Optimistic NAUTILUS navigator for multiobjective optimization with costly function evaluations

We introduce novel concepts to solve multiobjective optimization problems involving (computationally) expensive function evaluations and propose a new interactive method called O-NAUTILUS. It combines ideas of trade-off free search and navigation (where a decision maker sees changes in objective function values in real time) and extends the NAUTILUS Navigator method to surrogate-assisted optimization. Importantly, it utilizes uncertainty quantification from surrogate models like Kriging or properties like Lipschitz continuity to approximate a so-called optimistic Pareto optimal set. This enables the decision maker to search in unexplored parts of the Pareto optimal set and requires a small amount of expensive function evaluations. We share the implementation of O-NAUTILUS as open source code. Thanks to its graphical user interface, a decision maker can see in real time how the preferences provided affect the direction of the search. We demonstrate the potential and benefits of O-NAUTILUS with a problem related to the design of vehicles.

Understanding Population Dynamics in Multi- and Many-Objective Evolutionary Algorithms for High-Resolution Approximations

Achieving a high-resolution approximation and hitting the Pareto optimal set with some if not all members of the population is the goal for multi- and many-objective optimization problems, and more so in real-world applications where there is also the desire to extract knowledge about the problem from this set. The task requires not only to reach the Pareto optimal set but also to be able to continue discovering new solutions, even if the population is filled with them. Particularly in many-objective problems where the population may not be able to accommodate the full Pareto optimal set. In this work, our goal is to investigate some tools to understand the behavior of algorithms once they converge and how their population size and particularities of their selection mechanism aid or hinder their ability to keep finding optimal solutions. Through the use of features that look into the population composition during the search process, we will look into the algorithm’s behavior and dynamics and extract some insights. Features are defined in terms of dominance status, membership to the Pareto optimal set, recentness of discovery, and replacement of optimal solutions. Complementing the study with features, we also look at the approximation through the accumulated number of Pareto optimal solutions found and its relationship to a common metric, the hypervolume. To generate the data for analysis, the chosen problem is MNK-landscapes with settings that make it easy to converge, enumerable for instances with 3 to 6 objectives. Studied algorithms were selected from representative multi- and many-objective optimization approaches such as Pareto dominance, relaxation of Pareto dominance, indicator-based, and decomposition.

Pareto-based Dynamic Difficulty Adjustment of a Competitive Exergame for Arm Rehabilitation (Preprint)

BACKGROUND Lack of motivation is a major hindrance to frequent and intense exercise which is critical to rehabilitating people with arm disabilities due to old age, neurological disorders or stroke. Recently, the use of interpersonal exergames has been associated with increased motivation and exercise intensity in arm rehabilitation and is becoming a common trend. However, the Dynamic Difficulty Adjustment (DDA) of such games is still an open issue because unlike the traditional DDA frameworks where game intensity is simply adapted to suit the players' performance, the aim of DDA for exergames is to optimize the conflicting objectives namely of intensity and performance. Objective: To design a dedicated DDA for rehabilitation exergames that optimize the conflicting objectives of intensity and performance by generating a set of feasible trade-off solutions. Based on the rehabilitative needs, the tradeoff worth information of each solution is to be used to select a unique solution. OBJECTIVE To design a dedicated DDA for rehabilitation exergames that optimizes the conflicting objectives of intensity and performance by generating a set of feasible trade-off solutions. Based on the rehabilitative needs, the tradeoff worth information of each solution is to be used to select a unique solution. METHODS We designed a Pareto-based DDA for a competitive exergame that optimizes the two conflicting objectives. Using a set of feasible solutions generated during the first episode of the game, the proposed Pareto-based DDA is used to modify the parameters of the game. Optimizing conflicting objectives generally results in a set of trade-off solutions called Pareto optimal set instead of a single solution. Therefore, the DDA is capable of selecting a single solution from the optimal Pareto based on the trade-off worth information of each solution in the optimal Pareto set. RESULTS Results: Experimental results with 12 unimpaired participants show the capability of the proposed Pareto-based DDA to online adjust the game parameters effectively based on a trade-off between the intensity and motivation. CONCLUSIONS Since rehabilitation outcomes rely on both intensity and motivation, unlike traditional DDA approaches, the capability of Pareto-based DDA to provide trade-off solutions between conflicting objectives of intensity and motivation is very promising to rehabilitation outcomes. However, multi-session investigation over a period of time needs to be carried out to examine if they influence rehabilitation outcomes positively. CLINICALTRIAL This work is not a clinical trial. Although humans participated in this study, they participate in the evaluation of a single-session of a rehabilitation exergame rather than a comprehensive rehabilitation intervention with no health outcomes investigated.

Multi-Objective Constructal Optimization for Marine Condensers

A marine condenser with exhausted steam as the working fluid is researched in this paper. Constructal designs of the condenser are numerically conducted based on single and multi-objective optimizations, respectively. In the single objective optimization, there is an optimal dimensionless tube diameter leading to the minimum total pumping power required by the condenser. After constructal optimization, the total pumping power is decreased by 42.3%. In addition, with the increase in mass flow rate of the steam and heat transfer area and the decrease in total heat transfer rate, the minimum total pumping power required by the condenser decreases. In the multi-objective optimization, the Pareto optimal set of the entropy generation rate and total pumping power is gained. The optimal results gained by three decision methods in the Pareto optimal set and single objective optimizations are compared by the deviation index. The optimal construct gained by the TOPSIS decision method corresponding to the smallest deviation index is recommended in the optimal design of the condenser. These research ideas can also be used to design other heat transfer devices.

Solving dynamic multi-objective problems with a new prediction-based optimization algorithm

This paper proposes a new dynamic multi-objective optimization algorithm by integrating a new fitting-based prediction (FBP) mechanism with regularity model-based multi-objective estimation of distribution algorithm (RM-MEDA) for multi-objective optimization in changing environments. The prediction-based reaction mechanism aims to generate high-quality population when changes occur, which includes three subpopulations for tracking the moving Pareto-optimal set effectively. The first subpopulation is created by a simple linear prediction model with two different stepsizes. The second subpopulation consists of some new sampling individuals generated by the fitting-based prediction strategy. The third subpopulation is created by employing a recent sampling strategy, generating some effective search individuals for improving population convergence and diversity. Experimental results on a set of benchmark functions with a variety of different dynamic characteristics and difficulties illustrate that the proposed algorithm has competitive effectiveness compared with some state-of-the-art algorithms.

Designing convolutional neural networks with constrained evolutionary piecemeal training

The automated architecture search methodology for neural networks is known as Neural Architecture Search (NAS). In recent times, Convolutional Neural Networks (CNNs) designed through NAS methodologies have achieved very high performance in several fields, for instance image classification and natural language processing. Our work is in the same domain of NAS, where we traverse the search space of neural network architectures with the help of an evolutionary algorithm which has been augmented with a novel approach of piecemeal-training. In contrast to the previously published NAS techniques, wherein the training with given data is considered an isolated task to estimate the performance of neural networks, our work demonstrates that a neural network architecture and the related weights can be jointly learned by combining concepts of the traditional training process and evolutionary architecture search in a single algorithm. The consolidation has been realised by breaking down the conventional training technique into smaller slices and collating them together with an integrated evolutionary architecture search algorithm. The constraints on architecture search space are placed by limiting its various parameters within a specified range of values, consequently regulating the neural network’s size and memory requirements. We validate this concept on two vastly different datasets, namely, the CIFAR-10 dataset in the domain of image classification, and PAMAP2 dataset in the Human Activity Recognition (HAR) domain. Starting from randomly initialized and untrained CNNs, the algorithm discovers models with competent architectures, which after complete training, reach an accuracy of of 92.5% for CIFAR-10 and 94.36% PAMAP2. We further extend the algorithm to include an additional conflicting search objective: the number of parameters of the neural network. Our multi-objective algorithm produces a Pareto optimal set of neural networks, by optimizing the search for both the accuracy and the parameter count, thus emphasizing the versatility of our approach.

Evaluation of Cloud 3D Printing Order Task Execution Based on the AHP-TOPSIS Optimal Set Algorithm and the Baldwin Effect

Focusing on service control factors, rapid changes in manufacturing environments, the difficulty of resource allocation evaluation, resource optimization for 3D printing services (3DPSs) in cloud manufacturing environments, and so on, an indicator evaluation framework is proposed for the cloud 3D printing (C3DP) order task execution process based on a Pareto optimal set algorithm that is optimized and evaluated for remotely distributed 3D printing equipment resources. Combined with the multi-objective method of data normalization, an optimization model for C3DP order execution based on the Pareto optimal set algorithm is constructed with these agents’ dynamic autonomy and distributed processing. This model can perform functions such as automatic matching and optimization of candidate services, and it is dynamic and reliable in the C3DP order task execution process based on the Pareto optimal set algorithm. Finally, a case study is designed to test the applicability and effectiveness of the C3DP order task execution process based on the analytic hierarchy process and technique for order of preference by similarity to ideal solution (AHP-TOPSIS) optimal set algorithm and the Baldwin effect.

Quieter and Greener rotorcraft: concurrent aerodynamic and acoustic optimization

Within the DLR project VicToria an aerodynamic and aero-acoustic optimization of helicopter rotor blades is performed. During the optimization, three independent flight conditions are considered: hover, cruise and descent flight. The first two flight conditions drive the power requirements of the helicopter rotor, while the descent flight is the loudest flight condition for current helicopter generations. To drive down the required power and the emitted noise, a multi-objective design approach coupled with surrogate models is utilized to find a Pareto optimal set of rotors. This approach allows to identify the trade-offs to be made when laying emphasis on either goal function. The underlying CFD simulations utilize fourth-order accurate spatial schemes to capture the vortex dominated flow of helicopter rotor blades. The paper presents the validation of the setups, the optimization results and the off-design analysis of a chosen set of blades from the Pareto front. The conclusion is that the utilization of the Pareto front approach is necessary to find good rotor designs, while the utilization of high-order methods allows for efficient CFD setups.

A Framework for Time-Cost-Quality Optimization in Project Management Problems Using an Exploratory Grid Concept in the Multi-Objective Simulated-Annealing

Time, cost, and quality are the three indispensable factors for the realization and success of a project. In this context, we propose a framework composed of a multi-objective approach and multi-criteria decision-making methods (MCDM) to solve time-cost-quality trade-off optimization problems. A multi-objective Simulated Annealing (MOSA) algorithm is used to compute an approximation to the Pareto optimal set. The concept of the exploratory grid is introduced in the MOSA to improve its performance. MCDM are used to assist the decision-making process. The Shannon entropy and AHP methods assign weights to criteria. The first methodology is for the inexperienced decision-makers, and the second concedes a personal and flexible weighting of the criteria weights, based on the project manager’s assessment. The TOPSIS and VIKOR methods are considered to rank the solutions. Although they have the same purpose, the rankings achieved are different. A tool is implemented to solve a time-cost-quality trade-off problem on a project activities network. The computational experiments are analyzed and the results with the exploratory grid in Simulated Annealing (SA) are promising. Despite the framework aims to solve multi-objective trade-off optimization problems, supporting the decisions of the project manager, the methodologies used can also be applied in other areas.