Evolutionary Many-objective Optimization Research Articles

Identification of energy management configuration concepts from a set of pareto-optimal solutions

Implementing resource efficient energy management systems in facilities and buildings becomes increasingly important in the transformation to a sustainable society. However, selecting a suitable configuration based on multiple, typically conflicting objectives, such as cost, robustness with respect to uncertainty of grid operation, or renewable energy utilization, is a difficult multi-criteria decision making problem. The recently developed concept identification technique can facilitate a decision maker by sorting configuration options into semantically meaningful groups (concepts).In this process, the partitioning of the objectives and design parameters into different sets (called description spaces) is a very important step. In this study we focus on utilizing the concept identification technique for finding relevant and viable energy management configurations from a very large data set of Pareto-optimal solutions. The data set consists of 20,000 realistic Pareto-optimal building energy management configurations generated by a many-objective evolutionary optimization of a high quality Digital Twin energy management simulator. We analyze how the choice of description spaces, i.e., the partitioning of the objectives and parameters, impacts the type of information that can be extracted. We show that the decision maker can introduce constraints and biases into that process to meet expectations and preferences. The iterative approach presented in this work allows for the generation of valuable insights into trade-offs between specific objectives, and constitutes a powerful and flexible tool to support the decision making process when designing large and complex energy management systems.

A Pareto dominance relation based on reference vectors for evolutionary many-objective optimization

Pareto dominance based approach is a classical method for solving multi-objective optimization problems (MOPs). However, as the number of objectives increases, the selection pressure drops sharply. Solutions with good convergence and diversity are hardly obtained. To tackle these issues, this paper proposes a Pareto dominance relation based on reference vectors (called PRV-dominance) for evolutionary many-objective optimization. In PRV-dominance, solutions in the population are divided into several subregions according to a set of uniform reference vectors. To enhance the convergence, a new convergence metric based on the ranking of objective function values is designed to determine the dominance relationship between two solutions. Then, the density in different subregions is considered to maintain the diversity. In order to verify the performance of our approach, WFG and MaF benchmark problems with 3, 5, 8, and 15 objectives are utilized. Experimental results demonstrate that the proposed PRV-dominance outperforms eight existing dominance relations in balancing convergence and diversity. An improved NSGA-II is suggested based on the proposed PRV-dominance, which shows the competitive performance when compared with six other state-of-the-art algorithms in solving many-objective optimization problems (MaOPs). The effectiveness of the proposed PRV-dominance is also verified on two other existing many-objective evolutionary algorithms.

Transfer learning based covariance matrix adaptation for evolutionary many-objective optimization

Evolutionary Algorithms (EA) have proven successful in solving Multi- and Many-objective Optimization Problems (MOPs/MaOPs) in numerous application areas. However, the various linkages among the decision variables may have posed a challenge for traditional evolutionary algorithms for solving such problems. In this paper, a transfer learning based covariance matrix adaptation algorithm, shortened as TL-M2M-CMA, is proposed to handle MOPs/MaOPs with complex decision variable linkage. In TL-M2M-CMA, the search population is first decomposed into a set of subpopulations and each subpopulation corresponds to a specific part of the Pareto-optimal Front (PF) of the MOP/MaOP. During the search, a covariance matrix adaptation process is utilized to learn the linkage among the decision variables, and then the covariance matrix is incorporated into the crossover and mutation operators for better efficiency. To facilitate performance comparison, a set of scalable MOP test instances with various linkage complexities is constructed for experimental studies. The performance of the proposed TL-M2M-CMA on these constructed instances is verified by comparing it to the performance of five state-of-the-art EA methods.

Expensive many-objective evolutionary optimization guided by two individual infill criteria

Expensive many-objective evolutionary optimization guided by two individual infill criteria

A Performance Indicator-Based Infill Criterion for Expensive Multi-/Many-Objective Optimization

In surrogate-assisted multi-/many-objective evolutionary optimization, each solution normally has an approximated value on each objective, resulting in increased difficulties in selecting solutions for expensive objective evaluations due to complicated trade-off between different objectives and accumulated uncertainty in the approximation of the objective functions. Thus, it is highly challenging to design an efficient model management strategy for surrogate-assisted expensive multi-/many-objective optimization. In this paper, a surrogate model is built for each objective function, based on which a set of promising candidate solutions are found. Additionally, a Gaussian process model is constructed to approximate a newly designed performance indicator measuring both convergence and diversity properties of individual solutions. Finally, the solution of the found candidate solutions having the maximum expected improvement in terms of the performance indicator is selected for evaluation using the expensive objective functions. Comparative experiments are conducted on 3-, 5-, and 10-objective DTLZ, WFG, and MaF test functions, as well as two real-world applications. The experimental results show that the proposed method is competitive compared to five state-of-the-art surrogate-assisted evolutionary algorithms for expensive multi-/many-objective optimization.

Exploring near-optimal locations for bioretention systems in catchment scale using many-objective evolutionary optimization

ABSTRACT Low impact developments (LIDs) are control measures to restore the hydrologic regime and enhance stormwater quality. Due to LID’s expensive capital and maintenance cost, the placement of LID controls in a watershed is an important planning task and still an open question in the specialized literature. This study proposes a simulation-optimization approach to place bioretention systems within a watershed to optimize their effectiveness. The Stormwater Management Model (SWMM) and the Non-dominated Sorting Genetic Algorithm III (NSGAIII) were coupled to identify the near-optimal locations of bioretentions for near-optimal quality and quantity controls, considering runoff volume, peak flow, total suspended solids, total nitrogen, and cost. Trade-offs were identified between cost versus other objective functions. The results suggest no specific spatial preference in placement of bioretentions under different rainfall regimes in watershed scale. However, in subcatchment scale, the near-optimal placement under single storm events is either maximum or none, while distributed under continuous simulation.

Growing neural gas assisted evolutionary many-objective optimization for handling irregular Pareto fronts

Reference vector adjustment approaches pose a considerable potential to strengthen the capability of decomposition-based evolutionary many-objective algorithms in handling many-objective optimization problems (MaOPs) with irregular Pareto-optimal fronts (PFs). However, most existing approaches often rely on the current population’s distribution, which may not well match MaOPs’ PFs. This can easily mislead the reference vector adjustment and impair algorithms’ performance. To address the abovementioned issue, this paper designs a growing neural gas-assisted evolutionary many-objective optimization algorithm, called GNG-EMO. Specifically, the proposal contains an environmental selection without reference vectors to maintain a well-diversified and converged archive over the PFs. Also, the GNG-EMO leverages a growing neural gas (GNG) network to learn Pareto-optimal fronts’ topologies using the solutions in the archive. In addition, to alleviate the issue that the nodes of the GNG network cannot reach the boundaries of Pareto-optimal fronts, we design an expansion mechanism to further diversify the nodes of the GNG network for constructing a set of better reference vectors. To evaluate the performance of the GNG-EMO, we compare it with five state-of-the-art competitors in the context of 48 test cases with irregular PFs. The numerical results demonstrate the GNG-EMO’s superior competitiveness by significantly outperforming all the five competitors on 27 test cases with respect to the indicator Hypervolume.

Coordinated Adaptation of Reference Vectors and Scalarizing Functions in Evolutionary Many-Objective Optimization

It is highly desirable to adapt the reference vectors to unknown Pareto fronts (PFs) in decomposition-based evolutionary many-objective optimization. While adapting the reference vectors enhances the diversity of the achieved solutions, it often decelerates the convergence performance. To address this dilemma, we propose to adapt the reference vectors and the scalarizing functions in a coordinated way. On the one hand, the adaptation of the reference vectors is based on a local angle threshold, making the adaptation better tuned to the distribution of the solutions. On the other hand, the weights of the scalarizing functions are adjusted according to the local angle thresholds and the reference vectors’ age, which is calculated by counting the number of generations in which one reference vector has at least one solution assigned to it. Such coordinated adaptation enables the algorithm to achieve a better balance between diversity and convergence, regardless of the shape of the PFs. Experimental studies on MaF, DTLZ, and DPF test suites demonstrate the effectiveness of the proposed algorithm in solving problems with both regular and irregular PFs.

A Many-Objective Evolutionary Algorithm Based on Indicator and Decomposition

In the field of many-objective evolutionary optimization algorithms (MaOEAs), how to maintain the balance between convergence and diversity has been a significant research problem. With the increase of the number of objectives, the number of mutually nondominated solutions increases rapidly, and multi-objective evolutionary optimization algorithms, based on Pareto-dominated relations, become invalid because of the loss of selection pressure in environmental selection. In order to solve this problem, indicator-based many-objective evolutionary algorithms have been proposed; however, they are not good enough at maintaining diversity. Decomposition-based methods have achieved promising performance in keeping diversity. In this paper, we propose a MaOEA based on indicator and decomposition (IDEA) to keep the convergence and diversity simultaneously. Moreover, decomposition-based algorithms do not work well on irregular PFs. To tackle this problem, this paper develops a reference-points adjustment method based on the learning population. Experimental studies of several well-known benchmark problems show that IDEA is very effective compared to ten state-of-the-art many-objective algorithms.

A new adaptive decomposition-based evolutionary algorithm for multi- and many-objective optimization

In decomposition-based multi-objective evolutionary algorithms (MOEAs), a set of uniformly distributed reference vectors (RVs) is usually adopted to decompose a multi-objective optimization problem (MOP) into several single-objective sub-problems, and the RVs are fixed during evolution. When it comes to multi-objective optimization problems (MOPs) with complex Pareto fronts (PFs), the effectiveness of the multi-objective evolutionary algorithm (MOEA) may degrade. To solve this problem, this article proposes an adaptive decomposition-based evolutionary algorithm (ADEA) for both multi- and many-objective optimization. In ADEA, the candidate solutions themselves are used as RVs, so that the RVs can be automatically adjusted to the shape of the Pareto front (PF). Also, the RVs are successively generated one by one, and once a reference vector (RV) is generated, the corresponding sub-objective space is dynamically decomposed into two sub-spaces. Moreover, a variable metric is proposed and merged with the proposed adaptive decomposition approach to assist the selection operation in evolutionary many-objective optimization (EMO). The effectiveness of ADEA is compared with several state-of-the-art MOEAs on a variety of benchmark MOPs with up to 15 objectives. The empirical results demonstrate that ADEA has competitive performance on most of the MOPs used in this study.

K-Pareto Optimality-Based Sorting with Maximization of Choice and Its Application to Genetic Optimization

Deterioration of the searchability of Pareto dominance-based, many-objective evolutionary optimization algorithms is a well-known problem. Alternative solutions, such as scalarization-based and indicator-based approaches, have been proposed in the literature. However, Pareto dominance-based algorithms are still widely used. In this paper, we propose to redefine the calculation of Pareto-dominance. Instead of assigning solutions to non-dominated fronts, they are ranked according to the measure of dominating solutions referred to as k-Pareto optimality. In the case of probability measures, such re-definition results in an elegant and fast approximate procedure. Through experimental results on the many-objective 0/1 knapsack problem, we demonstrate the advantages of the proposed approach: (1) the approximate calculation procedure is much faster than the standard sorting by Pareto dominance; (2) it allows for achieving higher hypervolume values for both multi-objective (two objectives) and many-objective (25 objectives) optimization; (3) in the case of many-objective optimization, the increased ability to differentiate between solutions results in a better compared to NSGA-II and NSGA-III. Apart from the numerical improvements, the probabilistic procedure can be considered as a linear extension of multidimentional topological sorting. It produces almost no ties and, as opposed to other popular linear extensions, has an intuitive interpretation.

A general framework for enhancing relaxed Pareto dominance methods in evolutionary many-objective optimization

A general framework for enhancing relaxed Pareto dominance methods in evolutionary many-objective optimization

A multiplicative maximin-based evaluation approach for evolutionary many-objective optimization

This paper presents a new fitness evaluation approach based on aggregated pairwise comparisons (APC), i.e., a multiplicative maximin fitness ranking indicator with norm-p (M2F-p), for solving multi/many-objective problems. The M2F-p uses an adjustable aggregation of pairwise comparisons induced by p to alleviate the incomparability of solutions in terms of Pareto dominance when the number of objectives increases. We analyze the search ability of M2F-p under different p values. It is shown that the p values can control the shape of contour lines (i.e., a set of equal M2F-p values), which can affect the convergence and uniformity of solutions. Then, we illustrate that the M2F-p offers a set of promising properties that can enhance the discriminability of solutions. Further, we develop an efficient algorithm based on M2F-p by using an adaptive p-selection strategy and a diversity-maintenance mechanism. We conduct experiments on a suit of test problems with up to 10 objectives. The experimental results validate the effectiveness of the proposed algorithm on both multi-objective problems and many-objective problems.

A local search-based many-objective five-element cycle optimization algorithm

The conception of memetic algorithms (MAs) has provided a new perspective in algorithmic design through hybridizing and combining of local search techniques and population-based search. Previous research has proven that the performance of some multi-objective evolutionary algorithms (MOEAs) could be improved by hybridization with local search strategy. However, when designing many-objective evolutionary optimization algorithms, if the ranking scheme relies on the Pareto dominance relation, it is quite challenging to evaluate solutions with several objective values and distinguish the most effective solutions from a population full of “the first rank” solutions. In this study, a new many-objective five-element cycle optimization algorithm based on a gradient-based local search method (termed LSMaOFECO) is proposed. In the evolutionary search part of LSMaOFECO, within the five-element cycle model, the forces exerted on every individual on different objective dimensions are summed up as an evaluating criterion to decide whether a solution should be accepted directly or updated. In the selection phase, this evaluation method is used to choose the next generation from the parents and the offspring when the dominance relation ranking loses effectiveness. In the local search part, three search tactics are proposed, among which the worst-objective-search tactic outperforms the other two in the experiment and is subsequently used in the updating phase of LSMaOFECO. The performance of the proposed algorithm is compared with six state-of-the-art multi- and many-objective algorithms by solving a set of many-objective test problems. The results obtained verify the utility of the LSMaOFECO in solving many-objective optimization problems (MaOPs).

Performance limits of the single screw expander in organic Rankine cycle with ensemble learning and hyperdimensional evolutionary many-objective optimization algorithm intervention

The operating performance of the expander, as the core component of the ORC system, directly determines the comprehensive performance of the system. Single screw expander (SSE) has received widespread attention due to its advantages such as large single-stage expansion pressure ratio, insensitivity to liquid, wide working range, and balanced forces. This study fully considers the strong coupling, high nonlinearity, large time variability and uncertainty between SSE performance evaluation indexes and operating parameters. On this basis, a scatter–bilinear interpolation hybrid feature selection approach is proposed, and the feature selection and analysis of the correlation degree among SSE performance evaluation indexes are conducted. In the high-dimensional space, the influence of operating parameters on different performance evaluation indexes is analyzed. Then, this study proposes the ensemble learning-driven non-dominated sorting genetic algorithm-III (NSGA-III) approach. An ensemble learning-driven NSGA-III model for SSE performance limit optimization is constructed on the basis of the scatter–bilinear interpolation hybrid feature selection method and the ensemble learning-driven NSGA-III approach. In the hyperdimensional space, the performance limits of SSE are obtained. When the comprehensive performance of SSE reaches its limit, the shaft efficiency, expansion pressure ratio, and power output are 53.71%, 7.76, and 10.83 kW, respectively. This research provides a reliable reference for analyzing, designing, and optimizing the SSE performance limits, and it also provides a direct guidance for obtaining the SSE performance limits in the ORC system.

On self-adaptive stochastic ranking in decomposition many-objective evolutionary optimization

Evolutionary multi-objective optimization problems have attracted increasingly attention in the evolutionary computing community. Now a lot of efforts have been devoted to this direction. For example, the proposed Pareto-dominated, decomposition-based and indicator-based methods have improved the scalability of multi-objective evolutionary algorithms (MOEAs). However, with the increase of the number of objectives, the portion of non-dominated individuals in the population is too large, and the distinguishability of individuals in the objective space decreases, which will affect the selection of elite solutions, thereby losing the balance of convergence and diversity. In this paper, a self-adaptive stochastic ranking method (SSR) is proposed to adaptively balance the convergence and diversity in high-dimensional space according to the state of the population. It has been embedded into the MOEA/D framework to form a novel multi-objective optimization algorithm, named MOEA/D-SSR. In addition, an improved shift-based density estimation strategy (ISDE) is adopted to enhance the convergence and diversity. Compared with the existing MOEAs on benchmark suite DTLZ and WFG with up to 10 objectives, the performance of the our algorithm has been verified. Experimental results show that the proposed algorithm is competitive compared with the most advanced MOEAs.

Dynamical Decomposition and Selection Based Evolutionary Algorithm for Many-Objective Evolutionary Optimization

Dynamical Decomposition and Selection Based Evolutionary Algorithm for Many-Objective Evolutionary Optimization

A comprehensive optimal design method for magnetorheological dampers utilized in DMU power package

The diesel multiple unit (DMU) has been widely used in high-speed railway service due to its flexibility and economy. Considering the broadband and complex vibration generated by DMU power package, the advanced semi-active suspension with magnetorheological (MR) dampers is introduced to promote anti-vibration performance. In this work, a comprehensive optimal design approach for MR damper used in DMU power package is proposed. Quasi-static modeling process is conducted to obtain MR damper's low-frequency outputs, while its high-frequency damping forces are calculated by physical modeling considering the fluid compressibility and piston assembly inertia. Then the objective functions and optimization variables are determined. Based on response surface and linear correlation analysis, the influence of the optimal variables on the objective functions is discussed. Using reference-point based nondominated sorting approach (NSGA-III), the evolutionary many-objective optimization is conducted. In addition, magnetic design is incorporated into the optimal process to ensure the magnetic flux density in the effective working area. Finally, an optimized MR damper prototype is manufactured and tested. By comparing the experimental damping force with calculated results in both low-frequency and high-frequency ranges, the effectiveness of the presented optimal method for MR dampers is validated.

An interactive tri-level multi-energy management strategy for heterogeneous multi-microgrids

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.

Thermodynamic analysis and high-dimensional evolutionary many-objective optimization of dual loop organic Rankine cycle (DORC) for CNG engine waste heat recovery

The complex and changeable working conditions of compressed natural gas (CNG) engines have brought great challenges to the efficient recovery of waste heat energy. The dual loop organic Rankine cycle (DORC) system can effectively recover and utilize CNG engine waste heat due to its structural advantages. Determining the nonlinear variations between operating parameters and thermodynamic performance serves as the basis for obtaining the thermodynamic performance limits of the DORC system. However, traditional analysis methods have obvious limitations in this area. Based on the bilinear interpolation algorithm, this paper comprehensively analyzes and evaluates the nonlinear and strong coupling characteristics between operating parameters and net power output, thermal efficiency, and exergy destruction. In addition, the comprehensive thermodynamic performance limits of the DORC system have a critical effect on its engineering application yet have not been thoroughly and comprehensively optimized. Therefore, this paper proposes an equilibrium-based thermodynamic high-dimensional evolutionary many-objective optimization (EMO) method for the DORC system. The optimal thermal efficiency, net power output, and total exergy destruction of the DORC system reached 37.11 kW, 14.27%, and 104.58 kW, respectively. Based on the optimization results under equilibrium and unequilibrium weight, the dominant relationship between the different thermodynamic performances of the DORC system is then analyzed. This research can provide a direct reference for analyzing and optimizing the comprehensive thermodynamic performance of the DORC system.