Search

Decomposition-based multiobjective evolutionary algorithms are widely utilized for solving multiobjective optimization problems (MOPs). These algorithms have a higher degree of diversity due to a uniform distribution of the reference vectors in the objective space. However, these algorithms may struggle to select a suitable candidate set for solving many-objective optimization problems (MaOPs) with irregular Pareto fronts (PFs). To solve this problem, a solution potential-based adaptation reference vector evolutionary algorithm (SPARVEA) is proposed in this paper. In the algorithm, a concept called solution potential is presented to assess whether the direction of convergence of the solution to the ideal solution has potential. The solution potential is obtained with an evaluation function to calculate the potentials of the corresponding solutions. A solution potential-based adaptation strategy is then designed for adapting the reference vector to better guide the direction of convergence of the solution when solving MaOPs with irregular PFs. A modified angle penalty distance (mAPD) is adjusted to improve the convergence rate of the solution set in many-objective optimization problems. The proposed algorithm SPARVEA is compared with state-of-the-art many-objective evolutionary algorithms on four test sets with irregular PFs and four practical problems. Experimental results demonstrate the superior performance of SPARVEA on many-objective optimization problems. This contribution helps to advance the development of efficient algorithms for solving many-objective optimization problems. • SPARVEA is proposed for solving many-objective optimization problems with irregular Pareto fronts. • A concept of solution potential is evaluated to assess the direction of the solution to the ideal point. • A solution potential-based adaptation strategy is presented to adjust the reference vectors to guide the direction of convergence of the solution. • A modified angle penalty distance is adapted to control the convergence rate of the population. • The SPARVEA outperforms other contrasting state-of-the-art many-objective optimization algorithms. [ABSTRACT FROM AUTHOR]

Many engineering optimization problems fall into the category of Mixed-Integer Nonlinear Programming (MINLP) problems, which combine nonlinear relations, constraint conditions, and different types of variables, including continuous, integer, and/or discrete variables. Solving MINLP problems can be a challenging exploration process since their landscape can be composed of many discontinuous feasible parts with different sizes. In this scheme, Evolutionary Algorithms (EAs) often fail to generate enough diversity to explore the discontinuous feasible parts. Consequently, EAs are vulnerable to being attracted to larger discontinuous feasible parts, even if they are not promising regions. In this paper, a new proposal based on two fundamental strategies is presented to improve the performance of the differential evolution algorithm when solving MINLP problems. The first strategy considers a set of "good fitness-infeasible solutions" that contribute to exploring promising regions from infeasible contours. It reduces the vulnerability of the solutions to be attracted to larger discontinuous feasible parts with unpromising objective function values. The second is a composite trial vector generation to improve the combinatorial exploration while ensuring a robust convergence capacity toward the final solution. Sixteen well-known MINLP problems are used in several experiments to evaluate the performance of the proposed algorithm, comparing it to state-of-the-art EAs. The results provided by the proposal show a better performance in terms of quality, robustness, and computational cost. • Solving mixed-integer nonlinear programming problems can be challenging. • Improved differential evolution for mixed-integer nonlinear programming problems. • Good fitness-infeasible solutions contribute to exploring the smaller feasible regions. [ABSTRACT FROM AUTHOR]