本研究考慮了彈性零工式排程問題(Flexible job shop scheduling problem)，旨在最小化總延遲時間(Total tardiness)和Total number of tardy stage-outs，其中限制條件包括批次處理(Batching)和順序相依整備時間(Sequence-dependent setup time)。兩個目標的解可以用分離圖(Conjunctive graph)來表示。再者，Total number of tardy stage-outs的目標可以用layer的方式呈現在分離圖中。NSGA-II將被採用作為基於帕累托(Pareto-based)的方法尋找解答來解決雙目標問題。鄰域結構(Neighborhood structure)將被使用於突變運算子(Mutation operator)中且包含兩種類型的移動(Move)。移動的可行性保證(Feasibility guarantees)確保移動後不會產生循環(Cycle)。對於兩個目標的下界(Lower bounds)期待能確保在兩個目標的移動之後不會有增加目標值。兩種移動的偏好值(Preference value)有助於選擇哪個作業(Operation)或子區塊(Sub-block)將進行移動。此外，基於下界的階層式移動分類(Hierarchy of moves)將被應用以試圖增強多樣性。;The study considers a flexible job-shop scheduling problem to minimize the total tardiness and the total number of tardy stage-outs with batching and sequence-dependent setup time. The solution representation for the two objectives can be described in a conjunctive graph. Besides, the objective of the total number of tardy stage-outs can be depicted in a disjunctive graph with layers. NSGA-II, a Pareto-based approach, is applied to find solutions for the bi-objective problem. The neighborhood structure is involved in the mutation operator, incorporating the two types of moves. Feasibility guarantees for the moves ensure that a cycle will not be generated after their execution. The lower bounds for the two objectives are found. The preference value for two types of moves helps select an operation or sub-block to move. Moreover, the hierarchy of moves based on the lower bounds is applied in an effort to enhance diversification.
