Studying Evolutionary Solution Adaption Using a Flexibility Benchmark Based on a Metal Cutting Process

TL;DR

This work defines a flexibility benchmark for evolutionary optimization in manufacturing using an extended Oxley model of orthogonal metal cutting to study transfer of solutions between related tasks. It demonstrates that reusing source-task solutions can dramatically reduce the number of evaluations required to reach a target objective, and introduces two NSGA-II extensions—varying goals and an active-inactive genotype—to further enhance adaptability. Hypervolume analyses and statistical tests show that adaptation generally outperforms from-scratch optimization, with additional gains from the proposed variants, though practical deployment requires validation against more realistic simulations. The benchmark provides a structured framework to explore rapid, transfer-aware optimization in dynamic manufacturing settings and points to future work in integrating with meta-learning and surrogate-based approaches for industrial applicability.

Abstract

We consider optimizing for different production requirements from the viewpoint of a bio-inspired framework for system flexibility that allows us to study the ability of an algorithm to transfer solutions from previous optimization tasks, which also relates to dynamic evolutionary optimization. Optimizing manufacturing process parameters is typically a multi-objective problem with often contradictory objectives such as production quality and production time. If production requirements change, process parameters have to be optimized again. Since optimization usually requires costly simulations based on, for example, the Finite Element method, it is of great interest to have means to reduce the number of evaluations needed for optimization. Based on the extended Oxley model for orthogonal metal cutting, we introduce a multi-objective optimization benchmark where different materials define related optimization tasks. We use the benchmark to study the flexibility of NSGA-II, which we extend by two variants: 1) varying goals, which optimizes solutions for two tasks simultaneously to obtain in-between source solutions expected to be more adaptable, and 2) active-inactive genotype, which accommodates different possibilities that can be activated or deactivated. Results show that adaption, i.e. transferring a solution from a previous optimization task, with standard NSGA-II greatly reduces the number of evaluations required for optimization to a target goal in comparison to starting from scratch. The proposed variants further improve the adaption costs, although further work is needed towards making the methods advantageous for real applications.

Figures (7)

• Figure 1: A graphical representation of the orthogonal machining model. The image has been taken from pantale-2022.
• Figure 2: (a) Example of a non-dominated sorting. Objectives $f_1$ and $f_2$ need to be minimized. Solutions in red, green, and blue, represent the first, second, and third non-domination classes, respectively. (b) Illustration of selection of a new population in NSGA-II. $R_g$ is the union of $P_g$ (population in generation $g$) and $Q_g$ (varied individuals in generation $g$). In this example, non-domination classes $F_1$ and $F_2$ go into new population of generation $g+1$, $P_{g+1}$. Adding the complete non-domination class $F_3$ would exceed the population size, thus individuals from $F_3$ with higher crowding distance are selected.
• Figure 3: (a) Example solution using the active-inactive genotype, with gene length $l=2$. The first position of a gene indicates which of the next $l$ positions is active. Active positions are in boldface. The decoded phenotype contains only the values in the active position for each gene. (b) Example of the application of the modified two-step mutation operator. First, indexes of active positions can be changed (in boldface after first step). Then, the individual is decoded, standard mutation is applied (boldface after second step), and the result is again encoded.
• Figure 4: Hypervolume of best Pareto front found so far across generations for search from scratch and adaption for each material (mean over 100 runs).
• Figure 5: Hypervolume of Pareto front found across generations for NSGA-II with varying goals for each material pair (mean over 100 runs). Here, $E=5$. For each epoch, the hypervolume shown correspond to the Pareto front evaluated on the objective of that epoch, and not the best one found so far.

Theorems & Definitions (4)

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