Constrained Multi-Objective Optimization of Simulated Tree Pruning with Heterogeneous Criteria

Abstract

Virtual pruning of simulated fruit tree models is a useful functionality provided by software tools for computer-aided horticultural education and research. It also enables algorithmic pruning optimization with respect to a set of quantitative objectives, which is important for analytical purposes and potential applications in automated pruning. However, the existing studies in pruning optimization focus on a single type of objective, such as light distribution within the crown. In this paper, we propose the use of heterogeneous objectives for discrete multi-objective optimization of simulated tree pruning. In particular, the average light intake, crown shape, and tree balance are used to observe the emergence of different pruning patterns in the non-dominated solution sets. We also propose the use of independent constraint objectives as a new mechanism to confine overfitting of solutions to individual pruning criteria. Finally, we perform the comparison of NSGA-II, SPEA2, and MOEA/D-EAM on this task. The results demonstrate that SPEA2 and MOEA/D-EAM, which use external solution archives, can produce better sets of non-dominated solutions than NSGA-II.

Multi-Objective Workflow Optimization Algorithm Based on a Dynamic Virtual Staged Pruning Strategy

“…Suppose the set N ∈ N (N = P∪P ), then the node interval represented by the minimum period Vt min and maximum period Vt max determined within a certain range in the set N' is taken as the candidate domain of the node set, expressed as HSY (i) = [Vt min ,Vt max ]. Vt min and Vt max can be calculated by Equation (3).…”

“…Interval A has a time constraint of 18 days. After analyzing the interval nodes and determining that they meet the requirements of virtual reconstruction and there are no N-route, the execution domain of interval nodes is as follows: HSY(p 1 ) = [0,7], HSY(p [2][3] ) = [2,9], HSY(p [4][5] ) = [2,9], HSY (p 6 ) = [8,15]. The calculation process is shown in Table 2.…”

“…Hence, the current stage's Pareto optimal solution set is ƒ q (p 1 ,4) = 0.926, ƒ t (p 1 ,4) = 18 days, ƒ c (p 1 ,4) = 7.8. The optimal path through forward scheduling interval A is as follows: R A = {S, p 1 (t 11 ), p [2][3][4][5] (t 23 ,t 32 ,t 41 ,t 52 ), p 6 (t 61 )}.…”

“…According to the DVSP algorithm, intervals A and B are combined, and the global Pareto optimal production parameter solution set is obtained using the inter-segment accumulation method. Under the condition that the total time constraint is satisfied, the global Pareto optimal solution set is R m = R A + R B = {S, p 1 (t 11 ), p [2][3][4][5] (t 23 ,t 32 ,t 41 ,t 52 ), p 6 (t 61 ), p 7 (t 71 ), p 8 (t 82 ), p 9 (t 92 ), E}. Final cumulative production quality: ƒ q (S-E) = 0.869; the cumulative time: ƒ t (S-E) = 18 + 14 = 32 days; the cumulative cost of ƒ c (S-E) = 7.8 + 5.0 = 12.8.…”

“…Time and cost optimization are the primary optimization objectives of scheduling algorithms, and these objectives have been widely studied. For instance, particle swarm optimization, genetic algorithms (GAS), and simulated annealing algorithms have been proposed and applied to solve scheduling problems [3][4][5][6][7][8].…”