Convergence performance comparison of quantum-inspired multi-objective evolutionary algorithms

In recent research, we proposed a general framework of quantum-inspired multi-objective evolutionary algorithms (QMOEA) and gave one of its sufficient convergence conditions to the Pareto optimal set. In this paper, two Q-gate operators, H gate and R&N gate, are experimentally validated as two Q-gate paradigms meeting the convergence condition. The former is a modified rotation gate, and the latter is a combination of rotation gate and NOT gate with the specified probability. To investigate their effectiveness and applicability, several experiments on the multi-objective 0/1 knapsack problems are carried out. Compared to two typical evolutionary algorithms and the QMOEA only with rotation gate, the QMOEA with H gate and R&N gate have more powerful convergence ability in high complex instances. Moreover, the QMOEA with R&N gate has the best convergence in almost all of the experimental problems. Furthermore, the appropriate ε value regions for two Q-gates are verified.     

Wind turbine selection for wind farm layout using multi-objective evolutionary algorithms

Wind energy has become the world’s fastest growing energy source. Although wind farm layout is a well known problem, its solution used to be heuristic, mainly based on the designer experience. A key in search trend is to increase power production capacity over time. Furthermore the production of wind energy often involves uncertainties due to the stochastic nature of wind speeds. The addressed problem contains a novel aspect with respect of other wind turbine selection problems in the context of wind farm design. The problem requires selecting two different wind turbine models (from a list of 26 items available) to minimize the standard deviation of the energy produced throughout the day while maximizing the total energy produced by the wind farm. The novelty of this new approach is based on the fact that wind farms are usually built using a single model of wind turbine. This paper describes the usage of multi-objective evolutionary algorithms (MOEAs) in the context of power energy production, selecting a combination of two different models of wind turbine along with wind speeds distributed over different time spans of the day. Several MOEAs variants belonging to the most renowned and widely used algorithms such as SPEA2 NSGAII, PESA and msPEA have been investigated, tested and compared based on the data gathered from Cancun (Mexico) throughout the year of 2008. We have demonstrated the powerful of MOEAs applied to wind turbine selection problem (WTS) and estimate the mean power and the associated standard deviation considering the wind speed and the dynamics of the power curve of the turbines. Among them, the performance of PESA algorithm looks a little bit superior than the other three algorithms. In conclusion, the use of MOEAs is technically feasible and opens new perspectives for assisting utility companies in developing wind farms.     

Seeding the initial population of multi-objective evolutionary algorithms: A computational study

Most experimental studies initialize the population of evolutionary algorithms with random genotypes. In practice, however, optimizers are typically seeded with good candidate solutions either previously known or created according to some problem-specific method. This seeding has been studied extensively for single-objective problems. For multi-objective problems, however, very little literature is available on the approaches to seeding and their individual benefits and disadvantages. In this article, we are trying to narrow this gap via a comprehensive computational study on common real-valued test functions. We investigate the effect of two seeding techniques for five algorithms on 48 optimization problems with 2, 3, 4, 6, and 8 objectives. We observe that some functions (e.g., DTLZ4 and the LZ family) benefit significantly from seeding, while others (e.g., WFG) profit less. The advantage of seeding also depends on the examined algorithm.     

Achieving super-linear performance in parallel multi-objective evolutionary algorithms by means of cooperative coevolution

This article introduces three new multi-objective cooperative coevolutionary variants of three state-of-the-art multi-objective evolutionary algorithms, namely, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Strength Pareto Evolutionary Algorithm 2 (SPEA2) and Multi-objective Cellular Genetic Algorithm (MOCell). In such a coevolutionary architecture, the population is split into several subpopulations or islands, each of them being in charge of optimizing a subset of the global solution by using the original multi-objective algorithm. Evaluation of complete solutions is achieved through cooperation, i.e., all subpopulations share a subset of their current partial solutions. Our purpose is to study how the performance of the cooperative coevolutionary multi-objective approaches can be drastically increased with respect to their corresponding original versions. This is specially interesting for solving complex problems involving a large number of variables, since the problem decomposition performed by the model at the island level allows for much faster executions (the number of variables to handle in every island is divided by the number of islands). We conduct a study on a real-world problem related to grid computing, the bi-objective robust scheduling problem of independent tasks. The goal in this problem is to minimize makespan (i.e., the time when the latest machine finishes its assigned tasks) and to maximize the robustness of the schedule (i.e., its tolerance to unexpected changes on the estimated time to complete the tasks). We propose a parallel, multithreaded implementation of the coevolutionary algorithms and we have analyzed the results obtained in terms of both the quality of the Pareto front approximations yielded by the techniques as well as the resulting speedups when running them on a multicore machine.     

Emergent nature inspired algorithms for multi-objective optimization

Many real-world decision-making situations possess both a discrete and combinatorial structure and involve the simultaneous consideration of conflicting objectives. Problems of this kind are in general of large size and contains several objectives to be “optimized”. Although Multiple Objective Optimization is a well-established field of research, one branch, namely nature inspired metaheuristics is currently experienced a tremendous growth. Over the last few years, developments of new methodologies, methods, and techniques to deal with multi-objective large size problems in particular those with a combinatorial structure and the strong improvement on computing technologies (during and after the 80s) made possible to solve very hard problems with the help of inspired nature based metaheuristics.     

Physical programming for preference driven evolutionary multi-objective optimization

Preference articulation in multi-objective optimization could be used to improve the pertinency of solutions in an approximated Pareto front. That is, computing the most interesting solutions from the designer's point of view in order to facilitate the Pareto front analysis and the selection of a design alternative. This articulation can be achieved in an a priori, progressive, or a posteriori manner. If it is used within an a priori frame, it could focus the optimization process toward the most promising areas of the Pareto front, saving computational resources and assuring a useful Pareto front approximation for the designer. In this work, a physical programming approach embedded in an evolutionary multi-objective optimization is presented as a tool for preference inclusion. The results presented and the algorithm developed validate the proposal as a potential tool for engineering design by means of evolutionary multi-objective optimization.     

A multi-objective evolutionary algorithm for examination timetabling

This paper considers the scheduling of exams for a set of university courses. The solution to this exam timetabling problem involves the optimization of complete timetables such that there are as few occurrences of students having to take exams in consecutive periods as possible but at the same time minimizing the timetable length and satisfying hard constraints such as seating capacity and no overlapping exams. To solve such a multi-objective combinatorial optimization problem, this paper presents a multi-objective evolutionary algorithm that uses a variable-length chromosome representation and incorporates a micro-genetic algorithm and a hill-climber for local exploitation and a goal-based Pareto ranking scheme for assigning the relative strength of solutions. It also imports several features from the research on the graph coloring problem. The proposed algorithm is shown to be a more general exam timetabling problem solver in that it does not require any prior information of the timetable length to be effective. It is also tested against a few influential and recent optimization techniques and is found to be superior on four out of seven publicly available datasets.     

Convergence of multi-objective evolutionary algorithms to a uniformly distributed representation of the Pareto front

In evolutionary multi-objective optimization (EMO), the convergence to the Pareto set of a multi-objective optimization problem (MOP) and the diversity of the final approximation of the Pareto front are two important issues. In the existing definitions and analyses of convergence in multi-objective evolutionary algorithms (MOEAs), convergence with probability is easily obtained because diversity is not considered. However, diversity cannot be guaranteed. By combining the convergence with diversity, this paper presents a new definition for the finite representation of a Pareto set, the B-Pareto set, and a convergence metric for MOEAs. Based on a new archive-updating strategy, the convergence of one such MOEA to the B-Pareto sets of MOPs is proved. Numerical results show that the obtained B-Pareto front is uniformly distributed along the Pareto front when, according to the new definition of convergence, the algorithm is convergent.     

Near optimal process plan selection for multiple jobs in networked based manufacturing using multi-objective evolutionary algorithms

The networked manufacturing offers several advantages in current competitive atmosphere by way of reducing the manufacturing cycle time and maintenance of the production flexibility, thereby achieving several feasible process plans. In this paper, we have addressed a Multi Objective Problem (MOP) which covers-minimize the makespan and to maximize the machine utilization while generating the feasible process plans for multiple jobs in the context of network based manufacturing system. A new multi-objective based Territory Defining Evolutionary Algorithm (TDEA) to resolve the above computationally challenge problem have been developed. In particular, with two powerful Multi-Objective Evolutionary Algorithms (MOEAs), viz. Non-dominated Sorting Genetic Algorithm (NSGA-II) and Controlled Elitist-NSGA-II (CE-NSGA-II) the performance of the proposed TDEA has been compared. An illustrative example along with three complex scenarios is presented to demonstrate the feasibility of the approach. The proposed algorithm is validated and the results are analyzed and compared.     

Feature selection for face recognition based on multi-objective evolutionary wrappers

Feature selection is a key issue in pattern recognition, specially when prior knowledge of the most discriminant features is not available. Moreover, in order to perform the classification task with reduced complexity and acceptable performance, usually features that are irrelevant, redundant, or noisy are excluded from the problem representation. This work presents a multi-objective wrapper, based on genetic algorithms, to select the most relevant set of features for face recognition tasks. The proposed strategy explores the space of multiple feasible selections in order to minimize the cardinality of the feature subset, and at the same time to maximize its discriminative capacity. Experimental results show that, in comparison with other state-of-the-art approaches, the proposed approach allows to improve the classification performance, while reducing the representation dimensionality.     

A multi-objective evolutionary approach for generator scheduling

This paper presents a novel, two-phase approach for optimal generation scheduling, taking into account the environmental issue of emission allowance trading in addition to the economic issue of operation cost. In the first phase, hourly-optimal scheduling is done to simultaneously minimize operation cost, emission, and transmission loss, while satisfying constraints such as power balance, spinning reserve and power generation limits. In the second phase, the minimum up/down time and ramp up/down rate constraints are considered, and a set of 24-h optimal schedules is obtained using the outputs of the first phase. Simulation results indicate effectiveness of the proposed approach.     

Memory-based adaptive partitioning (MAP) of search space for the enhancement of convergence in Pareto-based multi-objective evolutionary algorithms

A new algorithm, dubbed memory-based adaptive partitioning (MAP) of search space, which is intended to provide a better accuracy/speed ratio in the convergence of multi-objective evolutionary algorithms (MOEAs) is presented in this work. This algorithm works by performing an adaptive-probabilistic refinement of the search space, with no aggregation in objective space. This work investigated the integration of MAP within the state-of-the-art fast and elitist non-dominated sorting genetic algorithm (NSGAII). Considerable improvements in convergence were achieved, in terms of both speed and accuracy. Results are provided for several commonly used constrained and unconstrained benchmark problems, and comparisons are made with standalone NSGAII and hybrid NSGAII-efficient local search (eLS).     

一种基于CUDA的并行多目标进化算法

传统的多目标进化算法多是基于Pareto最优概念的类随机搜索算法,求解速度较慢,特别是当问题维度变高,需要群体规模较大时,上述问题更加凸显。这一问题已经获得越来越多研究人员以及从业人员的关注。实验仿真中可以发现,构造非支配集和保持群体多样性这两部分工作占用了算法99%以上的执行时间。解决上述问题的一个有效方法就是对这一部分算法进行并行化改造。本文提出了一种基于CUDA平台的并行化解决方案,采用小生境技术实现共享适应度来维持候选解集的多样性,将多目标进化算法的实现全部置于GPU端,区别于以往研究中非支配排序的部分工作以及群体多样性保持的全部工作仍在CPU上执行。通过对ZDT系列函数的仿真结果,可以看出本文算法性能远远优于NSGA-Ⅱ和NPGA。最后通过求解油品调和过程这一有约束多目标优化问题,可以看出在解决化工应用中的有约束多目标优化问题时,该算法依然表现出优异的加速效果。     

A dominance tree and its application in evolutionary multi-objective optimization

Most contemporary multi-objective evolutionary algorithms (MOEAs) store and handle a population with a linear list, and this may impose high computational complexities on the comparisons of solutions and the fitness assignment processes. This paper presents a data structure for storing the whole population and their dominating information in MOEAs. This structure, called a Dominance Tree (DT), is a binary tree that can effectively and efficiently store three-valued relations (namely dominating, dominated or non-dominated) among vector values. This paper further demonstrates DT’s potential applications in evolutionary multi-objective optimization with two cases. The first case utilizes the DT to improve NSGA-II as a fitness assignment strategy. The second case demonstrates a DT-based MOEA (called a DTEA), which is designed by leveraging the favorable properties of the DT. The simulation results show that the DT-improved NSGA-II is significantly faster than NSGA-II. Meanwhile, DTEA is much faster than SPEA2, NSGA-II and an improved version of NSGA-II. On the other hand, in regard to converging to the Pareto optimal front and maintaining the diversity of solutions, DT-improved NSGA-II and DTEA are found to be competitive with NSGA-II and SPEA2.     

A novel evolutionary root system growth algorithm for solving multi-objective optimization problems

This paper proposes a novel multi-objective root system growth optimizer (MORSGO) for the copper strip burdening optimization. The MORSGO aims to handle multi-objective problems with satisfactory convergence and diversity via implementing adaptive root growth operators with a pool of multi-objective search rules and strategies. Specifically, the single-objective root growth operators including branching, regrowing and auxin-based tropisms are deliberately designed. They have merits of appropriately balancing exploring & exploiting and self-adaptively varying population size to reduce redundant computation. The effective multi-objective strategies including the fast non-dominated sorting and the farthest-candidate selection are developed for saving and retrieving the Pareto optimal solutions with remarkable approximation as well as uniform spread of Pareto-optimal solutions. With comprehensive evaluation against a suit of benchmark functions, the MORSGO is verified experimentally to be superior or at least comparable to its competitors in terms of the IGD and HV metrics. The MORSGO is then validated to solve the real-world copper strip burdening optimization with different elements. Computation results verifies the potential and effectiveness of the MORSGO to resolve complex industrial process optimization.     

Multi-objective evolutionary algorithms based on the summation of normalized objectives and diversified selection

Most multi-objective evolutionary algorithms (MOEAs) use the concept of dominance in the search process to select the top solutions as parents in an elitist manner. However, as MOEAs are probabilistic search methods, some useful information may be wasted, if the dominated solutions are completely disregarded. In addition, the diversity may be lost during the early stages of the search process leading to a locally optimal or partial Pareto-front. Beside this, the non-domination sorting process is complex and time consuming. To overcome these problems, this paper proposes multi-objective evolutionary algorithms based on Summation of normalized objective values and diversified selection (SNOV-DS). The performance of this algorithm is tested on a set of benchmark problems using both multi-objective evolutionary programming (MOEP) and multi-objective differential evolution (MODE). With the proposed method, the performance metric has improved significantly and the speed of the parent selection process has also increased when compared with the non-domination sorting. In addition, the proposed algorithm also outperforms ten other algorithms.     

Multi-objective evolutionary algorithms for energy-aware scheduling on distributed computing systems

The ongoing increase of energy consumption by IT infrastructures forces data center managers to find innovative ways to improve energy efficiency. The latter is also a focal point for different branches of computer science due to its financial, ecological, political, and technical consequences. One of the answers is given by scheduling combined with dynamic voltage scaling technique to optimize the energy consumption. The way of reasoning is based on the link between current semiconductor technologies and energy state management of processors, where sacrificing the performance can save energy.This paper is devoted to investigate and solve the multi-objective precedence constrained application scheduling problem on a distributed computing system, and it has two main aims: the creation of general algorithms to solve the problem and the examination of the problem by means of the thorough analysis of the results returned by the algorithms.The first aim was achieved in two steps: adaptation of state-of-the-art multi-objective evolutionary algorithms by designing new operators and their validation in terms of performance and energy. The second aim was accomplished by performing an extensive number of algorithms executions on a large and diverse benchmark and the further analysis of performance among the proposed algorithms. Finally, the study proves the validity of the proposed method, points out the best-compared multi-objective algorithm schema, and the most important factors for the algorithms performance.     

NoC在纳米计算结构下的延迟与拥塞优化映射

片上网络(NoC)映射的性能严重依赖于该网络拥有的互联结构.在自组装的纳米计算结构上探索了NoC映射问题,特别研究了在该结构上与最小延迟与拥塞相关的映射问题.提出了一个用于评估传输延迟的模型,并提出了SWMAP映射算法,使应用任务能够映射到具有小世界特性的纳米计算结构上.该算法使用了两种应用任务测试样例进行测试,实验结...     

Convergence analysis of a self-adaptive multi-objective evolutionary algorithm based on grids

Evolutionary algorithms have been successfully applied to various multi-objective optimization problems. However, theoretical studies on multi-objective evolutionary algorithms, especially with self-adaption, are relatively scarce. This paper analyzes the convergence properties of a self-adaptive (μ+1)-algorithm. The convergence of the algorithm is defined, and general convergence conditions are studied. Under these conditions, it is proven that the proposed self-adaptive (μ+1)-algorithm converges in probability or almost surely to the Pareto-optimal front.     

Greedy-search-based multi-objective genetic algorithm for emergency logistics scheduling

To enable the immediate and efficient dispatch of relief to victims of disaster, this study proposes a greedy-search-based, multi-objective, genetic algorithm capable of regulating the distribution of available resources and automatically generating a variety of feasible emergency logistics schedules for decision-makers. The proposed algorithm dynamically adjusts distribution schedules from various supply points according to the requirements at demand points in order to minimize unsatisfied demand for resources, time to delivery, and transportation costs. The proposed algorithm was applied to the case of the Chi–Chi earthquake in Taiwan to verify its performance. Simulation results demonstrate that under conditions of a limited/unlimited number of available vehicles, the proposed algorithm outperforms the MOGA and standard greedy algorithm in ‘time to delivery’ by an average of 63.57% and 46.15%, respectively, based on 10,000 iterations.