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Abstract Binary optimization problems belong to the NP-hard class because their solutions are hard to find in a known time. The traditional techniques could not be applied to tackle those problems because the computational cost required by them increases exponentially with increasing the dimensions of the optimization problems. Therefore, over the last few years, researchers have paid attention to the metaheuristic algorithms for tackling those problems in an acceptable time. But unfortunately, those algorithms still suffer from not being able to avert local minima, a lack of population diversity, and low convergence speed. As a result, this paper presents a new binary optimization technique based on integrating the equilibrium optimizer (EO) with a new local search operator, which effectively integrates the single crossover, uniform crossover, mutation operator, flipping operator, and swapping operator to improve its exploration and exploitation operators. In a more general sense, this local search operator is based on two folds: the first fold borrows the single-point crossover and uniform crossover to accelerate the convergence speed, in addition to avoiding falling into local minima using the mutation strategy; the second fold is based on applying two different mutation operators on the best-so-far solution in the hope of finding a better solution: the first operator is the flip mutation operator to flip a bit selected randomly from the given solution, and the second operator is the swap mutation operator to swap two unique positions selected randomly from the given solution. This variant is called a binary hybrid equilibrium optimizer (BHEO) and is applied to three common binary optimization problems: 0–1 knapsack, feature selection, and the Merkle–Hellman knapsack cryptosystem (MHKC) to investigate its effectiveness. The experimental findings of BHEO are compared with those of the classical algorithm and six other well-established evolutionary and swarm-based optimization algorithms. From those findings, it is concluded that BHEO is a strong alternative to tackle binary optimization problems. Quantatively, BHEO could reach an average fitness of 0.090737884 for the feature section problem and an average difference from the optimal profits for some used Knapsack problems of 2.482.

Identification of complex communities in biological networks is a critical and ongoing challenge since lots of network-related problems correspond to the subgraph isomorphism problem known in the literature as NP-hard. Several optimization algorithms have been dedicated and applied to solve this problem. The main challenge regarding the application of optimization algorithms, specifically to handle large-scale complex networks, is their relatively long execution time. Thus, this paper proposes a parallel extension of the PSO algorithm to detect communities in complex biological networks. The main contribution of this study is summarized in three- fold; Firstly, a modified PSO algorithm with a local search operator is proposed to detect complex biological communities with high quality. Secondly, the variability in the capability of PSO to extract community structure in biological networks is studied when different types of crossover operators are used. Finally, to reduce the computational time needed to solve this problem, especially when detecting complex communities in large-scale biological networks, we have implemented parallel computing to execute the algorithm. The performance of the proposed algorithm was tested and evaluated on two real biological networks. The experimental results showed the effective performance of the proposed algorithm when using single-point crossover operator, and its superiority over other counterpart algorithms. Moreover, the use of parallel computing in the proposed algorithm representation has greatly reduced the computational time required for its execution. [ABSTRACT FROM AUTHOR]

Nowadays, optimization problems are solved through meta-heuristic algorithms based on stochastic search approaches borrowed from mimicking natural phenomena. Notwithstanding their successful capability to handle complex problems, the No-Free Lunch Theorem by Wolpert and Macready (1997) states that there is no ideal algorithm to deal with any kind of problem. This issue arises because of the nature of these algorithms that are not properly mathematics-based, and the convergence is not ensured. In the present study, a variant of the well-known swarm-based algorithm, the Particle Swarm Optimization (PSO), is developed to solve constrained problems with a different approach to the classical penalty function technique. State-of-art improvements and suggestions are also adopted in the current implementation (inertia weight, neighbourhood). Furthermore, a new local search operator has been implemented to help localize the feasible region in challenging optimization problems. This operator is based on hybridization with another milestone meta-heuristic algorithm, the Evolutionary Strategy (ES). The self-adaptive variant has been adopted because of its advantage of not requiring any other arbitrary parameter to be tuned. This approach automatically determines the parameters' values that govern the Evolutionary Strategy simultaneously during the optimization process. This enhanced multi-strategy PSO is eventually tested on some benchmark constrained numerical problems from the literature. The obtained results are compared in terms of the optimal solutions with two other PSO implementations, which rely on a classic penalty function approach as a constraint-handling method. [ABSTRACT FROM AUTHOR]

Feature selection (FS) is a vital data preprocessing task which aims at selecting a small subset of features while maintaining a high level of classification accuracy. FS is a challenging optimization problem due to the large search space and the existence of local optimal solutions. Particle swarm optimization (PSO) is a promising technique in selecting optimal feature subset due to its rapid convergence speed and global search ability. But PSO suffers from stagnation or premature convergence in complex FS problems. In this paper, a novel three layer PSO (TLPSO) is proposed for solving FS problem. In the TLPSO, the particles in the swarm are divided into three layers according to their evolution status and particles in different layers are treated differently to fully investigate their potential. Instead of learning from those historical best positions, the TLPSO uses a random learning exemplar selection strategy to enrich the searching behavior of the swarm and enhance the population diversity. Further, a local search operator based on the Gaussian distribution is performed on the elite particles to improve the exploitation ability. Therefore, TLPSO is able to keep a balance between population diversity and convergence speed. Extensive comparisons with seven state-of-the-art meta-heuristic based FS methods are conducted on 18 datasets. The experimental results demonstrate the competitive and reliable performance of TLPSO in terms of improving the classification accuracy and reducing the number of features. [ABSTRACT FROM AUTHOR]

Nowadays, optimization problems are solved through meta-heuristic algorithms based on stochastic search approaches borrowed from mimicking natural phenomena. Notwithstanding their successful capability to handle complex problems, the No-Free Lunch Theorem by Wolpert and Macready (1997) states that there is no ideal algorithm to deal with any kind of problem. This issue arises because of the nature of these algorithms that are not properly mathematics-based, and the convergence is not ensured. In the present study, a variant of the well-known swarm-based algorithm, the Particle Swarm Optimization (PSO), is developed to solve constrained problems with a different approach to the classical penalty function technique. State-of-art improvements and suggestions are also adopted in the current implementation (inertia weight, neighbourhood). Furthermore, a new local search operator has been implemented to help localize the feasible region in challenging optimization problems. This operator is based on hybridization with another milestone meta-heuristic algorithm, the Evolutionary Strategy (ES). The self-adaptive variant has been adopted because of its advantage of not requiring any other arbitrary parameter to be tuned. This approach automatically determines the parameters’ values that govern the Evolutionary Strategy simultaneously during the optimization process. This enhanced multi-strategy PSO is eventually tested on some benchmark constrained numerical problems from the literature. The obtained results are compared in terms of the optimal solutions with two other PSO implementations, which rely on a classic penalty function approach as a constraint-handling method.

Selecting the minimal best subset out of a huge number of factors for influencing the response is a fundamental and very challenging NP-hard problem because the presence of many redundant genes results in over-fitting easily while missing an important gene can more detrimental impact on predictions, and computation is prohibitive for exhaust search. We propose a modified memetic algorithm (MA) based on an improved splicing method to overcome the problems in the traditional genetic algorithm exploitation capability and dimension reduction in the predictor variables. The new algorithm accelerates the search in identifying the minimal best subset of genes by incorporating it into the new local search operator and hence improving the splicing method. The improvement is also due to another two novel aspects: (a) updating subsets of genes iteratively until the no more reduction in the loss function by splicing and increasing the probability of selecting the true subsets of genes; and (b) introducing add and del operators based on backward sacrifice into the splicing method to limit the size of gene subsets. Additionally, according to the experimental results, our proposed optimizer can obtain a better minimal subset of genes with a few iterations, compared with all considered algorithms. Moreover, the mutation operator is replaced by it to enhance exploitation capability and initial individuals are improved by it to enhance efficiency of search. A dataset of the body weight of Hu sheep was used to evaluate the superiority of the modified MA against the genetic algorithm. According to our experimental results, our proposed optimizer can obtain a better minimal subset of genes with a few iterations, compared with all considered algorithms including the most advanced adaptive best-subset selection algorithm.

A novel feature selection method based on a multi-swarm particle swarm optimization (MSPSO) is proposed in this paper. The canonical particle swarm optimization (PSO) has been widely used for feature selection problems. However, PSO suffers from stagnation in local optimal solutions and premature convergence in complex feature selection problems. This paper employs the multi-swarm topology in which the population is split into several small-sized sub-swarms. Particles in each sub-swarm update their positions with the guidance of the local best particle in its own sub-swarm. In order to promote information exchange among the sub-swarms, an elite learning strategy is introduced in which the elite particles in each sub-swarm learn from the useful information found by other sub-swarms. Moreover, a local search operator is proposed to improve the exploitation ability of each sub-swarm. MSPSO is able to improve the population diversity and better explore the entire feature space. The performance of the proposed method is compared with six PSO based wrappers, three traditional wrappers, and three popular filters on eleven datasets. Experimental results verify that MSPSO can find feature subsets with high classification accuracies and smaller numbers of features. The analysis of the search behavior of MSPSO demonstrates its effectiveness on maintaining population diversity and finding better feature subsets. The statistical test demonstrates that the superiority of MSPSO over other methods is significant. [ABSTRACT FROM AUTHOR]

Many engineering problems can be categorized into constrained optimization problems (COPs). The engineering design optimization problem is very important in engineering industries. Because of the complexities of mathematical models, it is difficult to find a perfect method to solve all the COPs very well. ε constrained differential evolution (εDE) algorithm is an effective method in dealing with the COPs. However, εDE still cannot obtain more precise solutions. The interaction between feasible and infeasible individuals can be enhanced, and the feasible individuals can lead the population finding optimum around it. Hence, in this paper we propose a new algorithm based on ε feasible individuals driven local search called as ε constrained differential evolution algorithm with a novel local search operator (εDE-LS). The effectiveness of the proposed εDE-LS algorithm is tested. Furthermore, four real-world engineering design problems and a case study have been studied. Experimental results show that the proposed algorithm is a very effective method for the presented engineering design optimization problems. [ABSTRACT FROM AUTHOR]

When the cassava tubers are lifted up by the dig-pull cassava tuber harvester, the harvester has low power consumption and a high adaptability to the soil. However, the control precision of the lifting velocity of cassava tuber is low, thus, the broken and loss rate of the cassava tubers are larger in the cassava tuber harvesting. And the control precision of the control system of the tuber lifting velocity mainly depends on the quality of control system's control parameters. Whether the optimal control parameters could be obtained by the optimization algorithm of the control system's control parameters determines the quality of the parameters. Therefore, the optimization algorithm of the control parameters of the lifting velocity control system of the cassava tuber lifting mechanism is studied using the advanced method and technology which has important significance to improve the control precision of the cassava tuber lifting velocity and the harvesting quality of the cassava tubers. The broken and loss rate of the cassava tubers are larger in the cassava tuber harvesting when the control precision of the tuber lifting velocity of the dig-pull cassava harvester is low. Firstly, the co-simulation model of the control system of the tuber lifting mechanism of the dig-pull type cassava tuber harvester was established. The fuzzy PI algorithm was used as the control algorithm of the mechanically optimal tuber lifting velocity of the tuber lifting mechanism. The multi-domain dynamics simulation technology was also used in the co-simulation model. The mechanically optimal lifting velocity model of the cassava tuber was obtained using the cassava tuber lifting tests of the experienced farmers and the optimized velocity model of manually pulling tubers as well as the numerical simulation tests. The mechanically optimal lifting velocity model of the cassava tuber was used as the control target, and meanwhile, the constant cassava tuber lifting force, the cassava tuber lifting force in the soft soil as well as the cassava tuber lifting force in the hard soil, respectively, were used as the condition. The study of the spider clustering algorithm combined with the local search operator was carried out. Then, using a combination of local search operator and spider cluster algorithm, the control parameters of the cassava tuber lifting mechanism system were optimized by iterative optimization. In addition, the common test function was used to verify the convergence and search accuracy of the spider cluster algorithm combined with local search operator. Finally, the cassava tuber lifting test verification was carried out in the field. The error analysis of the verification test was carried out by means of the mean error and the maximum error. The results show that the spider cluster algorithm combined with local search operator which can avoid getting into the local optimal solution in the iterative process, has faster convergence speed and higher search accuracy than the spider clustering algorithm. The spider clustering algorithm combined with the local search operator is suitable for solving the extremum problems of high-dimensional complex function. The optimization result of the Fuzzy PI control system's control parameters: Kp and Ki are 0.841 and 0.203 9, respectively. Using the optimized control parameter, the actual lifting speeds of the cassava tuber can follow mechanically optimal lifting velocity model. And the dynamic performance is great. The average relative error between the actual vertical lifting speed of the cassava tuber and mechanically optimal lifting velocity of the cassava tuber is 4.5%. The maximum error is 6.7%. The average relative error between actual slide displacement and the theoretical value is 3.7%. The maximum error is 5.4%. The spider clustering algorithm combined with local search operator can be used in controlling the cassava tuber lifting process of the dig-pull type cassava tuber harvester. The control precision of the tuber lifting velocity has high precision. [ABSTRACT FROM AUTHOR]

This paper presents a number of novel metaheuristic approaches that can efficiently map stream graphs on multicores. A stream graph consists of a set of actors performing different functions communicating through edges. Orchestrating stream graphs on multicores can be formulated as an Integer Linear Programming (ILP) problem but ILP solver takes exponential time to provide an optimal solution. We propose metaheuristic algorithms to achieve near optimal solutions within a reasonable amount of time. We employ six different variants of the Hill-Climbing (HC) algorithm employing different tweak operators that produce excellent result extremely quickly. We also propose six different variants of Genetic Algorithm (GA) to examine how effective these variants can be in escaping the local optima. We finally combine HC and GA techniques (which is also known as ‘ memetic algorithm ’) to produce hybrid techniques that outperform the individual performance of HC and GA techniques. We compare our results with the results generated by the CPLEX optimization tool. Our best technique has achieved a geometric mean speedup of 7.42× across a range of StreamIt benchmarks on an eight-core processor. [ABSTRACT FROM AUTHOR]

This paper employs the Memetic algorithm (MA) to optimize the urban transit network. Aiming at the optimal route configuration and service frequency for the urban transit network, the objective function of the proposed mathematical model is to minimize the passenger (user) cost and to reduce the unsatisfied passenger demand at most. MA is one of the recent growing evolutionary computation algorithms. It is imbedded with the local search operator based on the classical genetic algorithm (GA) to improve the computational performance. We represent the solution with two single link lists (SLL), and design four types of local search operators: 2-opt move (Type A), 2-opt move (Type B), swap move and relocation move to obtain the better chromosomes for the GA. At the same time, an effective try-an-error procedure for verifying the local search operator is presented to increase the search efficiency. The algorithm has been tested with benchmark problems reported in the existing literatures. Comparing the results obtained by our algorithm and traditional algorithms which have been proved to be efficient, it demonstrates that the proposed algorithm could improve the computational performance relative to other algorithms. [ABSTRACT FROM AUTHOR]

In this paper, an evolutionary multiobjective algorithm (NSGA-II) and some local search methods are employed to solve the power distribution network design problem. The design procedure takes into account three relevant aspects: monetary cost, fault cost (reliability) and robustness (ability to deal with different scenarios of load growth). The final objective is to identify topologies (conductor configuration and capacity) that are efficient with regard to cost and reliability at the same time they are robust enough for dealing with uncertainties on load prediction. Uncertainties in the load growth, energy price and interest rate are considered. Four local search methods are proposed in order to improve solution robustness and reliability, taking into account a given set of possible scenarios. The proposed algorithm achieves high-quality solutions with low computational cost, outperforming the results achieved by former works that dealt with similar problem formulations. Results for 21, 100 and 300 bus systems are presented in order to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Simple Summary: Due to lacking exploitation capability, traditional genetic algorithm cannot accurately identify the minimal best gene subset. Thus, the improved splicing method is introduced into a genetic algorithm to enhance exploitation capability for achieving balance between exploitation and exploration of GA. It can effectively identify true gene subsets with high probability. Furthermore, a dataset of the body weight of Hu sheep has been used to show that the proposed method can obtain a better minimal subset of genes with a few iterations, compared with all considered algorithms including genetic algorithm and adaptive best-subset selection algorithm. Selecting the minimal best subset out of a huge number of factors for influencing the response is a fundamental and very challenging NP-hard problem because the presence of many redundant genes results in over-fitting easily while missing an important gene can more detrimental impact on predictions, and computation is prohibitive for exhaust search. We propose a modified memetic algorithm (MA) based on an improved splicing method to overcome the problems in the traditional genetic algorithm exploitation capability and dimension reduction in the predictor variables. The new algorithm accelerates the search in identifying the minimal best subset of genes by incorporating it into the new local search operator and hence improving the splicing method. The improvement is also due to another two novel aspects: (a) updating subsets of genes iteratively until the no more reduction in the loss function by splicing and increasing the probability of selecting the true subsets of genes; and (b) introducing add and del operators based on backward sacrifice into the splicing method to limit the size of gene subsets. Additionally, according to the experimental results, our proposed optimizer can obtain a better minimal subset of genes with a few iterations, compared with all considered algorithms. Moreover, the mutation operator is replaced by it to enhance exploitation capability and initial individuals are improved by it to enhance efficiency of search. A dataset of the body weight of Hu sheep was used to evaluate the superiority of the modified MA against the genetic algorithm. According to our experimental results, our proposed optimizer can obtain a better minimal subset of genes with a few iterations, compared with all considered algorithms including the most advanced adaptive best-subset selection algorithm. [ABSTRACT FROM AUTHOR]