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Max-cut is one of the most classic NP-hard combinatorial optimization problems. The symmetry nature of it leads to special difficulty in extracting meaningful configuration information for learning; none of the state-of-the-art algorithms has employed any learning operators. This paper proposes an original learning method for max-cut, namely post-flip edge-state learning (PF-ESL). Different from previous algorithms, PF-ESL regards edge-states (cut or not cut) rather than vertex-positions as the critical information of a configuration, and extracts their statistics over a population for learning. It is based on following observations. 1) Edges are the only factors considered by the objective function. 2) Edge-states keep invariant when rotating a local configuration to its symmetry position, but vertex-positions do not. These suggest that edge-states contain more meaningful information about a configuration than vertex-positions do. It is impossible to set the state of an edge without influencing some other edges' states due to their dependencies. Therefore, instead of setting edge-states directly, PF-ESL samples the flips on vertices. Flips on vertices are sampled according to their capacities in increasing the similarity on edge-states between the given solution and a population. PF-ESL is employed in an EDA (Estimation of Distribution Algorithm) perturbation operator and a path-relinking operator. Experimental results show that our algorithm is competitive, and show that edge-state learning is value-added for both the two operators. The main contributions of this paper are as follows. Firstly, previous state-of-the-art evolutionary algorithms for max-cut focus on vertex positions in their evolutionary operation, this paper proposes a new and more reasonable perspective suggesting that edge-states are the critical information of divided graphs rather than vertex positions, and introduces a novel method to measure and utilize their similarities based on it. Such a perspective is fundamental to learning based algorithms design for max-cut and other graph partitioning problems, and can shed lights on future researches. Furthermore, since max-cut is one of the most classic and fundamental NP hard problems, many real-world problems involve dividing graph data into different parts to optimize certain functions, this new perspective may inspire related or similar problems. Secondly, besides the original edge-states based perspective, and the post-flip edge-states learning (PFESL) operator based on it, our memetic algorithm also incorporates a novel evolutionary framework which alternates between EDA based Iterated Tabu search (ITS) and path relinking based genetic algorithm. Finally, the proposed algorithm provides competitive results on two mostly used benchmark sets and improves the best-known results of 6 most challenging instances. • An original edge-state perspective for design learning operators for max-cut. • A novel learning operator to learn edge states. • A new evolutionary framework for max-cut. • It provides competitive results on two mostly used benchmark sets. [ABSTRACT FROM AUTHOR]

Metaheuristics, providing high level guidelines for heuristic optimisation, have successfully been applied to many complex problems over the past decades. However, their performances often vary depending on the choice of the initial settings for their parameters and operators along with the characteristics of the given problem instance handled. Hence, there is a growing interest into designing adaptive search methods that automate the selection of efficient operators and setting of their parameters during the search process. In this study, an adaptive binary parallel evolutionary algorithm, referred to as ABPEA, is introduced for solving the uncapacitated facility location problem which is proven to be an NP-hard optimisation problem. The approach uses a unary and two other binary operators. A reinforcement learning mechanism is used for assigning credits to operators considering their recent impact on generating improved solutions to the problem instance in hand. An operator is selected adaptively with a greedy policy for perturbing a solution. The performance of the proposed approach is evaluated on a set of well-known benchmark instances using ORLib and M*, and its scaling capacity by running it with different starting points on an increasing number of threads. Parameters are adjusted to derive the best configuration of three different rewarding schemes, which are instant, average and extreme. A performance comparison to the other state-of-the-art algorithms illustrates the superiority of ABPEA. Moreover, ABPEA provides up to a factor of 3.9 times acceleration when compared to the sequential algorithm based on a single-operator. • This paper proposes a multi-threaded adaptive evolutionary algorithm. • The proposed approach (ABPEA) is tested on the well-known binary-encoded problem UFLP. • An operator is selected adaptively with a greedy policy for perturbing a solution. • Three rewarding schemes, which are instant, average and extreme, are discussed. • Effect of varying the number of threads on the performance of ABPEA is investigated. [ABSTRACT FROM AUTHOR]

• A new method to solve global optimization called BGWO. • The beetle antenna strategy is adopted to provide hearing for the leader wolf. • Exploration and exploitation are balanced by a new nonlinear strategy. • Evaluation of proposed method on 23 benchmark functions and 4 engineering problems. • The performance of BGWO is better than other state-of-the-art algorithms. Finding feasible solutions to real-world problems is a crucial task. Metaheuristic algorithms are widely used in many fields due to the variety of solutions they can produce. The grey wolf optimizer (GWO) is a relatively novel population-based metaheuristic algorithm that has been shown to have good optimization performance. However, due to the insufficient diversity of wolves in some cases, this approach can lead to locally optimal situations. Therefore, this paper proposes a grey wolf optimization method based on a beetle antenna strategy (BGWO) that gives the leader wolf a sense of hearing to improve the global search ability and reduce unnecessary searches. In addition, to balance exploration and exploitation, a nonlinear dynamic control parameter update strategy based on the cosine function is proposed. To evaluate the performance of the proposed BGWO, this paper uses 23 standard benchmark functions to test the method in different dimensions. Moreover, four well-known engineering problems are used to evaluate the ability of the proposed algorithm to obtain real-world problem solutions. The experimental results show that BGWO has superior performance and is competitive with many state-of-the-art algorithms in terms of solution accuracy, convergence rate, and stability. [ABSTRACT FROM AUTHOR]

Sine cosine algorithm (SCA) is a recently developed and widely used metaheuristic to perform global optimization tasks. Due to its simplicity in structure and reasonable performance, it has been utilized to solve several real-world applications. This paper proposes an alternate version of the SCA by adopting the greedy approach of search, crossover and exponentially decreased transition control parameter to overcome the issues of low exploitation, insufficient diversity and premature convergence. The proposed algorithm, called ECr-SCA, is validated and compared with the original SCA using computational time, diversity, performance index, statistical and convergence analysis on a set of 23 standard benchmark problems. Later, the proposed ECr-SCA is compared with seventeen other algorithms including improved versions of the SCA and state-of-the-art algorithms. Furthermore, the ECr-SCA is used to train multi-layer perceptron and the results are compared with variants of SCA and other metaheuristics. Overall comparison based on several different metrics illustrates the significant improvement in the search strategy of the SCA by the proposal of the ECr-SCA. • The enhanced sine cosine algorithm (ECr-SCA) is proposed for global optimization. • A greedy search and modified transition parameter are used to increase exploitation. • The multi-parent crossover is embedded to enhance diversity and global search. • The excellent performance of the ECr-SCA is validated on benchmark problems. • The ECr-SCA is also used to train multilayer perceptron. [ABSTRACT FROM AUTHOR]

In the crowded environment of bio-inspired population-based metaheuristics, the Salp Swarm Optimization (SSO) algorithm recently appeared and immediately gained a lot of momentum. Inspired by the peculiar spatial arrangement of salp colonies, which are displaced in long chains following a leader, this algorithm seems to provide an interesting optimization performance. However, the original work was characterized by some conceptual and mathematical flaws, which influenced all ensuing papers on the subject. In this manuscript, we perform a critical review of SSO, highlighting all the issues present in the literature and their negative effects on the optimization process carried out by this algorithm. We also propose a mathematically correct version of SSO, named Amended Salp Swarm Optimizer (ASSO) that fixes all the discussed problems. We benchmarked the performance of ASSO on a set of tailored experiments, showing that it is able to achieve better results than the original SSO. Finally, we performed an extensive study aimed at understanding whether SSO and its variants provide advantages compared to other metaheuristics. The experimental results, where SSO cannot outperform simple well-known metaheuristics, suggest that the scientific community can safely abandon SSO. • Critical analysis of the widely-used salp optimization algorithm (SSO). • Definition of an amended version of SSO that fixed SSO's structural bias. • Extensive experimental phase using the CEC 2017 benchmark suite. • Results show that SSO does not provide any advantage w.r.t. existing heuristics. • Metaphor-based approach to design metaheuristics may introduce bias. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose PSO–EDA, a hybrid particle swarm optimization (PSO) with estimation of distribution algorithm (EDA) to solve permutation flowshop scheduling problem (PFSP). PFSP is an NP-complete problem, for which PSO was recently applied. The social cognition in the metaphor of canonical PSO is incomplete, since information conveyed in the non-gbest particles is lost. Also, the intelligence of the particles is totally neglected by the canonical PSO and most of other literatures. To tackle such problems, we propose to enable the sharing of information from the collective experience of the swarm by hybridizing an EDA operator with PSO and to add the primitive intelligence to each particle by using a local search mechanism. To enhance the performance of the algorithm proposed, a new local search algorithm, the minimization-of-waiting-time local search (MWL), is applied. The computational experiment on different benchmark suites in PFSP, in which two new best known solutions have been found, shows a superiority of PSO–EDA over other counterpart algorithms in terms of accuracy. [ABSTRACT FROM AUTHOR]

• A new optimization algorithm based on Lichtenberg figure pattern is presented. • Difussion Limited Aggregation is formulated to create new agents in search space. • Lichtenberg figure pattern presents exploration–exploitation balance. • Tested on complex functions and problems and compared with renowned metaheuristics. This paper proposes a novel global optimization algorithm called Lichtenberg Algorithm (LA), inspired by the Lichtenberg figures patterns. Optimization is an essential tool to minimize or maximize functions, obtaining optimal results on costs, mass, energy, gains, among others. Actual problems may be multimodal, nonlinear, and discontinuous and may not be minimized by classical analytical methods that depend on the gradient. In this context there are metaheuristics algorithms inspired by natural phenomena to optimize real problems. There is no algorithm that is the worst or the best, but more efficient for a given type of problem. Thus, an unprecedented metaheuristic algorithm was created inspired by the physical phenomenon of radial intra-cloud lightning and Lichtenberg figures, successfully exploiting the fractal power and it is different from many in the literature as it is a hybrid algorithm composed of methods of search based on population and trajectory. Several test functions, including a design problem in a welded beam, were used to verify the robustness and to validate the Lichtenberg Algorithm. In all cases, the results were satisfactory when compared to those in the literature. LA shown to be a powerful optimization tool for both unconstraint optimizations and real problems with linear and nonlinear constraints. [ABSTRACT FROM AUTHOR]