Towards Efficient Evaluation of Evolutionary Transfer Optimization: Case Studies on Task-Parameterized Applications

Yanchen Li; Xiaoming Xue; Kay Chen Tan

cs.AISep 4, 2026

Towards Efficient Evaluation of Evolutionary Transfer Optimization: Case Studies on Task-Parameterized Applications

Authors: Yanchen Li, Xiaoming Xue, Kay Chen Tan

Organizations: Department of Data Science and Artificial Intelligence, The Hong Kong Polytechnic University, Hong Kong SAR, China · School of Petroleum Engineering, China University of Petroleum (East China), Qingdao, China

Abstract

As evolutionary transfer optimization (ETO) scales to larger collections of related tasks, problem evaluation can become a major source of runtime growth. This work studies problem-side evaluation scaling in task-parameterized applications and reformulates application-specific serial computations into forms suitable for parallel execution. We organize evaluation scaling into two levels: the number of evaluated tasks and the workload within each task. In multi-task optimization, matrix-recursive kinematic-arm evaluation is reformulated using an accumulation-matrix representation of cumulative link directions. In sequential transfer optimization, pointwise B-spline trajectory evaluation is reformulated using a blending-matrix representation for trajectory and collision computations. Both reformulations maintain close numerical agreement with their reference evaluations and substantially reduce runtime, yielding $256.72\times$ and $93.91\times$ end-to-end speedups, respectively. These results demonstrate problem-side reformulation as a practical route toward scalable ETO. Both application implementations and experimental scripts are released as open source to support reproducibility and reuse.

Figures & tables

Fig. 2: Illustration and comparison of kinematic-arm evaluation for a single task with three joints. The joint angles

\alpha_{1}

\alpha_{2}

, and

\alpha_{3}

are the decision variables, giving a decision dimension of

D=3

; the three links have equal length

L/D

, where

L

is the total arm length. The target position is marked by the star, and the fitness is determined by the distance between the target and the end point of the final link. (a) Matrix-recursive evaluation, which computes the arm configuration joint by joint: at step

i

, the current orientation is rotated by

\alpha_{i}

and then extended by one link of length

L/D

. (b) Accumulation-matrix reformulation, which obtains the link directions from the cumulative joint angles and their horizontal and vertical link projections, eliminating the joint-wise recursive traversal regardless of the number of joints.

Fig. 3: Evaluation and end-to-end runtime results for the kinematic-arm optimization case study. All runtime values are reported as the mean over three repeated measurements, with error bars indicating the standard deviation. (a) Evaluation runtime for one individual under increasing arm joint counts

D

, comparing the matrix-recursive evaluation with its accumulation-matrix reformulation. (b) Evaluation runtime under increasing task counts

K

, where

K

denotes the number of evaluated tasks, comparing the same two forms at a fixed joint count. (c) One-generation end-to-end runtime of MA-MTO under increasing

K

; the annotated multiplier denotes the runtime speedup obtained by the accumulation-matrix reformulation over the matrix-recursive evaluation at the largest tested task count.

Fig. 4: Evaluation and end-to-end results for the B-spline trajectory optimization case study. Runtime values in (a) and (b) are reported as the mean over three repeated measurements, with error bars indicating the standard deviation. (a) Evaluation runtime under increasing numbers of trajectory sample points

R

, where

R

denotes the number of points used to discretize each B-spline trajectory for evaluation, comparing the pointwise evaluation with its blending-matrix reformulation. (b) One-generation end-to-end runtime of MS-STO under increasing

R

; the annotated multiplier denotes the runtime speedup obtained by the blending-matrix reformulation over the pointwise evaluation at the largest tested

R

. (c) Best feasible trajectory obtained over ten independent MS-STO runs under the fixed 100-generation budget, where

x

and

y

denote the normalized horizontal and vertical spatial coordinates, respectively.

Evolutionary Optimization

Evolutionary optimization searches for strong solutions through population-based variation, selection, and adaptation.

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First Mathematical Runtime Analyses of Evolutionary Multitask Multi-Objective Optimization

Danyang Zhang, Weijie Zheng

School of Computer Science and Technology, State Key Laboratory of Smart Farm Technologies and Systems, International Research Institute for Artificial Intelligence, Harbin Institute of Technology, Shenzhen, China · Pengcheng Laboratory, Shenzhen, China

Evolutionary Multitask Optimization Multi-Objective Evolutionary Optimization Multi-Task Optimization Multi-Objective Optimization Runtime Analysis of Evolutionary Algorithms

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To facilitate the solving of complex problems, evolutionary multitask optimization is regarded as a promising technique due to its capacity for cross-task knowledge transfer. In contrast to empirical evidences, no mathematical runtime support exists for this technique within the domain of multi-objective optimization. In this work, we aim to fill this important gap. We analyze how the representative multiobjective multifactorial evolutionary algorithm (MO-MFEA) covers the Pareto fronts of two bi-objective problems simultaneously. For the two-task problem of maximizing the classic bi-objective OMM and the multimodal OJZJ benchmarks, the MO-MFEA requires only an expected runtime of

O(n^2 \log n)

---the same as optimizing the simple OMM alone---yet achieves a speedup by a factor of

Θ(n^{k-1}/\log n)

compared to optimizing OJZJ alone (with gap size

k

). Similarly, for the task pair comprising the classic LOTZ and the multimodal DLTB benchmarks, a speedup of

Θ(n)

is attained over optimizing DLTB alone, while the runtime matches that of optimizing LOTZ alone.

Abstract

Evolutionary Optimization

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