Julian Blank

This paper presents the Inexpensive Objectives and Constraints Self-Adapting Multi-Objective Constraint Optimization algorithm using Radial Basis Function Approximations (IOC-SAMO-COBRA). This algorithm is introduced to address constraint multi-objective optimization problems that involve a mix of computationally expensive and inexpensive evaluation functions. The IOC-SAMO-COBRA algorithm iteratively learns the expensive functions with radial basis function surrogates, while the inexpensive functions are directly used in the search for promising solutions. Two benefits of using the inexpensive functions directly include: (1) The inexpensive functions do not introduce approximation errors like surrogates do. (2) Time can be saved as there is no need to fit and interpolate surrogate models for the inexpensive functions. Results on 22 test functions indicate that exploiting the inexpensive functions can be beneficial as this results in better Pareto front approximations compared to using surrogates for both expensive and inexpensive functions. This paper serves as an extended abstract for the Hot-off-the-Press track at GECCO 2024, building upon the paper Parallel Multi-Objective Optimization for Expensive and Inexpensive Objectives and Constraints by de Winter et al, published in Swarm and Evolutionary Computation, Volume 86 (2024) [4].

An optimal electric machine design task can be posed as a constrained multi-objective optimization problem. While the objectives require time-consuming finite element analysis, constraints, such as geometric constraints, can often be based on mathematical expressions. This article investigates this mixed computationally expensive optimization problem and proposes a computationally efficient optimization method based on evolutionary algorithms. The proposed method always generates feasible solutions by using a generalizable repair operator and also addresses time-consuming objective functions by incorporating surrogate models for their prediction. The article successfully establishes the superiority of the proposed method over a conventional optimization approach. This study demonstrates how a complex engineering design task can be optimized efficiently for multiple objectives and constraints requiring heterogeneous evaluation times. It also shows how optimal solutions can be analysed to select a single preferred solution and harnessed to reveal vital design features common to optimal solutions as design principles.

The underlying infrastructure paradigms behind the novel usage scenarios and services are becoming increasingly complex—from everyday life in smart cities to industrial environments. Both the number of devices involved and their heterogeneity make the allocation of software components quite challenging. Despite the enormous flexibility enabled by component-based software engineering, finding the optimal allocation of software artifacts to the pool of available devices and computation units could bring many benefits, such as improved quality of service (QoS), reduced energy consumption, reduction of costs, and many others. Therefore, in this paper, we introduce a model-based framework that aims to solve the software component allocation problem (CAP). We formulate it as an optimization problem with either single or multiple objective functions and cover both cases in the proposed framework. Additionally, our framework also provides visualization and comparison of the optimal solutions in the case of multi-objective component allocation. The main contributions introduced in this paper are: (1) a novel methodology for tackling CAP-alike problems based on the usage of model-driven engineering (MDE) for both problem definition and solution representation; (2) a set of Python tools that enable the workflow starting from the CAP model interpretation, after that the generation of optimal allocations and, finally, result visualization. The proposed framework is compared to other similar works using either linear optimization, genetic algorithm (GA), and ant colony optimization (ACO) algorithm within the experiments based on notable papers on this topic, covering various usage scenarios—from Cloud and Fog computing infrastructure management to embedded systems, robotics, and telecommunications. According to the achieved results, our framework performs much faster than GA and ACO-based solutions. Apart from various benefits of adopting a multi-objective approach in many cases, it also shows significant speedup compared to frameworks leveraging single-objective linear optimization, especially in the case of larger problem models.

Most evolutionary many-objective optimization (EMaO) algorithms start with a description of a number of predefined set of reference points on a unit simplex. So far, most studies have used the Das and Dennis’s structured approach for generating well-spaced reference points. Due to the highly structured nature of the procedure, this method cannot produce an arbitrary number of points, which is desired in an EMaO application. Although a layer-wise implementation has been suggested, EMO researchers always felt the need for a more generic approach. Motivated by earlier studies, we introduce a metric for defining well-spaced points on a unit simplex and propose a number of viable methods for generating such a set. We compare the proposed methods on a variety of performance metrics such as hypervolume, deviation in triangularized simplices, distance of the closest point pair, and variance of the geometric means to nearest neighbors in up to 15-dimensional spaces. We show that an iterative improvement based on Riesz s-Energy is able to effectively find an arbitrary number of wellspaced points even in higher-dimensional spaces. Reference points created using the proposed Riesz s-Energy method for a number of standard combinations of objectives and reference points as well as a source code written in Python are available publicly at https://www.egr.msu.edu/coinlab/blankjul/uniform.

Many engineering design problems are associated with computationally expensive and time-consuming simulations for design evaluation. In such problems, each candidate design should be selected carefully, even though it means extra algorithmic complexity. This study develops the Proximity-based Surrogate-Assisted Evolutionary Algorithm (PSA-EA) that aims at handling both single-objective and multi-objective computationally expensive problems. It controls the trade-off between exploration and exploitation by defining proximity and trust regions around high-fidelity solutions. The proximity measure aims to maximize the diversity of information about specific regions of the search space and to improve the goodness of the surrogate for future cycles simultaneously. The method employs an ensemble of metamodels and a parallel infill criterion. PSA-EA is evaluated and compared to a recently developed surrogate-assisted evolutionary algorithm on ten test problems. Thereafter, a case study involving a multi-objective design optimization of the cylinder head water jacket of a vehicle engine is presented and discussed. Online supplemental data for this article can be accessed at https://doi.org/10.1080/0305215X.2020.1808972.

In this paper, we propose a method to solve a bi-objective variant of the well-studied Traveling Thief Problem (TTP). The TTP is a multi-component problem that combines two classic combinatorial problems: Traveling Salesman Problem (TSP) and Knapsack Problem (KP). We address the BI-TTP, a bi-objective version of the TTP, where the goal is to minimize the overall traveling time and to maximize the profit of the collected items. Our proposed method is based on a biased-random key genetic algorithm with customizations addressing problem-specific characteristics. We incorporate domain knowledge through a combination of near-optimal solutions of each subproblem in the initial population and use a custom repair operator to avoid the evaluation of infeasible solutions. The bi-objective aspect of the problem is addressed through an elite population extracted based on the non-dominated rank and crowding distance. Furthermore, we provide a comprehensive study showing the influence of each parameter on the performance. Finally, we discuss the results of the BI-TTP competitions at EMO-2019 and GECCO-2019 conferences where our method has won first and second places, respectively, thus proving its ability to find high-quality solutions consistently.