Solving chemical dynamic optimization problems with ranking-based differential evolution algorithms

Squid Game Optimizer (SGO): a novel metaheuristic algorithm

In this paper, Squid Game Optimizer (SGO) is proposed as a novel metaheuristic algorithm inspired by the primary rules of a traditional Korean game. Squid game is a multiplayer game with two primary objectives: attackers aim to complete their goal while teams try to eliminate each other, and it is usually played on large, open fields with no set guidelines for size and dimensions. The playfield for this game is often shaped like a squid and, according to historical context, appears to be around half the size of a standard basketball court. The mathematical model of this algorithm is developed based on a population of solution candidates with a random initialization process in the first stage. The solution candidates are divided into two groups of offensive and defensive players while the offensive player goes among the defensive players to start a fight which is modeled through a random movement toward the defensive players. By considering the winning states of the players of both sides which is calculated based on the objective function, the position updating process is conducted and the new position vectors are produced. To evaluate the effectiveness of the proposed SGO algorithm, 25 unconstrained mathematical test functions with 100 dimensions are used, alongside six other commonly used metaheuristics for comparison. 100 independent optimization runs are conducted for both SGO and the other algorithms with a pre-determined stopping condition to ensure statistical significance of the results. Statistical metrics such as mean, standard deviation, and mean of required objective function evaluations are calculated. To provide a more comprehensive analysis, four prominent statistical tests including the Kolmogorov-Smirnov, Mann-Whitney, and Kruskal-Wallis tests are used. Meanwhile, the ability of the suggested SGOA is assessed through the cutting-edge real-world problems on the newest CEC like CEC 2020, while the SGO demonstrate outstanding performance in dealing with these complex optimization problems. The overall assessment of the SGO indicates that the proposed algorithm can provide competitive and remarkable outcomes in both benchmark and real-world problems.

Adaptive Differential Evolution Algorithm Based on Fitness Landscape Characteristic

Differential evolution (DE) is a simple, effective, and robust algorithm, which has demonstrated excellent performance in dealing with global optimization problems. However, different search strategies are designed for different fitness landscape conditions to find the optimal solution, and there is not a single strategy that can be suitable for all fitness landscapes. As a result, developing a strategy to adaptively steer population evolution based on fitness landscape is critical. Motivated by this fact, in this paper, a novel adaptive DE based on fitness landscape (FL-ADE) is proposed, which utilizes the local fitness landscape characteristics in each generation population to (1) adjust the population size adaptively; (2) generate DE/current-to-pcbest mutation strategy. The adaptive mechanism is based on local fitness landscape characteristics of the population and enables to decrease or increase the population size during the search. Due to the adaptive adjustment of population size for different fitness landscapes and evolutionary processes, computational resources can be rationally assigned at different evolutionary stages to satisfy diverse requirements of different fitness landscapes. Besides, the DE/current-to-pcbest mutation strategy, which randomly chooses one of the top p% individuals from the archive cbest of local optimal individuals to be the pcbest, is also an adaptive strategy based on fitness landscape characteristic. Using the individuals that are approximated as local optimums increases the algorithm’s ability to explore complex multimodal functions and avoids stagnation due to the use of individuals with good fitness values. Experiments are conducted on CEC2014 benchmark test suit to demonstrate the performance of the proposed FL-ADE algorithm, and the results show that the proposed FL-ADE algorithm performs better than the other seven highly performing state-of-art DE variants, even the winner of the CEC2014 and CEC2017. In addition, the effectiveness of the adaptive population mechanism and DE/current-to-pcbest mutation strategy based on landscape fitness proposed in this paper are respectively verified.

A hybrid differential evolution and simulated annealing algorithm for global optimization

Differential evolution (DE) is one of the most effective ways to solve global optimization problems. However, considering the traditional DE has lower search efficiency and easily traps into local optimum, a novel DE variant named hybrid DE and simulated annealing (SA) algorithm for global optimization (HDESA) is proposed in this paper. This algorithm introduces the concept of “ranking” into the mutation operation of DE and adds the idea of SA to the selection operation. The former is to improve the exploitation ability and increase the search efficiency, and the latter is to enhance the exploration ability and prevent the algorithm from trapping into the local optimal state. Therefore, a better balance can be achieved. The experimental results and analysis have shown its better or at least equivalent performance on the exploitation and exploration capability for a set of 24 benchmark functions. It is simple but efficient.

Improved Seagull Optimization Algorithm Combined with an Unequal Division Method to Solve Dynamic Optimization Problems

The numerical solution of the dynamic optimization problem is often sought for chemical processes, but the discretization of control variables is a difficult problem. Firstly, based on the analysis of the seagull optimization algorithm, this paper introduces the cognitive part in the process of a seagull’s attack behavior to make the group approach the best position. Secondly, the algorithm adds the mechanism of natural selection, where the fitness value is used to sort the population, and the best half is used to replace the worst half, so as to find out the optimal solution. Finally, the improved seagull optimization algorithm (ISOA) is combined with the unequal division method to solve dynamic optimization problems. The feasibility of the method is verified by three practical examples of dynamic optimization in chemical industry.

Quadratic Interpolation Based Simultaneous Heat Transfer Search Algorithm and Its Application to Chemical Dynamic System Optimization

Dynamic optimization problems (DOPs) are widely encountered in complex chemical engineering processes. However, due to the existence of highly constrained, nonlinear, and nonsmooth environment in chemical processes, which usually causes nonconvexity, multimodality and discontinuity, handling DOPs is not a straightforward task. Heat transfer search (HTS) algorithm is a relative novel metaheuristic approach inspired by the natural law of thermodynamics and heat transfer. In order to solve DOPs efficiently, a new variant of HTS algorithm named quadratic interpolation based simultaneous heat transfer search (QISHTS) algorithm is proposed in this paper. The QISHTS algorithm introduces three modifications into the original HTS algorithm, namely the effect of simultaneous heat transfer search, quadratic interpolation method, and population regeneration mechanism. These three modifications are employed to provide lower computational complexity, as well as to enhance the exploration and exploitation capabilities. Therefore, the ensemble of these modifications can provide a more efficient optimization algorithm with well-balanced exploration and exploitation capabilities. The proposed variant is firstly investigated by well-defined benchmark problems and then applied to solve four chemical DOPs. Moreover, it is compared with different well-established methods existing in the literature. The results demonstrate that QISHTS algorithm has the greatest robustness and precision than other competitors.