Development of Pareto-based evolutionary model integrated with dynamic goal programming and successive linear objective reduction

Multi-Objective History Matching with a Proxy Model for the Characterization of Production Performances at the Shale Gas Reservoir

“…rejected by the crowding-distance sorting for the diversity preservation. The crowding distance of the j th response C j can be defined using Equation (14) [24], as follows: (14) where N is the number of objective functions, d i j is the displacement between two neighboring points with the j th response in the direction of the i th objective function, r i max is the maximum response in the direction of the i th objective function, and r i min is the minimum response in the direction of the i th objective function (see Figure 5b). The responses with the lower crowding distance are rejected for diversity preservation, and upon the completion of the crowding-distance sorting, the surviving responses are selected for the next generation P t+1 .…”

“…The proposed multi-objective history matching shows a lesser number of errors for both the history matching and the prediction compared to the single-objective optimization. The single-objective optimization shows a scale-dependency problem whereby it leans toward its allocated objective function [23][24][25]. The case of the arithmetic averaged error, f 3 is located at the middle point between f 1 and f 2 , as shown in Figure 11a.…”

Quick Screening of Pareto-Optimal Operating Conditions for Expanding Solvent–Steam Assisted Gravity Drainage Using Hybrid Multi-Objective Optimization Approach

“…This result implies a possibility of objective-redundancy: discarding either RF or SR from the objective vector might yield similar optimization results. Because the convergence speed of non-dominated sorting is dependent on the number of objective functions, selection of essential objective functions is a salient issue in the process of multi-objective optimization [28]. Nonetheless, handling objective-redundancy is out of the scope of this study as the NSGA-II implemented in the proposed framework has explored the POFs of a variety of three-objective problems with reliability.…”

“…For a minimization problem, exploring the global optimum is to find the smallest objective-sum that depends on the weight factors determined a priori. As a result, solutions tend to evolve in the direction of minimizing the objective-sum regardless of the characteristics of each objective function [27][28][29]. For this reason, global-objective optimization approaches are inappropriate to provide diversified solutions in case individual objective functions conflict with each other.…”

“…This diversity-preservation of converged solutions highlights the significance of multi-objective optimization for avoiding artificial bias in uncertainty quantification. Multi-objective optimization algorithms have been examined to solve a variety of optimization issues in subsurface modeling as follows: monitoring the migration of contaminant plume [32][33][34][35]; reservoir characterization [27][28][29][36][37][38]; and production design [39,40].…”