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One of the limitations of the dung beetle optimization (DBO) is its susceptibility to local optima and its relatively low search accuracy. Several strategies have been utilized to improve the diversity, search precision, and outcomes of the DBO. However, the equilibrium between exploration and exploitation has not been achieved optimally. This paper presents a novel algorithm called the ODBO, which incorporates cat map and an opposition-based learning strategy, which is based on symmetry theory. In addition, in order to enhance the performance of the dung ball rolling phase, this paper combines the global search strategy of the osprey optimization algorithm with the position update strategy of the DBO. Additionally, we enhance the population’s diversity during the foraging phase of the DBO by incorporating vertical and horizontal crossover of individuals. This introduction of asymmetry in the crossover operation increases the exploration capability of the algorithm, allowing it to effectively escape local optima and facilitate global search.

For most of differential evolution (DE) algorithm variants, premature convergence is still challenging. The main reason is that the exploration and exploitation are highly coupled in the existing works. To address this problem, we present a novel DE variant that can symmetrically decouple exploration and exploitation during the optimization process in this paper. In the algorithm, the whole population is divided into two symmetrical subpopulations by ascending order of fitness during each iteration; moreover, we divide the algorithm into two symmetrical stages according to the number of evaluations (FEs). On one hand, we introduce a mutation strategy, DE/current/1, which rarely appears in the literature. It can keep sufficient population diversity and fully explore the solution space, but its convergence speed gradually slows as iteration continues. To give full play to its advantages and avoid its disadvantages, we propose a heterogeneous two-stage double-subpopulation (HTSDS) mechanism. Four mutation strategies (including DE/current/1 and its modified version) with distinct search behaviors are assigned to superior and inferior subpopulations in two stages, which helps simultaneously and independently managing exploration and exploitation in different components. On the other hand, an adaptive two-stage partition (ATSP) strategy is proposed, which can adjust the stage partition parameter according to the complexity of the problem. Hence, a two-stage differential evolution algorithm with mutation strategy combination (TS-MSCDE) is proposed. Numerical experiments were conducted using CEC2017, CEC2020 and four real-world optimization problems from CEC2011. The results show that when computing resources are sufficient, the algorithm is competitive, especially for complex multimodal problems.

Swarm-based algorithm can successfully avoid the local optimal constraints, thus achieving a smooth balance between exploration and exploitation. Salp swarm algorithm (SSA), as a swarm-based algorithm on account of the predation behavior of the salp, can solve complex daily life optimization problems in nature. SSA also has the problems of local stagnation and slow convergence rate. This paper introduces an improved salp swarm algorithm, which improve the SSA by using the chaotic sequence initialization strategy and symmetric adaptive population division. Moreover, a simulated annealing mechanism based on symmetric perturbation is introduced to enhance the local jumping ability of the algorithm. The improved algorithm is referred to SASSA. The CEC standard benchmark functions are used to evaluate the efficiency of the SASSA and the results demonstrate that the SASSA has better global search capability. SASSA is also applied to solve engineering optimization problems. The experimental results demonstrate that the exploratory and exploitative proclivities of the proposed algorithm and its convergence patterns are vividly improved.

Proposing new strategies to improve the optimization performance of differential evolution (DE) is an important research study. The jSO algorithm was the announced winner of the Congress on Evolutionary Computation (CEC) 2017 competition on numerical optimization, and is the state-of-the-art algorithm in the SHADE (Success-History based Adaptive Differential Evolution) algorithm series. However, the jSO algorithm converges prematurely in the search space with different dimensions and is prone to falling into local optimum during evolution, as well as the problem of decreasing population diversity. In this paper, a modified jSO algorithm (MjSO) is proposed which is based on cosine similarity with parameter adaptation and a novel opposition-based learning restart mechanism incorporated with symmetry to address the above problems, respectively. Moreover, it is well known that parameter setting has a significant impact on the performance of the algorithm and the search process can be divided into two symmetrical parts. Hence, a parameter control strategy based on a symmetric search process is introduced in the MjSO. The effectiveness of these designs is supported by presenting a population clustering analysis, along with a population diversity measure to evaluate the performance of the proposed algorithm, three state-of-the-art DE variant algorithms (EBLSHADE, ELSHADE-SPACMA, and SALSHADE-cnEPSin) and two original algorithms (jSO and LSHADE) are compared with it, for solving 30 CEC’17 benchmark functions and three classical engineering design problems. The experimental results and analysis reveal that the proposed algorithm can outperform other competitions in terms of the convergence speed and the quality of solutions. Promisingly, the proposed method can be treated as an effective and efficient auxiliary tool for more complex optimization models and scenarios.