Very often, we have to look into multiple agents' preferences, and compare or aggregate them. In this paper, we consider the well-known model, namely, lexicographic preference trees (LP-trees), for representing agents' preferences in combinatorial domains. We tackle the problem of calculating the dissimilarity/distance between agents' LP-trees. We propose an algorithm LpDis to compute the number of disagreed pairwise preferences between agents by traversing their LP-trees. The proposed algorithm is computationally efficient and allows agents to have different attribute importance structures and preference dependencies.

Cooperative co-evolution (CC) is an explicit means of problem decomposition in multipopulation evolutionary algorithms for solving large-scale optimization problems. For CC, subpopulations representing subcomponents of a large-scale optimization problem co-evolve, and are likely to have different contributions to the improvement of the best overall solution to the problem. Hence, it makes sense that more computational resources should be allocated to the subpopulations with greater contributions. In this paper, we study how to allocate computational resources in this context and subsequently propose a new CC framework named CCFR to efficiently allocate computational resources among the subpopulations according to their dynamic contributions to the improvement of the objective value of the best overall solution. Our experimental results suggest that CCFR can make efficient use of computational resources and is a highly competitive CCFR for solving large-scale optimization problems.

Cooperative Co-evolution (CC) is a promising framework for solving large-scale optimization problems. However, the round-robin strategy of CC is not an efficient way of allocating the available computational resources to components of imbalanced functions. The imbalance problem happens when the components of a partially separable function have non-uniform contributions to the overall objective value. Contribution-Based Cooperative Co-evolution (CBCC) is a variant of CC that allocates the available computational resources to the individual components based on their contributions. CBCC variants (CBCC1 and CBCC2) have shown better performance than the standard CC in a variety of cases. In this paper, we show that over-exploration and over-exploitation are two major sources of performance loss in the existing CBCC variants. On that basis, we propose a new contribution-based algorithm that maintains a better balance between exploration and exploitation. The empirical results show that the new algorithm is superior to its predecessors as well as the standard CC.

Cooperative Co-evolutionary (CC) techniques have demonstrated the promising performance in dealing with large-scale optimization problems. However, in many applications, their performance may drop due to the presence of imbalanced contributions to the objective function value from different subsets of decision variables. To remedy this drawback, Contribution-Based Cooperative Co-evolutionary (CBCC) algorithms have been proposed. They have presented significant improvements over traditional CC techniques when the decomposition is accurate and the imbalance level is very high. However, in real-world scenarios, we might not have the knowledge about the ideal decomposition and actual imbalance level of a problem to be solved. Therefore, this study aims at analysing the performance of existing CBCC techniques in more realistic settings, i.e., when the decomposition error is unavoidable and the imbalance level is low or moderate. Our in-depth analysis reveals that even in these situations, CBCC algorithms are superior alternatives to traditional CC techniques. We also observe that the variations of CBCC techniques may lead to the significantly different performance. Thus, we recommend practitioners to carefully choose a competent variant of CBCC which best suits their particular applications.

This work provides an in-depth investigation of the effects of population initialization on Differential Evolution (DE) for dealing with large scale optimization problems. Firstly, we conduct a statistical parameter sensitive analysis to study the effects of DE's control parameters on its performance of solving large scale problems. This study reveals the optimal parameter configurations which can lead to the statistically superior performance over the CEC-2013 large-scale test problems. Thus identified optimal parameter configurations interestingly favour much larger population sizes while agreeing with the other parameter settings compared to the most commonly employed parameter configuration. Based on one of the identified optimal configurations and the most commonly used configuration, which only differ in the population size, we investigate the influence of various population initialization techniques on DE's performance. This study indicates that initialization plays a more crucial role in DE with a smaller population size. However, this observation might be the result of insufficient convergence due to the use of a large population size under the limited computational budget, which deserve more investigations.

Although various population initialization techniques have been employed in evolutionary algorithms (EAs), there lacks a comprehensive survey on this research topic. To fill this gap and attract more attentions from EA researchers to this crucial yet less explored area, we conduct a systematic review of the existing population initialization techniques. Specifically, we categorize initialization techniques from three exclusive perspectives, i.e., randomness, compositionality and generality. Characteristics of the techniques belonging to each category are carefully analysed to further lead to several sub-categories. We also discuss several open issues related to this research topic, which demands further in-depth investigations.

Opposition-based learning (OBL) and cooperative co-evolution (CC) have demonstrated promising performance when dealing with large-scale global optimization (LSGO) problems. In this work, we propose a novel framework for hybridizing these two techniques, and investigate the performance of simple implementations of this new framework using the most recent LSGO benchmarking test suite. The obtained results verify the effectiveness of our proposed OBL-CC framework. Moreover, some advanced statistical analyses reveal that the proposed hybridization significantly outperforms its component methods in terms of the quality of finally obtained solutions.

Several population initialization methods for evolutionary algorithms (EAs) have been proposed previously. This paper categorizes the most well-known initialization methods and studies the effect of them on large scale global optimization problems. Experimental results indicate that the optimization of large scale problems using EAs is more sensitive to the initial population than optimizing lower dimensional problems. Statistical analysis of results show that basic random number generators, which are the most commonly used method for population initialization in EAs, lead to the inferior performance. Furthermore, our study shows, regardless of the size of the initial population, choosing a proper initialization method is vital for solving large scale problems.