Direct zigzag search for discrete multi-objective optimization

Multiple objective optimization (MOO) models and solution methods are commonly used for multi-criteria decision making in real-life engineering and management applications. Much research has been conducted for continuous MOO problems, but MOO problems with discrete or mixed integer variables and black-box objective functions arise frequently in practice. For example, in energy industry, optimal development problems of oil gas fields, shale gas hydraulic fracturing, and carbon dioxide geologic storage and enhanced oil recovery, may consider integer variables (number of wells, well drilling blocks), continuous variables (e.g. bottom hole pressures, production rates), and the field performance is typically evaluated by black-box reservoir simulation. These discrete or mixed integer MOO (DMOO) problems with black-box objective functions are more challenging and require new MOO solution techniques. We develop a direct zigzag (DZZ) search method by effectively integrating gradient-free direct search and zigzag search for such DMOO problems. Based on three numerical example problems including a mixed integer MOO problem associated with the optimal development of a carbon dioxide capture and storage (CCS) project, DZZ is demonstrated to be computationally efficient. The numerical results also suggest that DZZ significantly outperforms NSGA-II, a widely used genetic algorithms (GA) method.