Showing papers on "Multi-objective optimization published in 2020"

Pymoo: Multi-Objective Optimization in Python

Abstract: Python has become the programming language of choice for research and industry projects related to data science, machine learning, and deep learning. Since optimization is an inherent part of these research fields, more optimization related frameworks have arisen in the past few years. Only a few of them support optimization of multiple conflicting objectives at a time, but do not provide comprehensive tools for a complete multi-objective optimization task. To address this issue, we have developed pymoo, a multi-objective optimization framework in Python. We provide a guide to getting started with our framework by demonstrating the implementation of an exemplary constrained multi-objective optimization scenario. Moreover, we give a high-level overview of the architecture of pymoo to show its capabilities followed by an explanation of each module and its corresponding sub-modules. The implementations in our framework are customizable and algorithms can be modified/extended by supplying custom operators. Moreover, a variety of single, multi- and many-objective test problems are provided and gradients can be retrieved by automatic differentiation out of the box. Also, pymoo addresses practical needs, such as the parallelization of function evaluations, methods to visualize low and high-dimensional spaces, and tools for multi-criteria decision making. For more information about pymoo, readers are encouraged to visit: https://pymoo.org.

An Evolutionary Algorithm for Large-Scale Sparse Multiobjective Optimization Problems

Abstract: In the last two decades, a variety of different types of multiobjective optimization problems (MOPs) have been extensively investigated in the evolutionary computation community. However, most existing evolutionary algorithms encounter difficulties in dealing with MOPs whose Pareto optimal solutions are sparse (i.e., most decision variables of the optimal solutions are zero), especially when the number of decision variables is large. Such large-scale sparse MOPs exist in a wide range of applications, for example, feature selection that aims to find a small subset of features from a large number of candidate features, or structure optimization of neural networks whose connections are sparse to alleviate overfitting. This paper proposes an evolutionary algorithm for solving large-scale sparse MOPs. The proposed algorithm suggests a new population initialization strategy and genetic operators by taking the sparse nature of the Pareto optimal solutions into consideration, to ensure the sparsity of the generated solutions. Moreover, this paper also designs a test suite to assess the performance of the proposed algorithm for large-scale sparse MOPs. The experimental results on the proposed test suite and four application examples demonstrate the superiority of the proposed algorithm over seven existing algorithms in solving large-scale sparse MOPs.

Lexicographic Multiobjective Scatter Search for the Optimization of Sequence-Dependent Selective Disassembly Subject to Multiresource Constraints

Abstract: Industrial products’ reuse, recovery, and recycling are very important because of their environmental and economic benefits. Effective product disassembly planning methods can improve their recovery efficiency and reduce their bad environmental impact. However, the existing approaches pay little attention to sequence-dependent disassembly with resource constraints, such as limited disassembly operators and tools, which makes the current planning methods ineffective in practice. This paper considers a multiobjective resource-constrained and sequence-dependent disassembly optimization problem with disassembly precedence constraints. Energy consumption is adopted to evaluate the disassembly efficiency. Its use with traditional optimization criterion leads to a novel multiobjective optimization model such that the energy consumption and disassembly time are minimized while disassembly profit is maximized. Since the problem complexity increases with the number of components in a product, a lexicographic multiobjective scatter search (SS) method is proposed to solve the proposed multiobjective optimization problem. Its effectiveness is verified by comparing the results of linear weight SS and genetic algorithms. The results show that it is able to provide a better solution in a short execution time and fulfills the precedence requirement in a product structure and resource constraints.

A Knowledge-Based Cooperative Algorithm for Energy-Efficient Scheduling of Distributed Flow-Shop

Abstract: Facing increasingly serious ecological problems, sustainable development and green manufacturing have attracted much attention. Meanwhile, with the development of globalization, distributed manufacturing is becoming widespread. This paper addresses an energy-efficient scheduling of the distributed permutation flow-shop (EEDPFSP) with the criteria of minimizing both makespan and total energy consumption. Considering the distributed and multiobjective optimization complexity, a knowledge-based cooperative algorithm (KCA) is proposed to solve the EEDPFSP. First, a cooperative initialization scheme is presented with both extended energy-efficient Nawaz–Enscore–Ham heuristic and slowest allowable speed rule that are specially designed to produce good initial solutions with certain diversity. Second, several properties of the nondominated solutions are investigated based on the characteristics of the bi-objective problem, which are used to develop the knowledge-based search operators. Third, a cooperative search strategy of multiple operators is designed for the solutions with different characteristics to tradeoff two objectives. Fourth, a knowledge-based local intensification is used for exploiting better nondominated solutions sufficiently. Moreover, an energy saving method based on the critical path is used to further improve the performance. The effect of parameter setting on the KCA is investigated with the Taguchi method of design-of-experiment. Extensive computational tests and comparisons are carried out, which verify the effectiveness of the special designs of the KCA in solving the EEDPFSP.

CARS: Continuous Evolution for Efficient Neural Architecture Search

Abstract: Searching techniques in most of existing neural architecture search (NAS) algorithms are mainly dominated by differentiable methods for the efficiency reason. In contrast, we develop an efficient continuous evolutionary approach for searching neural networks. Architectures in the population that share parameters within one SuperNet in the latest generation will be tuned over the training dataset with a few epochs. The searching in the next evolution generation will directly inherit both the SuperNet and the population, which accelerates the optimal network generation. The non-dominated sorting strategy is further applied to preserve only results on the Pareto front for accurately updating the SuperNet. Several neural networks with different model sizes and performances will be produced after the continuous search with only 0.4 GPU days. As a result, our framework provides a series of networks with the number of parameters ranging from 3.7M to 5.1M under mobile settings. These networks surpass those produced by the state-of-the-art methods on the benchmark ImageNet dataset.

Hybrid Microgrid Many-Objective Sizing Optimization With Fuzzy Decision

Abstract: The economics, reliability, and carbon efficiency of hybrid microgrid systems (HMSs) are often in conflict; hence, a reasonable design for the sizing of the initial microgrid is important. In this article, we propose an improved two-archive many-objective evolutionary algorithm (TA-MaEA) based on fuzzy decision to solve the sizing optimization problem for HMSs. For the HMS simulated in this article, costs, loss of power supply probability, pollutant emissions, and power balance are considered as objective functions. For the proposed algorithm, we employ two archives with different diversity selection strategies to balance convergence and diversity in the high-dimensional objective space. In addition, a fuzzy decision making method is proposed to further help decision makers obtain a solution from the Pareto front that optimally balances the objectives. The effectiveness of the proposed algorithm in solving the HMS sizing optimization problem is investigated for the case of Yanbu, Saudi Arabia. The experimental results show that, compared with the two-archive evolutionary algorithm for constrained many-objective optimization (C-TAEA), the clustering-based adaptive many-objective evolutionary algorithm (CA-MOEA), and the improved decomposition-based evolutionary algorithm (I-DBEA), the proposed algorithm can reduce the system costs by 7%, 13%, and 21%, respectively.

A WOA-Based Optimization Approach for Task Scheduling in Cloud Computing Systems

Abstract: Task scheduling in cloud computing can directly affect the resource usage and operational cost of a system. To improve the efficiency of task executions in a cloud, various metaheuristic algorithms, as well as their variations, have been proposed to optimize the scheduling. In this article, for the first time, we apply the latest metaheuristics whale optimization algorithm (WOA) for cloud task scheduling with a multiobjective optimization model, aiming at improving the performance of a cloud system with given computing resources. On that basis, we propose an advanced approach called I mproved W OA for C loud task scheduling (IWC) to further improve the optimal solution search capability of the WOA-based method. We present the detailed implementation of IWC and our simulation-based experiments show that the proposed IWC has better convergence speed and accuracy in searching for the optimal task scheduling plans, compared to the current metaheuristic algorithms. Moreover, it can also achieve better performance on system resource utilization, in the presence of both small and large-scale tasks.

Efficient Large-Scale Multiobjective Optimization Based on a Competitive Swarm Optimizer

Abstract: There exist many multiobjective optimization problems (MOPs) containing a large number of decision variables in real-world applications, which are known as large-scale MOPs. Due to the ineffectiveness of existing operators in finding optimal solutions in a huge decision space, some decision variable division-based algorithms have been tailored for improving the search efficiency in solving large-scale MOPs. However, these algorithms will encounter difficulties when solving problems with complicated landscapes, as the decision variable division is likely to be inaccurate and time consuming. In this paper, we propose a competitive swarm optimizer (CSO)-based efficient search for solving large-scale MOPs. The proposed algorithm adopts a new particle updating strategy that suggests a two-stage strategy to update position, which can highly improve the search efficiency. The experimental results on large-scale benchmark MOPs and an application example demonstrate the superiority of the proposed algorithm over several state-of-the-art multiobjective evolutionary algorithms, including problem transformation-based algorithm, decision variable clustering-based algorithm, particle swarm optimization algorithm, and estimation of distribution algorithm.

Elephant Herding Optimization: Variants, Hybrids, and Applications

Abstract: Elephant herding optimization (EHO) is a nature-inspired metaheuristic optimization algorithm based on the herding behavior of elephants. EHO uses a clan operator to update the distance of the elephants in each clan with respect to the position of a matriarch elephant. The superiority of the EHO method to several state-of-the-art metaheuristic algorithms has been demonstrated for many benchmark problems and in various application areas. A comprehensive review for the EHO-based algorithms and their applications are presented in this paper. Various aspects of the EHO variants for continuous optimization, combinatorial optimization, constrained optimization, and multi-objective optimization are reviewed. Future directions for research in the area of EHO are further discussed.

A Two-Phase Multiobjective Local Search for the Device Allocation in the Distributed Integrated Modular Avionics

Abstract: In the distributed integrated modular avionics (DIMA), it is desirable to assign the DIMA devices to the installation locations of the aircraft for obtaining the optimal quality and cost, subject to the resource and safety constraints. Currently, the routine device assignments in DIMA are conducted manually or by experience, which becomes more and more difficult with the increasing number of devices. Especially, in the face of large-scale device assignment problems (DAPs), the manual allocation will become an almost impossible task. In this paper, a bi-objective safety-constraint device assignment model in DIMA is formulated with the integer encoding for better scalability. A two-phase multiobjective local search (2PMOLS) is proposed for addressing it. In the first phase of 2PMOLS, the fast convergence of the population toward the Pareto front (PF) is achieved by the weighted sum approach. In the second phase, Pareto local search is conducted on the solutions delivered in the first phase for the extension of the PF approximation. 2PMOLS is compared with three decomposition-based approaches and one domination-based approach on DAPs of different sizes in the experimental studies. The experimental results show that 2PMOLS outperforms all the compared algorithms, in terms of both the convergence and diversity. It has also been demonstrated that the solution obtained by 2PMOLS is better in terms of both objectives (mass and ship set costs), compared with the solution designed by the domain expert. The experimental results show that 2PMOLS performs increasingly better with the increase of the problem size, compared with other algorithms, which indicates it has better scalability.

A Similarity-Based Cooperative Co-Evolutionary Algorithm for Dynamic Interval Multiobjective Optimization Problems

Abstract: Dynamic interval multiobjective optimization problems (DI-MOPs) are very common in real-world applications. However, there are few evolutionary algorithms (EAs) that are suitable for tackling DI-MOPs up to date. A framework of dynamic interval multiobjective cooperative co-evolutionary optimization based on the interval similarity is presented in this paper to handle DI-MOPs. In the framework, a strategy for decomposing decision variables is first proposed, through which all the decision variables are divided into two groups according to the interval similarity between each decision variable and interval parameters. Following that, two subpopulations are utilized to cooperatively optimize decision variables in the two groups. Furthermore, two response strategies, i.e., a strategy based on the change intensity and a random mutation strategy, are employed to rapidly track the changing Pareto front of the optimization problem. The proposed algorithm is applied to eight benchmark optimization instances as well as a multiperiod portfolio selection problem and compared with five state-of-the-art EAs. The experimental results reveal that the proposed algorithm is very competitive on most optimization instances.

Accurate Multiobjective Design in a Space of Millions of Transition Metal Complexes with Neural-Network-Driven Efficient Global Optimization.

Abstract: The accelerated discovery of materials for real world applications requires the achievement of multiple design objectives. The multidimensional nature of the search necessitates exploration of mult...

Driving-Cycle-Oriented Design Optimization of a Permanent Magnet Hub Motor Drive System for a Four-Wheel-Drive Electric Vehicle

Abstract: The electrical drive system is crucial to the drive performance and safety of electric vehicles (EVs). In contrast to the traditional two-wheel-driven EVs, the hub motor four-wheel-drive system can steer the vehicle by controlling the torque and speed of each wheel independently, yielding a very simple distributed drivetrain with high efficiency and reliability. This article presents a system-level design optimization method for a permanent magnet hub motor drive system for a campus patrol EV based on a practical driving cycle. An outer rotor permanent-magnet synchronous hub motor (PMSHM) and an improved model predicate current control are proposed for the drive system. Due to the lack of reducers, the direct-drive PMSHM needs to face more complex working conditions and design constraints. In the implementation, the motor design requirements are obtained through the collection of practical EV driving cycles on the campus. Based on these requirements, two models are proposed as the preliminary designs for the PMSHM. To improve their performance, an efficient multiobjective optimization method is employed to the motor considering different operational conditions. The finite-element model and thermal network model are employed to verify the performance of the optimized PMSHM. An optimal design scheme is selected by comparing the comprehensive performance of the two optimized motors. In addition, a duty-cycle model predictive current control is adopted to drive the motor. Finally, a prototype is developed and tested, and the experimental results are presented.

Multi-objective optimization strategy for distribution network considering V2G-enabled electric vehicles in building integrated energy system

Abstract: Based on the large-scale penetration of electric vehicles (EV) into the building cluster, a multi-objective optimal strategy considering the coordinated dispatch of EV is proposed, for improving the safe and economical operation problems of distribution network. The system power loss and node voltage excursion can be effectively reduced, by taking measures of time-of-use (TOU) price mechanism bonded with the reactive compensation of energy storage devices. Firstly, the coordinate charging/discharging load model for EV has been established, to obtain a narrowed gap between load peak and valley. Next, a multi-objective optimization model of the distribution grid is also defined, and the active power loss and node voltage fluctuation are chosen to be the objective function. For improving the efficiency of optimization process, an advanced genetic algorithm associated with elite preservation policy is used. Finally, reactive compensation capacity supplied by capacitor banks is dynamically determined according to the varying building loads. The proposed strategy is demonstrated on the IEEE 33-node test case, and the simulation results show that the power supply pressure can be obviously relieved by introducing the coordinated charging/discharging behavior of EV; in the meantime, via reasonable planning of the compensation capacitor, the remarkably lower active power loss and voltage excursion can be realized, ensuring the safe and economical operation of the distribution system.

Joint Spectral and Energy Efficiency Optimization for Downlink NOMA Networks

Abstract: Non-orthogonal multiple access (NOMA) holds the promise to be a key enabler of 5G communication. However, the existing design of NOMA systems must be optimized to achieve maximum rate while using minimum transmit power. To do so, this paper provides a novel technique based on multi-objective optimization to efficiently allocate resources in the multi-user NOMA systems supporting downlink transmission. Specifically, our unique optimization technique jointly improves spectrum and energy efficiency while satisfying the constraints on users quality of services (QoS) requirements, transmit power budget and successive interference cancellation. We first formulate a joint problem for spectrum and energy optimization and then employ dual decomposition technique to obtain an efficient solution. For the sake of comparison, a low complexity single-objective NOMA optimization scheme is also provided as a benchmark scheme. The simulation results show that the proposed joint approach not only performs better than the traditional benchmark NOMA scheme but also significantly outperforms its counterpart orthogonal multiple access (OMA) scheme in terms of both energy and spectral efficiency.

A Survey of Weight Vector Adjustment Methods for Decomposition-Based Multiobjective Evolutionary Algorithms

Abstract: Multiobjective evolutionary algorithms based on decomposition (MOEA/D) have attracted tremendous attention and achieved great success in the fields of optimization and decision-making. MOEA/Ds work by decomposing the target multiobjective optimization problem (MOP) into multiple single-objective subproblems based on a set of weight vectors. The subproblems are solved cooperatively in an evolutionary algorithm framework. Since weight vectors define the search directions and, to a certain extent, the distribution of the final solution set, the configuration of weight vectors is pivotal to the success of MOEA/Ds. The most straightforward method is to use predefined and uniformly distributed weight vectors. However, it usually leads to the deteriorated performance of MOEA/Ds on solving MOPs with irregular Pareto fronts. To deal with this issue, many weight vector adjustment methods have been proposed by periodically adjusting the weight vectors in a random, predefined, or adaptive way. This article focuses on weight vector adjustment on a simplex and presents a comprehensive survey of these weight vector adjustment methods covering the weight vector adaptation strategies, theoretical analyses, benchmark test problems, and applications. The current limitations, new challenges, and future directions of weight vector adjustment are also discussed.

Indicator-based Multi-objective Evolutionary Algorithms: A Comprehensive Survey

Abstract: For over 25 years, most multi-objective evolutionary algorithms (MOEAs) have adopted selection criteria based on Pareto dominance. However, the performance of Pareto-based MOEAs quickly degrades when solving multi-objective optimization problems (MOPs) having four or more objective functions (the so-called many-objective optimization problems), mainly because of the loss of selection pressure. Consequently, in recent years, MOEAs have been coupled with indicator-based selection mechanisms in furtherance of increasing the selection pressure so that they can properly solve many-objective optimization problems. Several research efforts have been conducted since 2003 regarding the design of the so-called indicator-based (IB) MOEAs. In this article, we present a comprehensive survey of IB-MOEAs for continuous search spaces since their origins up to the current state-of-the-art approaches. We propose a taxonomy that classifies IB-mechanisms into two main categories: (1) IB-Selection (which is divided into IB-Environmental Selection, IB-Density Estimation, and IB-Archiving) and (2) IB-Mating Selection. Each of these classes is discussed in detail in this article, emphasizing the advantages and drawbacks of the selection mechanisms. In the final part, we provide some possible paths for future research.