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

This paper presents a new Pareto-based evolutionary model incorporated with preference-ordering and objective-dimension reduction to improve the multi-directional searches for multi-objective problems.It induces a convergence toward the Pareto-optimal front by adjusting aspiration levels allocated to objectives and by excluding redundant objectives during optimization.Its usefulness was validated for multi-objective test problems comparing to conventional single- and multi-objective optimization models. This study investigates the coupling effects of objective-reduction and preference-ordering schemes on the search efficiency in the evolutionary process of multi-objective optimization. The difficulty in solving a many-objective problem increases with the number of conflicting objectives. Degenerated objective space can enhance the multi-directional search toward the multi-dimensional Pareto-optimal front by eliminating redundant objectives, but it is difficult to capture the true Pareto-relation among objectives in the non-optimal solution domain. Successive linear objective-reduction for the dimensionality-reduction and dynamic goal programming for preference-ordering are developed individually and combined with a multi-objective genetic algorithm in order to reflect the aspiration levels for the essential objectives adaptively during optimization. The performance of the proposed framework is demonstrated in redundant and non-redundant benchmark test problems. The preference-ordering approach induces the non-dominated solutions near the front despite enduring a small loss in diversity of the solutions. The induced solutions facilitate a degeneration of the Pareto-optimal front using successive linear objective-reduction, which updates the set of essential objectives by excluding non-conflicting objectives from the set of total objectives based on a principal component analysis. Salient issues related to real-world problems are discussed based on the results of an oil-field application.

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