Fitness Assignment Research Articles

A double decomposition based coevolutionary algorithm for distributed multi-objective OPF solution

Due to the vast and complex nature of the power systems, the study of distributed solution to multi-objective OPF (MO-OPF) problem is vital. However, the existing distributed MO-OPF approaches are based on mathematical programming techniques. The tedious repetition of algorithmic executions is inevitable. Moreover, they can hardly solve the non-differential problem. In this paper, the coevolutionary multi-objective evolutionary algorithm (MOEA), combining the idea of decomposition, is introduced to solve the distributed MO-OPF problem. The decomposition first occurs on decision variables. After segmenting, multiple subpopulations can coevolve in a distributed manner under the support of a new proposed distributed fitness evaluation method. Further, an objective decomposition (OBD) method is applied to the proposed distributed MO-OPF approach. The problem is decomposed again based on objective functions. By this OBD method, the fitness assignment problem is effectively alleviated and a more extensively covered pareto front can be obtained. The experimental results on two systems of different scales first show the effectiveness of the proposed distributed approach and then demonstrate the excellence of the OBD method in large-scale system.

Frequency Fitness Assignment: Optimization Without Bias for Good Solutions Can Be Efficient

A fitness assignment process transforms the features (such as the objective value) of a candidate solution to a scalar fitness, which then is the basis for selection. Under Frequency Fitness Assignment (FFA), the fitness corresponding to an objective value is its encounter frequency in selection steps and is subject to minimization. FFA creates algorithms that are not biased towards better solutions and are invariant under all injective transformations of the objective function value. We investigate the impact of FFA on the performance of two theoryinspired, state-of-the-art EAs, the Greedy (2+1) GA and the Self-Adjusting (1+(λ,λ)) GA. FFA improves their performance significantly on some problems that are hard for them. In our experiments, one FFA-based algorithm exhibited mean runtimes that appear to be polynomial on the theory-based benchmark problems in our study, including traps, jumps, and plateaus. We propose two hybrid approaches that use both direct and FFAbased optimization and find that they perform well. All FFAbased algorithms also perform better on satisfiability problems than any of the pure algorithm variants.

An ensemble learning-based multi-population evolutionary framework for multi-scenario multi-objective optimization problems

Multi-scenario multi-objective optimization problems (MSMOPs) are a topic of considerable interest in the field of optimization. The MSMOP contains a set of multi-objective optimization problems arising from varying operating conditions, with the goal of determining a set of communal compromise solutions. However, there are few universal methods available for MSMOPs. This paper presents a general method incorporating transfer learning for MSMOPs. First, a multi-scenario ensemble framework that transfers knowledge between scenarios is developed to combine arbitrary multi-objective evolutionary algorithms, where a scenario-based comprehensive evaluation indicator is developed for combination with base learners. Then, an adaptive decomposition-based multi-objective evolutionary algorithm with a bi-layer selection (EADaBS) is proposed and embedded within the framework as a base learner. EADaBS incorporates an adaptive fitness assignment in its first layer to facilitate exploration, and density measurement in its second layer to ensure exploitation. A rebalancing operator is also designed to aid the population towards the Pareto front. Finally, a multitude of experiments is conducted to verify the effectiveness and efficiency of the proposed algorithms. Two three-scenario multi-objective optimization problems are designed and utilized as test problems. The experimental results clearly demonstrate that the proposed framework outperforms existing state-of-the-art algorithms. In conclusion, this research provides new insights into the solution of MSMOPs.

A Modified Strength Pareto Evolutionary Algorithm 2 based Environmental /Economic Power Dispatch

A Strength Pareto Evolutionary Algorithm 2 (SPEA 2) approach for solving the multi-objective Environmental / Economic Power Dispatch (EEPD) problem is presented in this paper. In the past fuel cost consumption minimization was the aim (a single objective function) of economic power dispatch problem. Since the clean air act amendments have been applied to reduce SO2 and NOX emissions from power plants, the utilities change their strategies in order to reduce pollution and atmospheric emission as well, adding emission minimization as other objective function made economic power dispatch (EPD) a multi-objective problem having conflicting objectives. SPEA2 is the improved version of SPEA with better fitness assignment, density estimation, and modified archive truncation. In addition fuzzy set theory is employed to extract the best compromise solution. Several optimization run of the proposed method are carried out on 3-units system and 6-units standard IEEE 30-bus test system. The results demonstrate the capabilities of the proposed method to generate well-distributed Pareto-optimal non-dominated feasible solutions in single run. The comparison with other multi-objective methods demonstrates the superiority of the proposed method.

Many-objective African vulture optimization algorithm: A novel approach for many-objective problems.

Several optimization problems can be abstracted into many-objective optimization problems (MaOPs). The key to solving MaOPs is designing an effective algorithm to balance the exploration and exploitation issues. This paper proposes a novel many-objective African vulture optimization algorithm (MaAVOA) that simulating the African vultures' foraging and navigation behaviours to solve the MaOPs. MaAVOA is an updated version of the African Vulture Optimization Algorithm (AVOA), which was recently proposed to solve the MaOPs. A new social leader vulture for the selection process is introduced and integrated into the proposed model. In addition, an environmental selection mechanism based on the alternative pool is adapted to improve the selection process to maintain diversity for approximating different parts of the whole Pareto Front (PF). The best-nondominated solutions are saved in an external Archive based on the Fitness Assignment Method (FAM) during the population evolution. FAM is based on a convergence measure that promotes convergence and a density measure that promotes variety. Also, a Reproduction of Archive Solutions (RAS) procedure is developed to improve the quality of archiving solutions. RAS has been designed to help reach out to the missing areas of the PF that the vultures easily miss. Two experiments are conducted to verify and validate the suggested MaAVOA's performance efficacy. First, MaAVOA was applied to the DTLZ functions, and its performance was compared to that of several popular many-objective algorithms and according to the results, MaAVOA outperforms the competitor algorithms in terms of inverted generational distance and hypervolume performance measures and has a beneficial adaptation ability in terms of both convergence and diversity performance measures. Also, statistical tests are implemented to demonstrate the suggested algorithm's statistical relevance. Second, MaAVOA has been applied to solve two real-life constrained engineering MaOPs applications, namely, the series-parallel system and overspeed protection for gas turbine problems. The experiments show that the suggested algorithm can tackle many-objective real-world applications and provide promising choices for decision-makers.

The structure of genotype-phenotype maps makes fitness landscapes navigable.

Fitness landscapes are often described in terms of 'peaks' and 'valleys', indicating an intuitive low-dimensional landscape of the kind encountered in everyday experience. The space of genotypes, however, is extremely high dimensional, which results in counter-intuitive structural properties of genotype-phenotype maps. Here we show that these properties, such as the presence of pervasive neutral networks, make fitness landscapes navigable. For three biologically realistic genotype-phenotype map models-RNA secondary structure, protein tertiary structure and protein complexes-we find that, even under random fitness assignment, fitness maxima can be reached from almost any other phenotype without passing through fitness valleys. This in turn indicates that true fitness valleys are very rare. By considering evolutionary simulations between pairs of real examples of functional RNA sequences, we show that accessible paths are also likely to be used under evolutionary dynamics. Our findings have broad implications for the prediction of natural evolutionary outcomes and for directed evolution.

Regret-Based Nash Equilibrium Sorting Genetic Algorithm for Combinatorial Game Theory Problems with Multiple Players.

We introduce a regret-based fitness assignment strategy for evolutionary algorithms to find Nash equilibria in noncooperative simultaneous combinatorial game theory problems where it is computationally intractable to enumerate all decision options of the players involved in the game. Applications of evolutionary algorithms to non-cooperative simultaneous games have been limited due to challenges in guiding the evolutionary search toward equilibria, which are usually inferior points in the objective space. We propose a regret-based approach to select candidate decision options of the players for the next generation in a multipopulation genetic algorithm called Regret-Based Nash Equilibrium Sorting Genetic Algorithm (RNESGA). We show that RNESGA can converge to multiple Nash equilibria in a single run using two- and three- player competitive knapsack games and other games from the literature. We also show that pure payoff-based fitness assignment strategies perform poorly in three-player games.

An elitist multi-objective particle swarm optimization algorithm for composite structures design

Optimization is an important area of research in Engineering, usually due to the potentiality of saving costs and improving structural safety. Composite structures are typically complex, and the Finite Element Method is frequently required to evaluate such structures. From another perspective, Robust Design Optimization (RDO) is an approach that aims to consider the variability of the composite structures response due to uncertainty in design variables or material properties. Under these conditions, the problem of maximizing the robustness is added to the optimality problem related to minimizing the structure's weight. This work combines the advantages of Particle Swarm Optimization (PSO), such as simplicity and greater exploration and exploitation capabilities, with fitness assignment methodologies and elitist strategies commonly applied to Genetic Algorithms. The purpose is to achieve a more perceptible Pareto front and faster. The development is applied to the RDO bi-objective optimization problem in composite structures. Results for optimal design variables, critical displacements and stresses are discussed. The results show that elitist-based PSO approaches lead to a Pareto front with a larger number of optimal solutions, with more robust and lighter solutions when compared to other methodologies.

A Decomposition based Multi-Objective Heat Transfer Search algorithm for structure optimization

Multi-objective (MO) problems are complex and challenging to solve due to multiple conflicting objectives and incommensurate constraints. Heat Transfer Search is a recently introduced thermodynamic laws-based algorithm for solving many single objective problems. But it faces criticism due to its shortcomings including local optima trap, computational complexity, and reliability issues while solving MO problems. Decompositions is a simple yet efficient framework that aids in resolving fitness assignments and diversity maintenance issues of MO problems. It is also popular for reducing computational complexity and improving solution quality. Therefore, this work proposes and investigates a novel, simple, and robust Decomposition-based Multi-Objective Heat Transfer Search (MOHTS/D) for solving real-world structural problems. To achieve the Pareto optimal solutions and to confirm their coverage behaviour, the evenly generated weight vectors sorting and Euclidean distance strategies were employed in the proposed posteriori method. The performance of MOHTS/D is investigated through eight constrained widely accepted benchmarks. The results contrast with the MOHTS, MO evolutionary algorithm based on decomposition, MO passing vehicle search, MO slime mould, MO symbiotic organisms search, and MO multi-verse optimization. The efficacy of MOHTS/D is evaluated based on hyper-volume, coverage, inverted generational distance, pure diversity, spacing, spread, coverage Pareto front, diversity maintenance, generational distance, and runtime metrics. The results reveal that MOHTS/D is a robust optimization approach compared to others for optimizing real-life structural problems. MOHTS/D was able to find the optimal solution with minor computational complexity, and the obtained solutions demonstrate a better convergence, coverage, diversity, and spread behaviour over Pareto fronts

Many-objective Particle Swarm Optimization Algorithm Based on New Fitness Allocation and Multiply Cooperative Strategies

Many-objective optimization problems (MaOPs) refer to those multi-objective problems (MOPs) withmore than three objectives. In order to solve MaOPs, a multi-objective particle swarm optimization algorithm based on new fitness assignment and multi cooperation strategy(FAMSHMPSO) is proposed. Firstly, this paper proposes a new fitness allocation method based on fuzzy information theory to enhance the convergence of the algorithm. Then a new multi criteria mutation strategy is introduced to disturb the population and improve the diversity of the algorithm. Finally, the external files are maintained by the three-point shortest path method, which improves the quality of the solution. The performance of FAMSHMPSO algorithm is evaluated by evaluating the mean value, standard deviation and IGD+ index of the target value on dtlz test function set of different targets of FAMSHMPSO algorithm and other five representative multi-objective evolutionary algorithms. The experimental results show that FAMSHMPSO algorithm has obvious performance advantages in convergence, diversity and robustness.

Segmentation of brain MRI using an altruistic Harris Hawks’ Optimization algorithm

Segmentation is an essential requirement in medicine when digital images are used in illness diagnosis, especially, in posterior tasks as analysis and disease identification. An efficient segmentation of brain Magnetic Resonance Images (MRIs) is of prime concern to radiologists due to their poor illumination and other conditions related to de acquisition of the images. Thresholding is a popular method for segmentation that uses the histogram of an image to label different homogeneous groups of pixels into different classes. However, the computational cost increases exponentially according to the number of thresholds. In this paper, we perform the multi-level thresholding using an evolutionary metaheuristic. It is an improved version of the Harris Hawks Optimization (HHO) algorithm that combines the chaotic initialization and the concept of altruism. Further, for fitness assignment, we use a hybrid objective function where along with the cross-entropy minimization, we apply a new entropy function, and leverage weights to the two objective functions to form a new hybrid approach. The HHO was originally designed to solve numerical optimization problems. Earlier, the statistical results and comparisons have demonstrated that the HHO provides very promising results compared with well-established metaheuristic techniques. In this article, altruism has been incorporated into the HHO algorithm to enhance its exploitation capabilities. We evaluate the proposed method over 10 benchmark images from the WBA database of the Harvard Medical School and 8 benchmark images from the Brainweb dataset using some standard evaluation metrics. On the Harvard WBA dataset, a Peak Signal to Noise Ratio (PSNR) of 26.61 and a Structural Similarity Index (SSIM) of 0.92 are achieved using 5 thresholds. For the same scenario, using the Brainweb dataset, a PSNR of 24.77 and SSIM of 0.86 are obtained. The obtained results justify the superiority of the proposed approach compared to existing state-of-the-art methods and baseline methods. The relevant codes for the proposed approach are available at: https://github.com/Rohit-Kundu/Segmentation-HHO_Altruism.

Capacity‐basedoptimization using whale optimization technique of a power distribution network

AbstractIn the power distribution network, real power loss and voltage profile management are critical issues. By providing active and reactive power support, both of these issues can be managed. Distributed generation (DG) and capacitor bank (QG) can be utilized to solve these issues. Therefore, this paper utilized optimally placed and sized DG and capacitor (QG) to minimize losses and improve the voltage profile. The overall problem is optimized using an upgraded method of the fitness assignment and solution chasing based on the aggregate approach called multi‐objective whale optimization algorithm (MWOA). Wind and solar photovoltaic sources with biomass are utilized as the DG sources with their probabilistic outputs. The developed method is tested using two practical feeders of Bahir Dar city distribution network, Ethiopia. The results of loss minimization and voltage profile enhancement with MWOA are compared with multi‐objective particle swam optimization (MPSO) with an equal number of iterations to show the superiority of the developed method.

Nash equilibrium sorting genetic algorithm for simultaneous competitive maximal covering location with multiple players

In this article, a new genetic algorithm (GA), called the Nash equilibrium sorting genetic algorithm (NESGA,) is introduced to identify Nash equilibria for the competitive maximal covering location problem with two and three competitors, which is a combinatorial game theory problem where it is computationally intractable to enumerate all decision options of the competitors. Although GAs are widely used in combinatorial optimization, their applications to non-cooperative, simultaneous games have been limited owing to challenges in guiding the evolutionary search to Nash equilibria, which are not necessarily on the Pareto front of the search space and cannot be found by current multi-objective GAs. A novel fitness assignment strategy is proposed to help the NESGA to converge to multiple Nash equilibria. Computational experiments show that the NESGA can discover multiple Nash equilibria in a single run and outperform other game-theoretic GAs.

Many-Objective Particle Swarm Optimization Algorithm Based on New Fitness Allocation and Multiple Cooperative Strategies

Many-objective optimization problems (MaOPs) refer to those multi-objective problems (MOPs) withmore than three objectives. In order to solve MaOPs, a multi-objective particle swarm optimization algorithm based on new fitness assignment and multi cooperation strategy(FAMSHMPSO) is proposed. Firstly, this paper proposes a new fitness allocation method based on fuzzy information theory to enhance the convergence of the algorithm. Then a new multi criteria mutation strategy is introduced to disturb the population and improve the diversity of the algorithm. Finally, the external files are maintained by the three-point shortest path method, which improves the quality of the solution. The performance of FAMSHMPSO algorithm is evaluated by evaluating the mean value, standard deviation and IGD+ index of the target value on dtlz test function set of different targets of FAMSHMPSO algorithm and other five representative multi-objective evolutionary algorithms. The experimental results show that FAMSHMPSO algorithm has obvious performance advantages in convergence, diversity and robustness.

A hybrid backtracking search algorithm for energy management in a microgrid

Recently, due to the high penetration of distributed generators and storages, and the rapid growth of environmental concerns, energy optimisation plays a vital role in the operation of microgrids. In this paper, we propose a hybrid backtracking search matheuristic algorithm with a multiobjective indirect encoding (H-MOBSA) for the multiobjective mixed-integer nonlinear formulation of economic-emission dispatch in a grid-connected microgrid. In this approach, each partial discrete solution represented by the backtracking search algorithm is associated with a set of Pareto solutions of the related continuous subproblem where the fitness and diversity assignments are adapted to take into account all associated decoded solutions. The proposed algorithm aims to provide generation planning and the battery size that satisfy the trade-off between the total operating cost and pollutant emissions under equality and inequality constraints. To show the effectiveness of our approach, the proposed H-MOBSA is tested on typical MG and compared to other algorithms.

Preference-inspired coevolutionary algorithm with active diversity strategy for multi-objective multi-modal optimization

Multi-objective multi-modal optimization problems have recently received increasing attention in the field of evolutionary computation. Addressing such problems is not easy for existing evolutionary multi-objective algorithms (EMOAs) since they require finding solutions with good convergence and diversity in both objective and decision spaces. This study therefore proposes a new algorithm, namely, the preference-inspired coevolutionary algorithm (PICEAg) with an active diversity strategy, to deal with multi-objective multi-modal optimization problems. The proposed algorithm, denoted as MMPICEAg, adopts the popular coevolutionary framework of PICEAg and introduces a diversity-aware fitness assignment and a double-diversity archive update strategy to promote diversity in objective and decision spaces simultaneously. The performance of MMPICEAg is compared with that of three general EMOAs as well as four state-of-the-art multi-modal EMOAs. The comparison results on three sets of widely used benchmarks clearly demonstrate the effectiveness of MMPICEAg for multi-objective multi-modal optimization.

A preference-based multi-objective algorithm for optimal service composition selection in cloud manufacturing

ABSTRACT Aiming at addressing several conflicting criteria of quality of service (QoS) that should be trade-off optimized during service composition and optimal selection (SCOS) in cloud manufacturing (CMfg), the improved non-dominated sorting genetic algorithm III (NSGA-III) is proposed and employed to address the SCOS issue. This is the first time that a preference-based multi-objective algorithm has been used to address the SCOS problem. In this paper, a novel K-layer preference reference point set approach is proposed for generating a reference point set with this algorithm to guide the search towards the interesting parts of the Pareto optimal region based on customer preferences, which improves the efficiency of the algorithm and the convergence of the obtained solution. A new fitness assignment strategy and environment selection scheme is developed accordingly to balance the relationship of diversity and convergence of preserved individuals in each generation. Additionally, the memetic algorithm is integrated into the evolutionary mechanism of the algorithm to address the insufficiency of local search. To validate the performance of the proposed algorithm, several test cases are conducted. The results demonstrate that the proposed algorithm is more competitive than other considered algorithms.

An Improved Artificial Electric Field Algorithm for Multi-Objective Optimization

Real-world problems such as scientific, engineering, mechanical, etc., are multi-objective optimization problems. In order to achieve an optimum solution to such problems, multi-objective optimization algorithms are used. A solution to a multi-objective problem is to explore a set of candidate solutions, each of which satisfies the required objective without any other solution dominating it. In this paper, a population-based metaheuristic algorithm called an artificial electric field algorithm (AEFA) is proposed to deal with multi-objective optimization problems. The proposed algorithm utilizes the concepts of strength Pareto for fitness assignment and the fine-grained elitism selection mechanism to maintain population diversity. Furthermore, the proposed algorithm utilizes the shift-based density estimation approach integrated with strength Pareto for density estimation, and it implements bounded exponential crossover (BEX) and polynomial mutation operator (PMO) to avoid solutions trapping in local optima and enhance convergence. The proposed algorithm is validated using several standard benchmark functions. The proposed algorithm’s performance is compared with existing multi-objective algorithms. The experimental results obtained in this study reveal that the proposed algorithm is highly competitive and maintains the desired balance between exploration and exploitation to speed up convergence towards the Pareto optimal front.

Selecting a diverse set of benchmark instances from a tunable model problem for black-box discrete optimization algorithms

As the number of practical applications of discrete black-box metaheuristics is growing faster and faster, the benchmarking of these algorithms is rapidly gaining importance. While new algorithms are often introduced for specific problem domains, researchers are also interested in which general problem characteristics are hard for which type of algorithm. The W-Model is a benchmark function for discrete black-box optimization, which allows for the easy, fast, and reproducible generation of problem instances exhibiting characteristics such as ruggedness, deceptiveness, epistasis, and neutrality in a tunable way. We conduct the first large-scale study with the W-Model in its fixed-length single-objective form, investigating 17 algorithm configurations (including Evolutionary Algorithms and local searches) and 8372 problem instances. We develop and apply a machine learning methodology to automatically discover several clusters of optimization process runtime behaviors as well as their reasons grounded in the algorithm and model parameters. Both a detailed statistical evaluation and our methodology confirm that the different model parameters allow us to generate problem instances of different hardness, but also find that the investigated algorithms struggle with different problem characteristics. With our methodology, we select a set of 19 diverse problem instances with which researchers can conduct a fast but still in-depth analysis of algorithm performance. The best-performing algorithms in our experiment were Evolutionary Algorithms applying Frequency Fitness Assignment, which turned out to be robust over a wide range of problem settings and solved more instances than the other tested algorithms.

Reinvestigation of evolutionary many-objective optimization: Focus on the Pareto knee front

Approximating the entire Pareto front (PF) in many-objective optimization is challenging but often unnecessary because a decision maker is usually only interested in a small portion of the PF. Assuming no preference, we argue that a more appropriate way to address many-objective optimization problems (MaOPs) is to find Pareto-optimal knee solutions—solutions where small improvements in one objective will lead to severe degradation in at least one other objective. Herein, we propose such a method, which uses a distance-based indicator to first identify knee points (knee-detection phase) and then uses a refined fitness assignment strategy to select solutions near the knee points (knee-selection phase). The proposed method is integrated into two traditional algorithms, resulting in k-NSGA-II and k-MOEA/D. We discuss the effects of the parameter that controls the width of the knee region(s) and then analyze the effects of different methods for identifying knee points in the knee-detection phase. Finally, we examine the performances of k-NSGA-II and k-MOEA/D on a set of knee benchmark problems. The experimental results show that k-NSGA-II is competitive on knee test problems with 2 and 4 objectives, while k-MOEA/D performs better than k-NSGA-II with 6 and 8 objectives.