Multi-objective bacterial foraging optimization algorithm based on parallel cell entropy for aluminum electrolysis production process

Environment-friendly aluminum electrolysis production process has long been a challenging industrial issue due to its built-in difficulty in optimizing numerous highly coupled and nonlinear parameters. This paper presents a multi-objective bacterial foraging optimization (MOBFO) algorithm to find optimal solutions that maximize the current efficiency and minimize the energy consumption and the production of perfluorocarbons (PFCs). Our method can be viewed as an enhanced version of the bacterial foraging optimization (BFO) in solving multi-objective optimization (MOO) problems (MOPs). We first propose a task-oriented optimization framework and model, and then parallel cell entropy and its difference are introduced to evaluate the evolutionary status of the Pareto solutions in a new objective space called parallel cell coordinate system (PCCS). In particular, the Pareto-archived evolution approach (PAEA) and the adaptive foraging strategy (AFS) are applied to balance the convergence and diversity of the Pareto front in the optimization procedure. Compared with traditional approaches, MOBFO not only increases speed of convergence toward the Pareto front, but also improves the diversity of the obtained solutions. Extensive experiment results on numerous benchmark problems and real-world aluminum electrolysis production process validated our proposed method\u27s effectiveness

Enhanced Harris's Hawk algorithm for continuous multi-objective optimization problems

Multi-objective swarm intelligence-based (MOSI-based) metaheuristics were proposed to solve multi-objective optimization problems (MOPs) with conflicting objectives. Harris’s hawk multi-objective optimizer (HHMO) algorithm is a MOSIbased algorithm that was developed based on the reference point approach. The reference point is determined by the decision maker to guide the search process to a particular region in the true Pareto front. However, HHMO algorithm produces a poor approximation to the Pareto front because lack of information sharing in its population update strategy, equal division of convergence parameter and randomly generated initial population. A two-step enhanced non-dominated sorting HHMO (2SENDSHHMO) algorithm has been proposed to solve this problem. The algorithm includes (i) a population update strategy which improves the movement of hawks in the search space, (ii) a parameter adjusting strategy to control the transition between exploration and exploitation, and (iii) a population generating method in producing the initial candidate solutions. The population update strategy calculates a new position of hawks based on the flush-and-ambush technique of Harris’s hawks, and selects the best hawks based on the non-dominated sorting approach. The adjustment strategy enables the parameter to adaptively changed based on the state of the search space. The initial population is produced by generating quasi-random numbers using Rsequence followed by adapting the partial opposition-based learning concept to improve the diversity of the worst half in the population of hawks. The performance of the 2S-ENDSHHMO has been evaluated using 12 MOPs and three engineering MOPs. The obtained results were compared with the results of eight state-of-the-art multi-objective optimization algorithms. The 2S-ENDSHHMO algorithm was able to generate non-dominated solutions with greater convergence and diversity in solving most MOPs and showed a great ability in jumping out of local optima. This indicates the capability of the algorithm in exploring the search space. The 2S-ENDSHHMO algorithm can be used to improve the search process of other MOSI-based algorithms and can be applied to solve MOPs in applications such as structural design and signal processing