Within U-shaped assembly lines, the increase of labour costs and subsequent utilisation of robots has led to growing energy consumption, which is the current main expense of auto and electronics industries. However, there are limited researches concerning both energy consumption reduction and productivity improvement on U-shaped robotic assembly lines. This paper first develops a nonlinear multi-objective mixed-integer programming model, reformulates it into a linear form by linearising the multiplication of two binary variables, and then refines the weight of multiple objectives so as to achieve a better approximation of true Pareto frontiers. In addition, Pareto artificial bee colony algorithm (PABC) is extended to tackle this new complex problem. This algorithm stores all the non-dominated solutions into a permanent archive set to keep all the good genes, and selects one solution from this set to overcome the strong local minima. Comparative experiments based on a set of newly generated benchmarks verify the superiority of the proposed PABC over four multi-objective algorithms in terms of generation distance, maximum spread, hypervolume ratio and the ratio of non-dominated solution.

In practical assembly enterprises, customization and rush orders lead to an uncertain demand environment. This situation requires managers and researchers to configure an assembly line that increases production efficiency and robustness. Hence, this work addresses cost-oriented mixed-model multimanned assembly line balancing under uncertain demand, and presents a new robust mixed-integer linear programming model to minimize the production and penalty costs simultaneously. In addition, a reinforcement learning-based multiobjective evolutionary algorithm (MOEA) is designed to tackle the problem. The algorithm includes a priority-based solution representation and a new task-worker-sequence decoding that considers robustness processing and idle time reductions. Five crossover and three mutation operators are proposed. The $Q$ -learning-based strategy determines the crossover and mutation operator at each iteration to effectively obtain Pareto sets of solutions. Finally, a time-based probability-adaptive strategy is designed to effectively coordinate the crossover and mutation operators. The experimental study, based on 269 benchmark instances, demonstrates that the proposal outperforms 11 competitive MOEAs and a previous single-objective approach to the problem. The managerial insights from the results as well as the limitations of the algorithm are also highlighted.