963 research outputs found
Effects of Crossover Operations on the Performance of EMO Algorithms
This paper visually demonstrates the effect of crossover operations on the performance of EMO algorithms through computational experiments on multi-objective 0/1 knapsack problems. In our computational experiments, we use the NSGA-II algorithm as a representative EMO algorithm. First we compare the performance of the NSGA-II algorithm between two cases: NSGA-II with/without crossover. Experimental results show that the crossover operation has a positive effect on the convergence of solutions to the Pareto front and a negative effect on the diversity of solutions. That is, the crossover operation decreases the diversity of solutions while it improves the convergence of solutions to the Pareto front. Next we examine the effects of recombining similar or dissimilar parents using a similarity-based mating scheme. Experimental results show that the performance of the NSGA-II algorithm is improved by recombining similar parents and degraded by recombining dissimilar ones. Finally we show that the recombination of extreme and similar parents using the similarity-based mating scheme drastically improves the diversity of obtained non-dominated solutions without severely degrading their convergence to the Pareto front. An idea of dynamically controlling the selection pressure toward extreme and similar parents is also illustrated through computational experiments
A Decomposition-based Large-scale Multi-modal Multi-objective Optimization Algorithm
A multi-modal multi-objective optimization problem is a special kind of
multi-objective optimization problem with multiple Pareto subsets. In this
paper, we propose an efficient multi-modal multi-objective optimization
algorithm based on the widely used MOEA/D algorithm. In our proposed algorithm,
each weight vector has its own sub-population. With a clearing mechanism and a
greedy removal strategy, our proposed algorithm can effectively preserve
equivalent Pareto optimal solutions (i.e., different Pareto optimal solutions
with same objective values). Experimental results show that our proposed
algorithm can effectively preserve the diversity of solutions in the decision
space when handling large-scale multi-modal multi-objective optimization
problems.Comment: 8 pages, 8 figures, 3 tables. Accepted by the 2020 IEEE Congress on
Evolutionary Computation (IEEE CEC
Evidence theory of exponential possibility distributions
AbstractThis paper studies a certain form of evidence theory using exponential possibility distributions. Because possibility distributions are obtained from an expert knowledge or can be identified from given data, a possibility distribution is regarded as a representation of evidence in this paper. A rule of combination of evidence is given similar to Dempster's rule. Also, the measures of ignorance and fuzziness of evidence are defined by a normality factor and the area of a possibility distribution, respectively. These definitions are similar to those given by G. Shafer and A. Kaufman et al., respectively. Next, marginal and conditional possibilities are discussed from a joint possibility distribution, and it is shown that these three definitions are well matched to each other. Thus, the posterior possibility is derived from the prior possibility in the same form as Bayes' formula. This fact shows the possibility that an information-decision theory can be reconstructed from the viewpoint of possibility distributions. Furthermore, linear systems whose variables are defined by possibility distributions are discussed. Operations of fuzzy vectors defined by multidimensional possibility distributions are well formulated, using the extension principle of L. A. Zadeh
On the Impact of Multiobjective Scalarizing Functions
Recently, there has been a renewed interest in decomposition-based approaches
for evolutionary multiobjective optimization. However, the impact of the choice
of the underlying scalarizing function(s) is still far from being well
understood. In this paper, we investigate the behavior of different scalarizing
functions and their parameters. We thereby abstract firstly from any specific
algorithm and only consider the difficulty of the single scalarized problems in
terms of the search ability of a (1+lambda)-EA on biobjective NK-landscapes.
Secondly, combining the outcomes of independent single-objective runs allows
for more general statements on set-based performance measures. Finally, we
investigate the correlation between the opening angle of the scalarizing
function's underlying contour lines and the position of the final solution in
the objective space. Our analysis is of fundamental nature and sheds more light
on the key characteristics of multiobjective scalarizing functions.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII,
Ljubljana : Slovenia (2014
Variable-depth adaptive large meighbourhood search algorithm for Open Periodic Vehicle Routing Problem with time windows
The Open Periodic Vehicle Routing Problem with Time Windows (OPVRPTW) is a practical transportation routing and scheduling problem arising from real-world scenarios. It shares some common features with some classic VRP variants. The problem has a tightly constrained large-scale solution space and requires well balanced diversification and intensification in search. In Variable Depth Neighbourhood Search, large neighbourhood depth prevents the search from trapping into local optima prematurely, while small depth provides thorough exploitation in local areas. Considering the multi-dimensional solution structure and tight constraints in OPVRPTW, a Variable-Depth Adaptive Large Neighbourhood Search (VD-ALNS) algorithm is proposed in this paper. Contributions of four tailored destroy operators and three repair operators at variable depths are investigated. Comparing to existing methods, VD-ALNS makes a good trade-off between exploration and exploitation, and produces promising results on both small and large size benchmark instances
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