This paper intends to understand and to improve the working principle of decomposition-based multi-objective evolutionary algorithms. We review the design of the well-established Moea/d framework to support the smooth integration of different strategies for sub-problem selection, while emphasizing the role of the population size and of the number of offspring created at each generation. By conducting a comprehensive empirical analysis on a wide range of multi-and many-objective combinatorial NK landscapes, we provide new insights into the combined effect of those parameters on the anytime performance of the underlying search process. In particular, we show that even a simple random strategy selecting sub-problems at random outperforms existing sophisticated strategies. We also study the sensitivity of such strategies with respect to the ruggedness and the objective space dimension of the target problem.
This paper presents a new robustness concept for uncertain multi-objective optimization problems. More precisely, in the paper the so-called recovery-to-efficiency robustness concept is proposed and investigated. Several approaches for generating recovery-to-efficiency robust sets in the context of multi-objective optimization are proposed as well. An extensive experimental analysis is performed to disclose differences among robust sets obtained using different concepts as well as to deduce some interesting observations. For testing purposes, instances from the bi-objective knapsack problem are considered.
User preference integration is of great importance in multi-objective optimization, in particular in many objective optimization. Preferences have long been considered in traditional multicriteria decision making (MCDM) which is based on mathematical programming. Recently, it is integrated in multi-objective metaheuristics (MOMH), resulting in focus on preferred parts of the Pareto front instead of the whole Pareto front. The number of publications on preference-based multi-objective metaheuristics has increased rapidly over the past decades. There already exist various preference handling methods and MOMH methods, which have been combined in diverse ways. This article proposes to use the Web Ontology Language (OWL) to model and systematize the results developed in this field. A review of the existing work is provided, based on which an ontology is built and instantiated with state-of-the-art results. The OWL ontology is made public and open to future extension. Moreover, the usage of the ontology is exemplified for different use-cases, including querying for methods that match an engineering application, bibliometric analysis, checking existence of combinations of preference models and MOMH techniques, and discovering opportunities for new research and open research questions.
It is a known fact that the performance of optimization algorithms for NP-Hard problems vary from instance to instance. We observed the same trend when we comprehensively studied multi-objective evolutionary algorithms (MOEAs) on a six benchmark instances of discrete time-cost trade-off problem (DTCTP) in a construction project. In this paper, instead of using a single algorithm to solve DTCTP, we use a portfolio approach that takes multiple algorithms as its constituent. We proposed portfolio comprising of four MOEAs, Non-dominated Sorting Genetic Algorithm II (NSGA-II), the strength Pareto Evolutionary Algorithm II (SPEA-II), Pareto archive evolutionary strategy (PAES) and Niched Pareto Genetic Algorithm II (NPGA-II) to solve DTCTP. The result shows that the portfolio approach is computationally fast and qualitatively superior to its constituent algorithms for all benchmark instances. Moreover, portfolio approach provides an insight in selecting the best algorithm for all benchmark instances of DTCTP.
In this paper, we develop a general interactive method to solve multi-objective combinatorial optimization problems with imprecise preferences. Assuming that preferences can be represented by a parameterized scalarizing function, we iteratively ask preferences queries to the decision maker in order to reduce the uncertainty over the preference parameters until being able to determine her preferred solution. To produce informative preference queries at each step, we generate promising solutions using the extreme points of the polyhedron representing the admissible preference parameters and then we ask the decision maker to compare two of these solutions (we propose different selection strategies). These extreme points are also used to provide a stopping criterion guaranteeing that the returned solution is optimal (or near-optimal) according to the decision maker's preferences. For the multi-objective spanning tree problem with a linear aggregation function, we provide numerical results to demonstrate the practical efficiency of our approach and we compare our results to a recent approach based on minimax regret, where preferences are asked during the construction of a solution. We show that better results are achieved by our method both in terms of running time and number of questions.