An Adaptive Reference Vector Adjustment Strategy and Improved Angle-Penalized Value Method for RVEA

Decomposition-based evolutionary multiobjective algorithms (MOEAs) divide a multiobjective problem into several subproblems by using a set of predefined uniformly distributed reference vectors and can achieve good overall performance especially in maintaining population diversity. However, they encounter huge difficulties in addressing problems with irregular Pareto fronts (PFs) since many reference vectors do not work during the searching process. To cope with this problem, this paper aims to improve an existing decomposition-based algorithm called reference vector-guided evolutionary algorithm (RVEA) by designing an adaptive reference vector adjustment strategy. By adding the strategy, the predefined reference vectors will be adjusted according to the distribution of promising solutions with good overall performance and the subspaces in which the PF lies may be further divided to contribute more to the searching process. Besides, the selection pressure with respect to convergence performance posed by RVEA is mainly from the length of normalized objective vectors and the metric is poor in evaluating the convergence performance of a solution with the increase of objective size. Motivated by that, an improved angle-penalized distance (APD) method is developed to better distinguish solutions with sound convergence performance in each subspace. To investigate the performance of the proposed algorithm, extensive experiments are conducted to compare it with 5 state-of-the-art decomposition-based algorithms on 3-, 5-, 8-, and 10-objective MaF1–MaF9. The results demonstrate that the proposed algorithm obtains the best overall performance.

Selection of Multimode Resource-Constrained Project Scheduling Scheme Based on DEA Method

A multimode resource-constrained project scheduling problem (MRCPSP) may have multifeasible solutions, due to its nature of targeting multiobjectives. Given the NP-hard MRCPSP and intricate multiobjective algorithms, finding the optimized result among those solutions seems impossible. This paper adopts data envelopment analysis (DEA) to evaluate a series of solutions of an MRCPSP and to find an appropriate choice in an objective way. Our approach is applied to a typical MRCPSP in practice, and the results validate that DEA is an effective and objective method for MRCPSP solution selection.

Simulation of MH370 Actual Route Using Multiobjective Algorithms

This chapter delivers the mathematical model to retrieve the definite route of MH370 and its debris, which is based on a multi-objective evolutionary algorithm. The chapter shows that the appropriate short route for Captian Zaharie to murder-suicide is the Gulf of Thailand, not in the Southern Indian Ocean, which is specified by 1000 iterations and 100 fitness. Needless to say that the MH370 path reclaimed from Inmarsat 3-F1 satellite data was not delivering the real scenario of MH370's vanishing, which is proving the multiobjective genetic algorithm.

Dynamic Shannon Performance in a Multiobjective Particle Swarm Optimization

Particle swarm optimization (PSO) is a search algorithm inspired by the collective behavior of flocking birds and fishes. This algorithm is widely adopted for solving optimization problems involving one objective. The evaluation of the PSO progress is usually measured by the fitness of the best particle and the average fitness of the particles. When several objectives are considered, the PSO may incorporate distinct strategies to preserve nondominated solutions along the iterations. The performance of the multiobjective PSO (MOPSO) is usually evaluated by considering the resulting swarm at the end of the algorithm. In this paper, two indices based on the Shannon entropy are presented, to study the swarm dynamic evolution during the MOPSO execution. The results show that both indices are useful for analyzing the diversity and convergence of multiobjective algorithms.

Enhancing Financial Portfolio Robustness with an Objective Based on ϵ-Neighborhoods

Financial portfolio optimization is a challenging task. One of the major difficulties is managing the uncertainty arising from different aspects of the process. This paper suggests a solution based on [Formula: see text]-neighborhoods that, combined with a time-stamped resampling mechanism, increases the robustness of the solutions. The approach is tested on four of the most popular evolutionary multiobjective algorithms over a long period of time. This results in a significant enhancement in the reliability of the estimated efficient frontier.