This paper proposes a hybrid harmony search algorithm that incorporates a method of reinitializing harmonies memory using a particle swarm optimization algorithm with an improved opposition-based learning method (IOBL) to solve continuous optimization problems. This method allows the algorithm to obtain better results by increasing the search space of the solutions. This approach has been validated by comparing the performance of the proposed algorithm with that of a state-of-the-art harmony search algorithm, solving fifteen standard mathematical functions, and applying the Wilcoxon parametric test at a 5% significance level. The state-of-the-art algorithm uses an opposition-based improvement method (IOBL). Computational experiments show that the proposed algorithm outperforms the state-of-the-art algorithm. In quality, it is better in fourteen of the fifteen instances, and in efficiency is better in seven of fifteen instances.

Most real-world problems require the optimization of multiple objective functions simultaneously, which can conflict with each other. The environment of these problems usually involves imprecise information derived from inaccurate measurements or the variability in decision-makers’ (DMs’) judgments and beliefs, which can lead to unsatisfactory solutions. The imperfect knowledge can be present either in objective functions, restrictions, or decision-maker’s preferences. These optimization problems have been solved using various techniques such as multi-objective evolutionary algorithms (MOEAs). This paper proposes a new MOEA called NSGA-III-P (non-nominated sorting genetic algorithm III with preferences). The main characteristic of NSGA-III-P is an ordinal multi-criteria classification method for preference integration to guide the algorithm to the region of interest given by the decision-maker’s preferences. Besides, the use of interval analysis allows the expression of preferences with imprecision. The experiments contrasted several versions of the proposed method with the original NSGA-III to analyze different selective pressure induced by the DM’s preferences. In these experiments, the algorithms solved three-objectives instances of the DTLZ problem. The obtained results showed a better approximation to the region of interest for a DM when its preferences are considered.

Multi-objective Evolutionary Algorithm based on Decomposition with Adaptive Adjustment of Control Parameters to Solve the Bi-objective Internet Shopping Optimization Problem (MOEA/D-AACPBIShOP)

In this research, two new methods for solving the Internet shopping optimization problem with sensitive prices are proposed, incorporating adaptive adjustment of control parameters. This problem is classified as NP-hard and is relevant to current electronic commerce. The first proposed solution method corresponds to a Memetic Algorithm incorporating improved local search and adaptive adjustment of control parameters. The second proposed solution method is a particle swarm optimization algorithm that adds a technique for diversification and adaptive adjustment of control parameters. We assess the effectiveness of the proposed algorithms by comparing them with the Branch and Bound algorithm, which presents the most favorable outcomes of the state-of-the-art method. Nine instances of three different sizes are used: small, medium, and large. For performance validation, the Wilcoxon and Friedman non-parametric tests are applied. The results show that the proposed algorithms exhibit comparable performance and outperform the Branch and Bound algorithm.