A multi-objective evolutionary algorithm based on mixed game strategy

A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems

Most evolutionary multiobjective optimization algorithms are designed to approximate the entire Pareto front. During the last decade, a series of preference-based evolutionary algorithms have been developed, where a part of the Pareto front is approximated by incorporating the preferences of a Decision Maker. However, only a few such algorithms are able to obtain well-distributed solutions covering the complete “region of interest” that is determined by a reference point. In this paper, a preference-based evolutionary algorithm for approximating the region of interest is proposed. It is based on the state-of-the-art genetic algorithm NSGA-II and the CHIM approach introduced in the NBI method which is used to obtain uniformly distributed solutions in the region of interest. The efficiency of the proposed algorithm has been experimentally evaluated and compared to other state-of-the-art multiobjective preference-based evolutionary algorithms by solving a set of multiobjective optimization benchmark problems. It has been shown that the incorporation of the Decision Maker’s preferences and the CHIM approach into the NSGA-II algorithm allows approximating the whole region of interest accurately while maintaining a good distribution of the obtained solutions.

In recent years, the use of decomposition methods has become a popular choice to solve complex multi-objective optimization problems. One possible approach to enhance the performance of a decomposition method is to couple it to a local search engine that speeds up convergence to the true Pareto front of a problem. Here, we propose a new local search strategy for continuous search spaces, which is based on the law of reflection of light. Our proposed approach computes reflected rays in order to explore and exploit promising subregions of the search space. The local search engine uses information of the Penalty Boundary Intersection method to create a scene with three elements: 1) a light source defined by the solution which is farthest from the ideal point, 2) a hyperspherical structure built by non-dominated neighboring solutions and 3) a set of reflected rays located in decision variable space. Our proposed local search engine is coupled to MOEA/D (a popular decomposition-based multi-objective optimizer) and is able to outperform three state-of-the-art multi-objective evolutionary algorithms, particularly in multifrontal problems.

Municipal solid waste incineration (MSWI) process is a complex industrial process with strong nonlinearity. It is a challenge to build a model for the MSWI process and carry out the corresponding optimization works. To solve this problem, the multiobjective optimization studies are conducted for both modeling and concerned indexes of the MSWI process, including the nitrogen oxides (NOx) emissions and the combustion efficiency (CE). First, a data-driven-based multiple-input multiple-output model is established for the NOx emissions and the CE of the MSWI process based on Takagi–Sugeno–Kang fuzzy neural network. Second, an adaptive large-scale multiobjective competitive swarm optimization (ALMOCSO) algorithm is designed for solving the multiobjective optimization problems (MOPs) of the MSWI process. A comprehensive evaluation system is proposed to complete the optimization foundation, and an adaptive scheme and multistrategy learning are proposed to improve the optimization effect of the ALMOCSO algorithm in solving complex MOPs. Then, a Pareto optimal set obtained from massive historical data is utilized as optimization reference to realize the dynamic multiobjective optimization for the NOx emissions and the CE of the MSWI process. Finally, the feasibility and effectiveness of the proposed methodology for optimizing the MSWI process are confirmed by the experiments using the data collected from a real MSWI plant. The results indicate that the modeling accuracy is satisfactory, and the CE is improved over 10% and the reduction of the NOx emissions is achieved 15.58%.

The potential and effectiveness of the newly developed Pareto-based multiobjective evolutionary algorithms (MOEA) for solving a real-world power system multiobjective nonlinear optimization problem are comprehensively discussed and evaluated in this paper. Specifically, nondominated sorting genetic algorithm, niched Pareto genetic algorithm, and strength Pareto evolutionary algorithm (SPEA) have been developed and successfully applied to an environmental/economic electric power dispatch problem. A new procedure for quality measure is proposed in this paper in order to evaluate different techniques. A feasibility check procedure has been developed and superimposed on MOEA to restrict the search to the feasible region of the problem space. A hierarchical clustering algorithm is also imposed to provide the power system operator with a representative and manageable Pareto-optimal set. Moreover, an approach based on fuzzy set theory is developed to extract one of the Pareto-optimal solutions as the best compromise one. These multiobjective evolutionary algorithms have been individually examined and applied to the standard IEEE 30-bus six-generator test system. Several optimization runs have been carried out on different cases of problem complexity. The results of MOEA have been compared to those reported in the literature. The results confirm the potential and effectiveness of MOEA compared to the traditional multiobjective optimization techniques. In addition, the results demonstrate the superiority of the SPEA as a promising multiobjective evolutionary algorithm to solve different power system multiobjective optimization problems.

<p style='text-indent:20px;'>In multi-objective evolutionary algorithms (MOEAs), non-domina-ted sorting is one of the critical steps to locate efficient solutions. A large percentage of computational cost of MOEAs is on non-dominated sorting for it involves numerous comparisons. By now, there are more than ten different non-dominated sorting algorithms, but their numerical performance comparing with each other is not clear yet. It is necessary to investigate the advantage and disadvantage of these algorithms and consequently give suggestions to specific users and algorithm designers. Therefore, a comprehensively numerical study of non-dominated sorting algorithms is presented in this paper. Firstly, we design a population generator. This generator can generate populations with specific features, such as population size, number of Pareto fronts and number of points in each Pareto front. Then non-dominated sorting algorithms were tested using populations generated in certain structures, and results were compared with respect to number of comparisons and time consumption. Furthermore, In order to compare the performance of sorting algorithms in MOEAs, we embed them into a specific MOEA, dynamic sorting genetic algorithm (DSGA), and use these variations of DSGA to solve some multi-objective benchmarks. Results show that dominance degree sorting outperforms the other methods, fast non-dominance sorting performs the worst and the other sorting algorithms performs equally.

A new approach in multi-objective evolutionary optimization is decomposition. Decomposition is a basic method in old multi-objective optimization which in evolutionary multiobjective optimization, has not been widely used. Using this method, a multi-objective optimization problem is converted into a number of scalar subproblems, and all the subproblems are simultaneously optimized. In this paper, the performance and efficiency of the algorithm MOEA/D (multi-objective evolutionary algorithm based on decomposition) with the performance of two algorithms NSGA-II and MOPSO (evolution optimization methods based on dominance) for solving constrained portfolio optimization in Tehran Stock Exchange, has been compared. Portfolio return and its risk, has been considered as the optimization objectives and CvaR has been considered as a risk measure. The results indicate the high potential of these algorithms for constrained portfolio optimization. Also, the results indicate that the optimization algorithm based on decomposition has lower computational complexity, and Pareto front is more extensive than the other two methods. (Abstract)

Distribution system (DS) service restoration is a very complex multi-objective and multi-constraint optimization problem, which requires high-quality Pareto fronts for helping the DS operators' work. This paper proposes a multi-objective evolutionary algorithm (MOEA) that combines the advantages of MOEAs in Tables with the properties of the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to recover Pareto fronts of the service problem. Its main differentials are its ability of recovering high-quality Pareto fronts, even in large-scale DSs, and of prioritizing switching operations in Remotely Controlled Switches (RCSs), independently of amount of RCSs. In opposite of Manually Controlled Switches (MCSs), RCS can be faster and cheapest operated from operating center. Several tests were carried out to validate and to compare the proposed MOEA to three MOEAs published in literature. Four metrics were used for assessing the quality of Pareto fronts generated and a Welch's t hypothesis test enabled the comparison of MOEAs' performance. Test results indicate the proposed MOEA outperforms those three MOEAs published in literature.

An Enhanced multi-objective evolutionary optimization algorithm based on decomposition (E-MOEA-D) proposed for optimal placement of Distributed Generation (DG) and Electric Vehicle (EV) Fast Charging Station (FCS) in distribution system. The diversity of the evolutionary algorithm improves the convergence and diverse solution in the process of evolutionary optimization. The proposed algorithm is improved using enhanced diversity algorithm, which yield diverse candidate solutions in population. The optimal placement of DGs and FCS are formulated using three objective functions as i) Active power loss ii) Voltage deviation iii) DG cost. The proposed algorithm is simulated on IEEE-33 bus distribution system. The proposed algorithm is compared with other competitive multi-objective evolutionary algorithms such as decomposition based multi-objective evolutionary algorithm (MOEA-D) and Non-dominated sorting multi-objective evolutionary algorithm (NSGA-II).

In order to protect the environment and slow down global warming trend, many governments and environmentalists are keen at promoting the use of plug-in hybrid electric vehicles (PHEVs). As a result, more and more PHEVs have been put into use. However, load peak caused by their disordered charging can be detrimental to an entire power grid. Several methods have been proposed to establish ordered PHEV charging. While focusing on single-objective load scheduling, they fail to meet the real requirements that need one to conduct multiple objective optimization. This paper formulates a multi-objective load scheduling problem to minimize two competing objectives: 1) potential serious peak-to-valley difference and 2) economic loss. When we apply existing multi-objective evolutionary algorithms (MOEAs), i.e., multi-objective particle swarm optimization (MOPSO), Nondominated Sorting Genetic Algorithm II, MOEA based on decomposition, and multi-objective differential evolutionary algorithm to solve it, because its high dimension and special conditions we find that they fail to reach the Pareto Front or converge into a relatively small area only. Therefore, we propose a weight aggregation (WA) strategy and implement a novel MOEA algorithm named WA-MOPSO by incorporating WA into MOPSO to solve the problem. Its effectiveness and efficiency to generate a Pareto front of this problem are verified and compared with those of the state-of-the-art approaches. Furthermore, WA is also combined with other MOEAs to solve the defined scheduling problem.

In this paper, we propose a Multi-objective Five-element Cycle Optimization algorithm based on Multi-strategy fusion (MOFECO-MS) to address the Bi-objective Traveling Thief Problem (BITTP), an extension of the Traveling Thief Problem that incorporates two conflicting objectives. The novelty of our approach lies in a unique individual selection strategy coupled with an innovative element update mechanism rooted in the Five-element Cycle Model. To balance global exploration and local exploitation, the algorithm categorizes the population into distinct groups and applies crossover operations both within and between these groups, while also employing a mutation operator for local searches on the best individuals. This coordinated approach optimizes parameter settings and enhances the search capabilities of the algorithm. Extensive experiments were conducted on nine BITTP instances, comparing MOFECO-MS against eight state-of-the-art multi-objective optimization algorithms. The results show that MOFECO-MS excels in both Hypervolume (HV) and Spread (SP) indicators, while also maintaining a high level of Pure Diversity (PD). Overall, MOFECO-MS outperformed the other algorithms in most instances, demonstrating its superiority and robustness in solving complex multi-objective optimization problems.

The parameter estimation tuning is one of the procedures of system identification. One of the identification problems is to find an optimal model structure especially for representing the complex multivariable dynamic systems. Therefore, this problem needs to be solved by using multi-objective optimization with two objective functions namely minimum predictive error and model complexity. In this paper, the tuning of control parameters is studied before comparing multi-objective evolutionary algorithms. The framework is based on the system identification problems. In parameter tuning, two main qualitative parameters of evolutionary algorithms are focused on crossover rate and mutation rate. The multi-objective evolutionary algorithms used for this study are an elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective optimization using differential evolution (MOODE). The different parameter settings are compared in order to obtain good parameter setting for NSGA-II and MOODE. Then, the performance for both algorithms is also compared using Pareto front. The plotted graphs of two objective functions show the non-dominated fronts achieved by the algorithms. The results proved that MOODE shows an advantage in solving system identification problems in a multivariable nonlinear dynamic system.

Runtime analysis of a multi-objective evolutionary algorithm for obtaining finite approximations of Pareto fronts

Multi-objective optimisation of software application mappings on heterogeneous MPSoCs: TONPET versus R2-EMOA

Broad learning approach to Surrogate-Assisted Multi-Objective evolutionary fuzzy clustering algorithm based on reference points for color image segmentation