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Constrained multi-objective optimization problems (CMOPs) are common in engineering design fields. To solve such problems effectively, this paper proposes a new differential evolution variant named IMDE with infeasible-guiding mutation operators and a multistrategy technique. In IMDE, an infeasible solution with lower objective values is maintained for each individual in the main population, and this infeasible solution is then incorporated into some common differential evolution’s mutation operators to guide the search toward the region with promising objective values. Moreover, multiple mutation strategies and control parameters are adopted during the trial vector generation procedure to enhance both the convergence and the diversity of differential evolution. The superior performance of IMDE is validated via comparisons with some state-of-the-art constrained multi-objective evolutionary algorithms over 3 sets of artificial benchmarks and 4 widely used engineering design problems. The experiments show that IMDE outperforms other algorithms or obtains similar results. It is an effective approach for solving CMOPs, basically due to the use of infeasible-guiding mutation operators and multiple strategies.

Moth-Flame Optimization (MFO) algorithm is a new population-based meta-heuristic algorithm for solving global optimization problems. Flames generation and spiral search are two key components that affect the performance of MFO. To improve the diversity of flames and the searching ability of moths, an improved Moth-Flame Optimization (IMFO) algorithm is proposed. The main features of the IMFO are: the flames are generated by orthogonal opposition-based learning (OOBL); the modified position updating mechanism of moths with linear search and mutation operator. To evaluate the performance of IMFO, the IMFO algorithm is compared with other 20 algorithms on 23 benchmark functions and IEEE (Institute of Electrical and Electronics Engineers) CEC (Congress on Evolutionary Computation) 2014 benchmark test set. The comparative results show that the IMFO is effective and has good performance in terms of jumping out of local optimum, balancing exploitation ability and exploration ability. Moreover, the IMFO is also used to solve three engineering optimization problems, and it is compared with other well-known algorithms. The comparison results show that the IMFO algorithm can improve the global search ability of MFO and effectively solve the practical engineering optimization problems.

Arising from the need of all time for optimization of irrigation systems, distribution network and cable network, Clustered Shortest-Path Tree Problem (CluSPT) has been attracting a lot of attention and interest from the research community. On the other hand, the Multifactorial Evolutionary Algorithm (MFEA) is one of the most recently exploited realms of Evolutionary Algorithms (EAs) and its performance in solving optimization problems has been very promising. Considering these characteristics, this paper describes a new approach using the MFEA for solving the CluSPT. The MFEA has two tasks: the goal of the first task is to determine the best tree (w.r.t. cost minimization) which envelops all vertices of the CluSPT while the goal of the second task is to find the fittest solution possible for the problem. The purpose of the second task is to find good materials for implicit genetic transfer process in MFEA to improve the quality of CluSPT. To apply this new algorithm, a decoding scheme for deriving individual solutions from the unified representation in the MFEA is also introduced in this paper. Furthermore, evolutionary operators such as population initialization, crossover and mutation operators are also proposed. These operators are applicable for constructing valid solution from both sparse and complete graph. Although the proposed algorithm is slightly complicated for implementation, it can enhance ability to explore and exploit the Unified Search Space (USS). To prove this increment in performance i.e, to assess the effectiveness of the proposed algorithm and methods, the authors implemented them on both Euclidean and Non-Euclidean instances. Experiment results show that the proposed MFEA outperformed existing heuristic algorithms in most of the test cases. The impact of the proposed MFEA was analyzed and a possible influential factor that may be useful for further study was also pointed out.

Due to the lack of global search capacity, most evolutionary or swarm intelligence based algorithms show their inefficiency when optimizing multi-modal problems. In this paper, we propose a grouping particle swarm optimizer (GPSO) to solve this kind of problem. In the proposed algorithm, the swarm consists of several groups. For every several iterations, an elite group is constructed and used to replace the worst one. The thought of grouping is helpful for improving the diversity of the solutions, and then enhancing the global search ability of the algorithm. In addition, we apply a simple mutation operator to the best solution so as to help it escape from local optima. The GPSO is compared with several variants of particle swarm optimizer (PSO) and some state-of-the-art evolutionary algorithms on CEC15 benchmark functions and three practical engineering problems. As demonstrated by the experimental results, the proposed GPSO outperforms its competitors in most cases.

Artificial immune system is a class of computational intelligence methods drawing inspiration from biological immune system. As one type of popular artificial immune computing model, clonal selection algorithm (CSA) has been widely used for many optimization problems. When dealing with complex optimization problems, such as the characteristics of multimodal, high-dimension, rotational, the traditional CSA often suffers from diversity loss, poor search ability, premature convergence and stagnation. To address the problems, a modified combinatorial recombination is introduced to bring diversity to the population and avoid the premature convergence. Moreover, the success-history based adaptive mutation strategy is introduced to form a success-history based adaptive mutation based clonal selection algorithm to improve the search ability. The mutation operator is also modified and analyzed through experimental comparison. To further improve the precision and cope with the stagnation, the gene knockout strategy is proposed. The proposed algorithm is tested on CEC 2014 benchmarks and compared with state-of-the-art evolutionary algorithms. The experimental results show that MSHCSA is quite competitive.

Dynamic optimization problems challenge the evolutionary algorithms, owing to the diversity loss or the low search efficiency of the algorithms, especially when the problems change frequently. This paper presents a novel differential evolution algorithm to address the dynamic optimization problems. Unlike the most used “DE/rand/1” mutation operator, in this paper, the “DE/best/1” mutation is employed to generate a mutant individual. In order to enhance the search efficiency of differential evolution, the classical differential evolution algorithm is modified by a novel replacement operator, in which the worst individual in the whole population is replaced by the newly generated trial vector as a “steady-state” manner. During optimizing, some newly generated solutions are stored into a memory set, in which these stored solutions are located around the current best solution. When the environmental change is detected, the stored solutions are expected to guide the reinitialized solutions to track the new location of global optimum as soon as possible. The performance of the proposed algorithm is compared with six state-of-the-art dynamic evolutionary algorithms over some benchmark problems. The experimental results show that the proposed algorithm clearly outperforms the competitors.

The problem in software cost estimation revolves around accuracy. To improve the accuracy, heuristic/meta-heuristic algorithms have been known to yield better results when it is applied in the domain of software cost estimation. For the sake of accuracy in results, we are still modifying these algorithms. Here we have proposed a new meta-heuristic algorithm based on Differential Evolution (DE) by Homeostasis mutation operator. Software development requires high prediction and low Root Mean Squared Error (RMSE) and mean magnitude relative error(MMRE). The problem in software cost estimation relates to accurate prediction and minimization of RMSE and MMRE, which are used to solve multiobjective optimization. Many versions of DE were proposed, however multi-objective versions where the concept of Pareto optimality is used, are most popular. Pareto-Based Differential Evolution (PBDE) is one of them. Although the performance of this algorithm is very good, its convergence rate can be further improved by minimizing the time complexity of nondominated sorting, and by improving the diversity of solutions. This has been implemented by using efficient nondominated algorithm whose time complexity is better than the previous one and a new mutation scheme is implemented in DE which can provide more diversity among solutions. The proposed variant multiplies the Homeostasis value with one more vector, named the Homeostasis mutation vector, in the existing mutation vector to provide more bandwidth for selecting effective mutant solutions. The proposed approach provides more promising solutions to guide the evolution and helps DE escape the situation of stagnation. The performance of the proposed algorithm is evaluated on twelve benchmark test functions (bi-objective and tri-objective) on the Pareto-optimal front. The performance of the proposed algorithm is compared with other state-of-the-art algorithms on five multi-objective evolutionary algorithms (MOEAs). The result verifies that our proposed Homeostasis mutation strategy performs better than other state-of-the-art algorithms. Finally, application of MODE-HBM is applied to solve in terms of Pareto front, representing the trade-off between development RMSE, MMRE, and prediction for COCOMO model.

© 2015, Springer Science+Business Media New York. This paper proposes a modified harmony search (MHS) algorithm with an intersect mutation operator and cellular local search for continuous function optimization problems. Instead of focusing on the intelligent tuning of the parameters during the searching process, the MHS algorithm divides all harmonies in harmony memory into a better part and a worse part according to their fitness. The novel intersect mutation operation has been developed to generate new -harmony vectors. Furthermore, a cellular local search also has been developed in MHS, that helps to improve the optimization performance by exploring a huge search space in the early run phase to avoid premature, and exploiting a small region in the later run phase to refine the final solutions. To obtain better parameter settings for the proposed MHS algorithm, the impacts of the parameters are analyzed by an orthogonal test and a range analysis method. Finally, two sets of famous benchmark functions have been used to test and evaluate the performance of the proposed MHS algorithm. Functions in these benchmark sets have different characteristics so they can give a comprehensive evaluation on the performance of MHS. The experimental results show that the proposed algorithm not only performs better than those state-of-the-art HS variants but is also competitive with other famous meta-heuristic algorithms in terms of the solution accuracy and efficiency.

With its unique migration operator and mutation operator, Biogeography-Based Optimization (BBO), which simulates migration of species in natural biogeography, is different from existing evolutionary algorithms, but it has shortcomings such as poor convergence precision and slow convergence speed when it is applied to solve complex optimization problems. Therefore, we put forward a Cooperative Coevolutionary Biogeography-Based Optimizer (CBBO) in this paper. In CBBO, the whole population is divided into multiple sub-populations first, and then each subpopulation is evolved with an improved BBO separately. The fitness evaluation of habitats of a subpopulation is conducted by constructing context vectors with selected habitats from other sub-populations. Our CBBO tests are based on 13 benchmark functions and are also compared with several other evolutionary algorithms. Experimental results demonstrate that CBBO is able to achieve better results than other evolutionary algorithms on most of the benchmark functions.

Community detection can be used to help mine the potential information in social networks, and uncovering community structures in social networks can be regarded as clustering optimization problems. In this paper, an overlapping community detection algorithm based on biogeography optimization is proposed. Firstly, the algorithm takes the method of label propagation based on local max degree and neighborhood overlap for initial network partitioning. The preliminary partition result used to construct initial population by cloning and mutating to accelerate the algorithm’s convergence. Next, to make biogeography optimization algorithm suitable for community detection, we design problem-specific migration rules and mutation operators based on a novel affinity degree to improve the effectiveness of the algorithm. Experiments on benchmark test data, including two synthetic networks and four real-world networks, show that the proposed algorithm can achieve results with better accuracy and stability than the compared evolutionary algorithms.

The differential evolution (DE) algorithm is a notably powerful evolutionary algorithm that has been applied in many areas. Therefore, the question of how to improve the algorithm's performance has attracted considerable attention from researchers. The mutation operator largely impacts the performance of the DE algorithm The control parameters also have a significant influence on the performance. However, it is not an easy task to set a suitable control parameter for DE. One good method is to considering the mutation operator and control parameters simultaneously. Thus, this paper proposes a new DE algorithm with a hybrid mutation operator and self-adapting control parameters. To enhance the searching ability of the DE algorithm, the proposed method categorizes the population into two parts to process different types of mutation operators and self-adapting control parameters embedded in the proposed algorithm framework. Two famous benchmark sets (including 46 functions) are used to evaluate the performance of the proposed algorithm and comparisons with various other DE variants previously reported in the literature have also been conducted. Experimental results and statistical analysis indicate that the proposed algorithm has good performance on these functions.

This paper reports the investigation on the sandpile mutation, an unconventional mutation control scheme for binary Genetic Algorithms (GA) inspired by the Self-Organized Criticality (SOC) theory. The operator, which is based on a SOC system known as sandpile, is able to generate mutation rates that, unlike those given by other methods of parameter control, oscillate between low values and very intense mutations events. The distribution of the mutation rates suggests that the algorithm can be an efficient and yet simple and context-independent approach for the optimization of non-stationary fitness functions. This paper studies the mutation scheme of the algorithm and proposes a new strategy that optimizes is performance. The results also demonstrate the advantages of using the fitness distribution of the population for controlling the mutation. An extensive experimental setup compares the sandpile mutation GA (GGASM) with two state-of-the-art evolutionary approaches to non-stationary optimization and with the Hypermutation GA, a classical approach to dynamic problems. The results demonstrate that GGASM is able to improve the other algorithms in several dynamic environments. Furthermore, the proposed method does not increase the parameter set of traditional GAs. A study of the distribution of the mutation rates shows that the distribution depends on the type of problem and dynamics, meaning that the algorithm is able to self-regulate the mutation. The effects of the operator on the diversity of the population during the run are also investigated. Finally, a study on the effects of the topology of the sandpile mutation on its performance demonstrates that an alternative topology has minor effects on the performance.

Many methods have been recently suggested for promoting the performance of Evolutionary Programming (EP) in finding the optimum point of functions or applications. EP has some shortcomings that slow down its convergence to the global minimum, especially for multimodal functions. As it is known, mutation is one of the most important operators in EP, which produces new attributes in variables. Mutation must be kept under control; otherwise, it destroys heritage information. In EP, mutation is implemented by adding strategy parameters to variable vectors of parents to produce offspring. When one of the strategy parameters is a large value, adding it to the related variable causes abrupt changes in that variable. Thus, the variable grows with large steps and deviates far from the optimum point, whereas some of the other variables do not sense considerable changes. If this event continues for more iterations, the variable will go further. This event slows down EP in some iterations. To avoid such an occurrence, this paper introduces a new method that can overcome these disadvantages and enhance the performance of classical evolutionary programming. This paper describes a modification of evolutionary programming by using a rotational method to prevent large and small changes to the strategy parameters. This method adds one function to the mutation operator. This function operates on strategy parameters and changes the sequence of these parameters. Because this method does not directly operate on variables, it will not destroy the heritage information of the parents. This method was tested on fifty well-known test functions used in the literature and was compared with nine well-known EP variants. The results are robust and demonstrate the efficiency of the technique.

Evolutionary algorithms (EAs) are becoming increasingly popular tools for solving complex search problems. Their popularity in various problem domains has led to the introduction and development of numerous variants of two standard EA operators—crossover and mutation. Unfortunately, there are few if any effective guidelines for choosing which operators will be most effective in a given problem. In this paper, a self-tuning EA is introduced that employs several crossover and mutation operators simultaneously. The probability of using a given operator changes during the course of an evolutionary run whereby the most effective operators are selected based on which part of the search space is currently being explored. The self-tuning EA is used to solve an inverse partial differential equation—considered to be one of the more difficult problems in the realm of engineering mathematics. Results indicate that for the particular inverse partial differential equation considered, the self-tuning EA provides an effective solution methodology.

Traditional genetic algorithms use only one crossover and one mutation operator to generate the next generation. The chosen crossover and mutation operators are critical to the success of genetic algorithms. Different crossover or mutation operators, however, are suitable for different problems, even for different stages of the genetic process in a problem. Determining which crossover and mutation operators should be used is quite difficult and is usually done by trial-and-error. In this paper, a new genetic algorithm, the dynamic genetic algorithm (DGA), is proposed to solve the problem. The dynamic genetic algorithm simultaneously uses more than one crossover and mutation operators to generate the next generation. The crossover and mutation ratios change along with the evaluation results of the respective offspring in the next generation. By this way, we expect that the really good operators will have an increasing effect in the genetic process. Experiments are also made, with results showing the proposed algorithm performs better than the algorithms with a single crossover and a single mutation operator.

Genetic algorithms are adaptive methods based on natural evolution that may be used for search and optimization problems. They process a population of search space solutions with three operations: selection, crossover, and mutation. Under their initial formulation, the search space solutions are coded using the binary alphabet, however other coding types have been taken into account for the representation issue, such as real coding. The real-coding approach seems particularly natural when tackling optimization problems of parameters with variables in continuous domains. A problem in the use of genetic algorithms is premature convergence, a premature stagnation of the search caused by the lack of population diversity. The mutation operator is the one responsible for the generation of diversity and therefore may be considered to be an important element in solving this problem. For the case of working under real coding, a solution involves the control, throughout the run, of the strength in which real genes are mutated, i.e., the step size. This paper presents TRAMSS, a Two-loop Real-coded genetic algorithm with Adaptive control of Mutation Step Sizes. It adjusts the step size of a mutation operator applied during the inner loop, for producing efficient local tuning. It also controls the step size of a mutation operator used by a restart operator performed in the outer loop, for reinitializing the population in order to ensure that different promising search zones are focused by the inner loop throughout the run. Experimental results show that the proposal consistently outperforms other mechanisms presented for controlling mutation step sizes, offering two main advantages simultaneously, better reliability and accuracy.