Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)




Computing and Decision Sciences

First Advisor

Prof. WONG Man Leung

Second Advisor

Prof. SEE-TO Wing Kuen Eric


Evolutionary computation is interdisciplinary research which has been widely incorporated in various disciplines from different research fields. As a result, it leads to somewhat different research focuses like multimodal optimization, constrained optimization, and expensive optimization. In this dissertation, we focus on multiobjective-based differential evolution in computer science which refers to computational intelligence and artificial intelligence.

Many NP-hard optimization problems are highly constrained and multimodal. The optimizer needs to handle constraints, minimize the objective function, and locate multiple global or local optimal solutions. Meanwhile, this kind of optimization problems is difficult to have a mathematically deterministic formulation, and in some cases, it is also very expensive to compute. The research of multiobjective-based differential evolution has solved these problems in a new perspective of multiobjective-based transformation.

We first study the nonlinear equation systems with many and infinitely many roots. One of our contributions is an attempt to deploy the decomposition-based multiobjective optimization to solve nonlinear equation systems, especially with infinite roots. In our novel approach, a given system is transformed into a bi-objective optimization problem using reference points. An improved decomposition-based multiobjective optimization is then applied to solve the transformed bi-objective optimization problem. Furthermore, to ensure this optimization suits the characteristics of the transformed problem, we develop an adaptive local search. As a result, the roots of the original nonlinear equation system can then be identified together with the Pareto-optimal solutions of the transformed problem.

Furthermore, we improved the transformation to solve the most common nonlinear equation systems that include multiple roots. The major contributions are twofold. First, we transform a given system with any type and any number of nonlinear equations into a dynamic triobjective optimization problem. Second, we develop a self-adaptive ranking multi-objective differential evolution. In addition, a probability distribution-based local search is introduced, which aims to identify the optimal solutions with a high level of accuracy. Based on the studies of numerical optimizations with multiple solutions, the proposed approach has been demonstrated more suitable for a nonlinear equation system.

According to the successful achievement on nonlinear equation systems, we extended the idea of transformation into power economic dispatch system, which is a kind of typical constrained optimization problems. An economic dispatch problem is first transformed into a triobjective optimization problem, and then multiobjective optimization techniques are employed to fully optimize the constraints and cost function simultaneously. The first two objectives are derived from the original economic dispatch problem, while the third one is a novel density objective constructed by niching methods to enhance population diversity. These three objectives are optimized simultaneously by a dynamic dominance relation, which can make a good balance among feasibility, diversity, and convergence.

In addition, an attempt has been made to explore the multiobjective-based transformation for constrained multiobjective optimization problems. We have improved the e-constrainthandling method which is originally devised to solve constrained optimization problems with only one objective. Another contribution is the development of a linear population size expansion strategy that can achieve a better approximation to the feasible Pareto front. As a result, a simple yet efficient constrained multiobjective differential evolution has been designed.

Finally, the expensive multimodal optimization is proposed as a new research topic for the future study. Surrogate-assisted evolutionary algorithms for expensive optimization problems have gained considerable attention in recent years. However, few studies have been made to solve expensive multimodal optimization problems characterized by multiple optimal solutions. Locating multiple optima for such expensive problems is qualitatively challenging. This study proposes a surrogate-assisted differential evolution based on region decomposition to seek multiple optima for expensive multimodal optimization problems. Correspondingly, three major components: 1) the adaptive region decomposition, 2) the multilayer perceptronbased global surrogate, and 3) the self-adaptive gradient descent-based local search has been designed to locate multiple optimal solutions under a limited expensive computational budget. Correspondingly, an attempt has been made to solve expensive multimodal optimization problems.



Recommended Citation

Ji, J. (2023). Using multiobjective optimization to solve multimodal optimization and constrained optimization problems (Doctor's thesis, Lingnan University, Hong Kong). Retrieved from

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