution of optimization problems. With the continuous advancement of evolutionary algorithm optimization, a fitness landscape can present more abundant feature information, such as the local fitness, fitness distance correlation, and landscape roughness. These landscape features reflect the optimal solution distribution, quantity, and local unimodal topology of the optimization problem from various angles. This paper expresses the adaptability landscape features of typical optimization problems, engages in a quantitative analysis of the fitness distance correlation information, evaluates the difficulty of solving the problem within the search space, and obtains the correlation degree classification result. The search strategy adapts the mixed mutation and the fitness distance correlation for differential evolution. Empirical studies show that, the fitness distance correlation search strategy for the differential evolution algorithm can avoid falling into the local optimum, improve accuracy and convergence, and solve the single-objective optimization problem in a more comprehensive manner. [ABSTRACT FROM AUTHOR]

Coal consumption and free calcium oxide (f-CaO) content are two important production indicators in the cement calcination process, and its collaborative optimization is of great significance to improve the production performance. However, due to the multiple dynamic interferences and multiple conflicts between coal consumption and f-CaO, product quality is unstable and coal consumption becomes high. To address the problems, this paper proposes a multi-objective collaborative optimization method for cement calcination process. This method takes the coal consumption and f-CaO content as the optimization objectives to establish a multi-objective optimization model. In addition, to solve the problem that static single-step optimization is difficult to track the continuous change of working conditions, we propose a time domain rolling multi-objective Jaya algorithm (TDRM-Jaya) to optimize the model. The algorithm, involving a population update strategy, a selection strategy and a time domain rolling strategy, realizes the dynamic rolling optimization for the cement calcination process. The test comparison with several common intelligent optimization algorithms demonstrates the advantages of using TDRM-Jaya. Besides, practical industrial data validates the effectiveness of the proposed optimization method. [Display omitted] • A multi-objective optimization model of cement calcination process is developed. • A TDRM-Jaya algorithm is proposed applied to solve the optimization model. • The multi-objective collaborative optimization using data-driven model is studied. • Computational results show that the expected optimization effect can be achieved. [ABSTRACT FROM AUTHOR]

A large number of metaheuristic algorithms have been proposed in the last three decades, but no metaheuristic algorithm is superior to the others for all the optimization problems. It is laborious to select an appropriate metaheuristic algorithm to solve a problem, especially for laymen. In this paper, a framework for co-evolutionary algorithm using Q-learning with the meme is proposed, which is called as QLMA. The solution generation method in the metaheuristic algorithm is named meme, which is also viewed as the action for an agent in Q-learning, and multiple memes form the action set. In the initial stage, the tent map and opposition based learning are employed to obtain the initial population. In updating stage, a new population is generated by an action that is chosen from the action set by the agent in Q-learning, then the disruption operation is applied, avoiding excessive aggregation of solutions around the current global optimal solution and improving the balance between exploration and exploitation. QLMA is compared to sixteen algorithms on 23 classical benchmark functions, CEC 2017, and CEC 2019 benchmark functions. The experimental results demonstrate that QLMA is superior to the peer algorithms and has a good balance between exploration and exploitation. [ABSTRACT FROM AUTHOR]

This paper tries to extend the idea of single-objective differential evolution (DE) algorithm to a multi-objective algorithm. Most of the existing algorithms face the problem of diversity loss and convergence rate. In this paper, we propose a novel multi-objective DE algorithm to deal with this problem. In the validation process, the proposed method is validated in two steps. Firstly, the new homeostasis factor-based mutation operator incorporates multi-objective differential evolution algorithms (MODE). In this method, we use the Pareto optimality principle. We incorporate a new adaptive-based mutation operator (MODE) to create more diversity and enhance convergence rate among candidate solutions which provide better solutions to help the evolution. The effectiveness of the proposed method is evaluated on eight benchmarks of bi-objective and tri-objective test functions. Our proposed method performed well compared to the latest variants of multi-objective evolutionary algorithms (MOEAs). Secondly, the proposed method is used for an application-based test by applying it for software cost estimation. This method also incorporates multi-objective parameters, i.e., two objectives-based software cost estimation and three objectives-based software cost estimation. The proposed approach achieves better results in most software projects in terms of reducing effort and minimum error. • A novel multi-objective version of differential evolution is presented for solving complex problems. • A new homeostasis factor-based mutation operator is proposed. • The proposed algorithm is evaluated on eight well-known benchmarks test functions. • It is further applied to automatically predict the software cost models. [ABSTRACT FROM AUTHOR]

Prediction problems are difficult to be carried out in a dynamic environment, for two key questions: one is how to monitor environmental changes, the other is how to make respond timely after the environment has changed. Multi-population strategy is often adopted to address both two key problems. However, there are two stubborn questions that limit and affect the effectiveness of the strategy, i.e., (1) Search overlaps are easy to occur which lead to lose the ability of local exploit, (2) In the course of evolution, the search range of subpopulations tends to assimilate, so the subpopulation will gradually lose the ability to explore whole search space. Therefore, this paper adopts multi-population strategy, and presents a novel intelligence algorithm based on particle swarm optimization to solve the above problem, called adaptively reversed diffusion dual-drive evolutionary algorithm (ARDDEA). (1) Firstly, ARDDEA monitors the environmental changes by setting the global dynamic sentry in each subgroup. (2) Secondly, in order to avoid searching overlapping of the sub-population, a new exclusion strategy is proposed in this paper. A new distance determination method, i.e., between-swarms average Mahalanobis​ distance, is devised in the exclusion strategy to decide the inter-population distance. If the distance is too small between two sub-populations, furtherly, a Hill–valley decision function is used to determine whether they tracked the same peak or not. If so, the inferior subpopulations will be reinitialized by a reverse diffusion operation (RD) proposed in this paper. Besides, (3) a new dual-drive kinetic updating equation is proposed to enhance the search capability of the population. The new algorithm compared with several state-of-art dynamic optimization algorithms on the moving peak problem. The results show that the ARDDEA algorithm can track the optimal solution more effectively in the dynamic environment, and shows strong robustness and adaptability. It is a hope algorithm applied to prediction problems. • A novel dual-drive kinetic updating formula is proposed. • A between-swarms average Mahalanobis distance is devised in the exclusion strategy. • A Hill-valley decision is used to judge whether the two subpopulations overlap. • A reverse diffusion operation is proposed to reinitialize subpopulation. [ABSTRACT FROM AUTHOR]

There has been a growing interest in analyzing the dynamics and characteristics of networked systems, and the influence maximization problem is a recent hotspot to determine influential seeds from nodal members. Widespread applicable values can be found in marketing and information digging tasks, which boost more attention on related studies. Several diffusion models and seed determination techniques have been developed. Meanwhile, networked systems are threatened by sabotages and structural perturbances, and recent literature indicated that the robustness of the diffusion process is significant in daily applications, which can be modeled as the robust influence maximization problem. However, existing studies have not touched upon the node-based attack and its impact on the performance of seeds; corresponding robust seeds determination strategies are also lacked. For solving the robust influence maximization problem considering node-based attacks, a numerical measure is designed in this paper to assess the performance of given seeds. A sensitivity analysis is also conducted to test the impairing effect of several nodal importance metrics. Further, guided by the proposed measure, a memetic algorithm with the niching strategy has been devised to search for seeds with robust influential ability, termed NMA-RIM. Experiments on synthetic and real-world networks validate the competitiveness of NMA-RIM over existing algorithms, and the improved efficiency achieved by the niching strategy is also demonstrated. Meanwhile, the difference between selection results guided by the proposed measure and previous ones is shown via empirical analysis. As demonstrated by the obtained results, NMA-RIM outperforms existing approaches, and a better computational efficiency can be achieved. Competitive candidates can be provided for decision makers to solve information diffusion dilemmas. • The robustness of the influence diffusion process against node-based attacks has been investigated and evaluated. • The sensitivity the robustness of seeds against different importance metrics is tested. • A Memetic algorithm containing the niching strategy has been devised to solve the optimization problem. [ABSTRACT FROM AUTHOR]

• Propose a niching backtracking search algorithm with adaptive local search. • Backtracking search algorithm is applied in this field for the first time. • Develop a novel mutation based on the affinity propagation clustering. • Develop an adaptive local search strategy for the proposed algorithm. Multimodal multiobjective optimization problems,which widely exist in real-world applications, have multiple Pareto optimal sets in decision space corresponding to the same Pareto front in objective space. The key to handling such problems is locating and maintaining all Pareto optimal solutions in decision space simultaneously. The distribution of Pareto optimal solutions obtained by some existing multimodal multiobjective evolutionary algorithms is still not satisfactory. This paper proposes a niching backtracking search algorithm with adaptive local search to solve such problems. In the proposed algorithm, the affinity propagation clustering method as a parameter-free automatic niching technique is adopted to form multiple niches. A novel mutation based on affinity propagation clustering is then developed to search for more Pareto solutions within each niche. In addition, an adaptive local search strategy is designed in each niche to improve the search efficiency and the accuracy of Pareto optimal solutions. The proposed algorithm is compared with seven state-of-the-art multimodal multiobjective evolutionary algorithms on a multimodal multiobjective optimization test suite with 22 benchmark functions from CEC 2019 competition and a map-based practical application problem. The experimental results show that the proposed algorithm outperforms its competitors on 14 out of 22 benchmark functions in terms of the reciprocal of Pareto sets proximity and inverted generational distance in decision space metrics. Also, the proposed method is more effective and competitive than its competitors when solving the map-based practical application problem. [ABSTRACT FROM AUTHOR]

Multiobjective optimization is important in practical engineering applications. With the increased number of objectives, multiobjective optimization becomes more challenging due to the difficulty of convergence in population selection. A number of many-objective evolutionary algorithms (MaOEAs) have been designed to enhance population selection, but studies selecting parents for evolution are still rare. Fortunately, multiobjective immune algorithms (MOIAs) provide a promising approach to select high-quality parents for evolution. However, the existing MOIAs are not effective for solving many-objective optimization problems (MaOPs), as these algorithms consider only the local information of solutions for cloning but ignore the global information of populations; consequently, the populations of these algorithms may easily be trapped in local optima. To solve this problem, this paper proposes a many-objective immune algorithm with a novel immune cloning operator. In this approach, the global information in the population is used to estimate the quality of each solution, and only a few offspring from high-quality parents are generated in each generation to improve the convergence and diversity of the population. When the proposed algorithm is compared with nine MaOEAs and six MOIAs on three MaOP benchmarks with 5, 10, and 15 objectives, the experimental results validate that the proposed algorithm obtains the best performance in most cases. Moreover, the effectiveness of the proposed algorithm is also validated on one real-world optimization problem. [ABSTRACT FROM AUTHOR]

Students generally attempt to improve themselves with different manners in their spare time. Inspired by this fact, this paper presents a multi-objective elitist feedback teaching–learning-based optimization (MEFTO) algorithm for multi-objective optimization problems. To promote the exploration capacity and convergence of the basic teaching–learning-based optimization (TLBO), a feedback phase that simulates the spare-time learning phenomenon is introduced at the end of the learner phase. Students should compare their score with the average class score to select an appropriate means for further improvement. Poorly performing students can learn from the teacher directly for rapid improvement, whereas high-performing students prefer to motivate themselves for reinforcement learning. Non-dominated sorting is incorporated to permit this heuristic to solve problems with several objectives. Crowding distance calculation is adopted to maintain the diversity of the obtained solution set in a single run. Elitism strategy is also employed to provide a great improvement for the algorithm. The performance of the MEFTO algorithm is compared with seven other well-known algorithms by using a set of unconstrained benchmark test problems and three constrained engineering optimization problems. The qualitative and quantitative results indicate that the proposed algorithm can provide considerably competitive results and outperforms the other algorithms. • A novel multi-objective evolutionary algorithm (MEFTO) is developed. • The developed algorithm is evaluated on a series of benchmark functions. • The performance of the MEFTO is demonstrated using various metrics. • The developed algorithm is applied to solve three constrained engineering problem. [ABSTRACT FROM AUTHOR]

In this paper, a new compact algorithm is proposed. Two sinusoidal formulas are used to automatically adjust the crossover rate and the mutation scaling factor in the compact Differential Evolution (cDE) metaheuristic. The proposed algorithm, called Compound Sinusoidal cDE, CScDE, is compared to seven state-of-the-art compact algorithms on the well-known BBOB test-bed, the CEC-2014 test suite for continuous optimisation, as well as five real-world optimisation problems chosen from the CEC-2011 benchmarks. The CScDE algorithm outperformed its competitors for most problem categories and over most dimensions. It is also compared to some well-established population-based metaheuristics. • A compact compound sinusoidal differential evolution, CScDE, is proposed. • CScDE uses sinusoidal formulas to adjust the parameters of compact DE. • Both binomial and exponential crossover are tested. • CScDE is applied on 89 reference problems with several dimensions. • CScDE outperformed state-of-the-art compact algorithms. [ABSTRACT FROM AUTHOR]

• A two-stage evolution strategy is proposed for solving multi-objective problem. • The convergence and diversity should be balanced in multi-objective optimization. • A local searching method can improve the diversity of solutions in the space. • Experimental results have been presented by using statistical method. The balance of convergence and diversity plays a significant role to the performance of multi-objective evolutionary algorithms (MOEAs). The MOEA/D is a very popular multi-objective optimization algorithm and has been used to solve various real world problems. Like many other algorithms, the MOEA/D also has insufficient ability of convergence and diversity when tackling certain complex multi-objective optimization problems (MOPs). In this paper, a novel algorithm named MOEA/D-TS is proposed for effectively solving MOPs. The new algorithm adopts two stages evolution strategies, the first stage is focused on pushing the solutions into the area of the Pareto front and speeding up its convergence ability, after that, the second stage conducts in the operating solution's diversity and makes the solutions distributed uniformly. The performance of MOEA/D-TS is validated in the ZDT, DTLZ and IMOP problems. Compared with others popular and variants algorithms, the experimental results demonstrate that the proposed algorithm has advantage over other algorithms with regard to the convergence and diversity in most of the tested problems. [ABSTRACT FROM AUTHOR]

This paper tackles the short-term hydro-power unit commitment problem in a multi-reservoir system — a cascade-based operation scenario. For this, we propose a new mathematical modeling in which the goal is to maximize the total energy production of the hydro-power plant in a sub-daily operation, and, simultaneously, to maximize the total water content (volume) of reservoirs. For solving the problem, we discuss the Multi-objective Evolutionary Swarm Hybridization (MESH) algorithm, a recently proposed multi-objective swarm intelligence-based optimization method which has obtained very competitive results when compared to existing evolutionary algorithms in specific applications. The MESH approach has been applied to find the optimal water discharge and the power produced at the maximum reservoir volume for all possible combinations of turbines in a hydro-power plant. The performance of MESH has been compared with that of well-known evolutionary approaches such as NSGA-II, NSGA-III, SPEA2, and MOEA/D in a realistic problem considering data from a hydro-power energy system with two cascaded hydro-power plants in Brazil. Results indicate that MESH showed a superior performance than alternative multi-objective approaches in terms of efficiency and accuracy, providing a profit of $412,500 per month in a projection analysis carried out. • An efficient Multi-objective Evolutionary Swarm Hybrid algorithm is proposed. • Development of a nonlinear model to operational control of Hydro-power plants. • Hydro-power plant data regression obtains the maximum efficiency of the power units. • Efficiency energy goals achieved an increasing the profit in the energy production. [ABSTRACT FROM AUTHOR]

When evolutionary algorithms are employed to solve constrained optimization problems (COPs), how to efficiently make use of the information of some promising infeasible solutions is very important in the process of searching for the optimal feasible solution. In this paper, for selecting and making full use of some better infeasible solutions, a rankings-based fitness function method is designed. Specifically, the final fitness function of each individual is obtained by weighting two rankings, which are got after sorting the population based on the ɛ constraint technique and only based on the objective function, respectively. Furthermore, the weight is dynamically adjusted by considering the proportion of feasible solutions and generation information. By doing this, the tradeoff in constraints and objective can be addressed. Moreover, the promising offspring are generated by three differential evolution strategies with distinct characters to balance diversity and convergence. In addition, 116 benchmark problems from three test suites are used to evaluate the performance of the proposed method. Nine commonly used practical problems are selected to test the potential of the algorithm to solve real-world problems. Experimental results indicate that the proposed method shows superior or competitive to other state-of-the-art methods tailored for COPs. Moreover, the effectiveness of each introduced component in the proposed algorithm is investigated by the ablation study. • A new constrained evolutionary optimization algorithm is developed, denoted as DERFF. • Two rankings are got for each individual by two ways, one prefers constraint and the other prefers objective function. • The weight for summing these two rankings is dynamically adjusted by the proportion of feasible solutions and generation information. • Three evolutionary strategies are combined to balance the convergence and diversity of the population. • Experimental results indicate the effectiveness of the DERFF against other advanced algorithms. [ABSTRACT FROM AUTHOR]

With the development of cloud computing (CC), service-oriented architecture (SOA), and container technology, modeling and simulation (M&S) resources, such as simulation software and different sorts of models, can be shared and reused in a cloud environment. Modeling and Simulation as a Service (MSaaS), as a new paradigm, supports sharing simulation models or modeling tools and has enabled a wide range of model reuse. However, reusing or combining some immature models may result in inefficient M&S activities or even false simulation results. To make sure the appropriate reuse and composition of simulation models in cloud environments, which is also termed as model service composition for simulation (MSCS), this paper incorporates model maturity with service cooperation as a metric to evaluate the quality of model composition in cloud. Then, as a multi-objective optimization problem with multiple constraints, the MSCS problem and its process are described in detail. To solve the MSCS problem, a novel evolutionary algorithm named CA-AO-NSGAII is proposed. In the algorithm, adaptive crossover and mutation operators, as well as probabilistic initialization are developed. Furthermore, a half-local search algorithm in an elitist mechanism is designed for efficient decision-making. To validate the performance of CA-AO-NSGAII, experiments with respect to four different cases are conducted. Results show that the proposed method for addressing MSCS issue is effective and feasible. [ABSTRACT FROM AUTHOR]

This paper proposes a multi-level multi-energy management framework for the coordinated and interactive operation of heterogeneous multi-microgrids (MMGs) based on many-criteria optimality. With the proposed framework, the highly nonlinear and complex MMG multi-energy management (MMGMEM) problem is formulated into tri-level scheduling subproblems with multi-energy couplings and multi-level interactions, in which the multi-energy trading with energy networks and multi-energy couplings within MGs are optimized in the upper and middle level, and a middle level is added to correct scheduling decisions of the upper level for coordinating the MMG multi-energy sharing. Then, a multi-step matrix decomposition technique is developed to decompose the high dimensional multi-energy coupling matrix of MMGs into the sum of three linear and sparse submatrices for improving the computation efficiency and scalability. Furthermore, a many-criteria decision making (MCDM) model is proposed for the multi-energy sharing problem to achieve an optimum tradeoff in which all microgrids (MGs) can benefit from electricity-gas exchanges, and an evolutionary many-objective optimization based on hyperplane transformation algorithm is used to solve the MCDM problem. Simulation results verify that the proposed framework can achieve a cost saving for each MG (over 19%), and validate its scalability in solving large-scale MMGMEM problems. • A tri-level interactive framework is proposed for the coordinated operation of MMGs. • An extended multi-energy coupling matrix with MMG interactions is formulated. • A multi-step matrix decomposition technique is used to reduce the problem complexity. • A many-criteria optimality model is proposed for the tradeoff of all MGs' benefits. • The utilization of renewables can be enhanced with the minimal total operation cost. [ABSTRACT FROM AUTHOR]

Recently, decomposition has gained a wide interest in solving multi-objective optimization problems involving more than three objectives also known as Many-objective Optimization Problems (MaOPs). In the last few years, there have been many proposals to use decomposition to solve unconstrained problems. However, fewer is the amount of works that has been devoted to propose new decomposition-based algorithms to solve constrained many-objective problems. In this paper, we propose the ISC-Pareto dominance (Isolated Solution-based Constrained Pareto dominance) relation that has the ability to: (1) handle constrained many-objective problems characterized by different types of difficulties and (2) favor the selection of not only infeasible solutions associated to isolated sub-regions but also infeasible solutions with smaller CV (Constraint Violation) values. Our constraint handling strategy has been integrated into the framework of the Constrained Non-Dominated Sorting Genetic Algorithm-III (C-NSGA-III) to produce a new algorithm called Isolated Solution-based Constrained NSGA-III (ISC-NSGA-III). The empirical results have demonstrated that our constraint handling strategy is able to provide better and competitive results when compared against three recently proposed constrained decomposition-based many-objective evolutionary algorithms in addition to a penalty-based version of NSGA-III on the CDTLZ benchmark problems involving up to fifteen objectives. Moreover, the efficacy of ISC-NSGA-III on a real world water management problem is showcased. [ABSTRACT FROM AUTHOR]