Understanding the search dynamics of multiobjective evolutionary algorithms (MOEAs) is still an open problem. This paper extends a recent network-based tool, search trajectory networks (STNs), to model the behavior of MOEAs. Our approach uses the idea of decomposition, where a multiobjective problem is transformed into several single-objective problems. We show that STNs can be used to model and distinguish the search behavior of two popular multiobjective algorithms, MOEA/D and NSGA-II, using 10 continuous benchmark problems with 2 and 3 objectives. Our findings suggest that we can improve our understanding of MOEAs using STNs for algorithm analysis.

Finding good solutions for Multi-objective Optimization (MOPs) Problems is considered a hard problem, especially when considering MOPs with constraints. Thus, most of the works in the context of MOPs do not explore in-depth how different constraints affect the performance of MOP solvers. Here, we focus on exploring the effects of different Constraint Handling Techniques (CHTs) on MOEA/D, a commonly used MOP solver when solving complex real-world MOPs. Moreover, we introduce a simple and effective CHT focusing on the exploration of the decision space, the Three Stage Penalty. We explore each of these CHTs in MOEA/D on two simulated MOPs and six analytic MOPs (eight in total). The results of this work indicate that while the best CHT is problem-dependent, our new proposed Three Stage Penalty achieves competitive results and remarkable performance in terms of hypervolume values in the hard simulated car design MOP.

Recent studies on resource allocation suggest that some subproblems are more important than others in the context of the MOEA/D, and that focusing on the most relevant ones can consistently improve the performance of that algorithm. These studies share the common characteristic of updating only a fraction of the population at any given iteration of the algorithm. In this work we investigate a new, simpler partial update strategy, in which a random subset of solutions is selected at every iteration. The performance of the MOEA/D using this new resource allocation approach is compared experimentally against that of the standard MOEA/D-DE and the MOEA/D with relative improvement-based resource allocation. The results indicate that using the MOEA/D with this new partial update strategy results in improved HV and IGD values, and a much higher proportion of non-dominated solutions, particularly as the number of updated solutions at every iteration is reduced.

Soil characteristics are extremely important when determining yield potential. Fertilization and liming are commonly used to adapt soils to the nutritional requirements of the crops to be cultivated. Planting the crop that will best fit the soil characteristics is an interesting alternative to minimize the need for soil treatment, reducing costs and potential environmental damages. In addition, farmers usually look for investments that offer the greatest potential earnings with the least possible risks. Regarding the objectives to be considered, the crop-selection problem may be difficult to solve using traditional tools.

Farm managers have to deal with many conflicting objectives when planning which crop to cultivate. Soil characteristics are extremely important when determining yield potential. According to the objectives to be considered the crop selection problem may be difficult to solve using traditional tools. Therefore, this work proposes an approach based on Multiobjective Evolutionary Algorithms to help in the selection of an appropriate cultivation plan considering five crop alternatives and five objectives simultaneously.