Adaptive heuristic search algorithm for discrete variables based multi-objective optimization

Although metamodel technique has been successfully used to enhance the efficiency of the multi-objective optimization (MOO) with black-box objective functions, the metamodel could become less accurate or even unavailable when the design variables are discrete. In order to overcome the bottleneck, this work proposes a novel random search algorithm for discrete variables based multi-objective optimization with black-box functions, named as k-mean cluster based heuristic sampling with Utopia-Pareto directing adaptive strategy (KCHS-UPDA). This method constructs a few adaptive sampling sets in the solution space and draws samples according to a heuristic probability model. Several benchmark problems are supplied to test the performance of KCHS-UPDA including closeness, diversity, efficiency and robustness. It is verified that KCHS-UPDA can generally converge to the Pareto frontier with a small quantity of number of function evaluations. Finally, a vehicle frontal member crashworthiness optimization is successfully solved by KCHS-UPDA.     

Enhanced colliding bodies optimization for design problems with continuous and discrete variables

Colliding Bodies Optimization (CBO) is a new multi-agent algorithm inspired by a collision between two objects in one-dimension. Each agent is modeled as a body with a specified mass and velocity. A collision occurs between pairs of objects and the new positions of the colliding bodies are updated based on the collision laws. In this paper, Enhanced Colliding Bodies Optimization (ECBO) which uses memory to save some best solutions is developed. In addition, a mechanism is utilized to escape from local optima. The performance of the proposed algorithm is compared to those of standard CBO and some optimization techniques on some benchmark mathematical functions and three standard discrete and continuous structural design problems. Optimization results confirm the validity of the proposed approach.     

Multidisciplinary design optimization with discrete and continuous variables of various uncertainties

As a powerful design tool, Reliability Based Multidisciplinary Design Optimization (RBMDO) has received increasing attention to satisfy the requirement for high reliability and safety in complex and coupled systems. In many practical engineering design problems, design variables may consist of both discrete and continuous variables. Moreover, both aleatory and epistemic uncertainties may exist. This paper proposes the formula of RFCDV (Random/Fuzzy Continuous/Discrete Variables) Multidisciplinary Design Optimization (RFCDV-MDO), uncertainty analysis for RFCDV-MDO, and a method of RFCDV-MDO within the framework of Sequential Optimization and Reliability Assessment (RFCDV-MDO-SORA) to solve RFCDV-MDO problems. A mathematical problem and an engineering design problem are used to demonstrate the efficiency of the proposed method.     

无参分组大规模变量的多目标算法研究

目前大多数多目标优化算法没有考虑到决策变量之间的交互性,只是将所有变量当作一个整体进行优化。随着决策变量的增加,多目标优化算法的性能会急剧下降。针对上述问题,提出一种无参变量分组的大规模变量的多目标优化算法(MOEA/DWPG)。该算法将协同优化与基于分解的多目标优化算法(MOEA/D)相结合,设计了一种不含参数的分组方式来提高交互变量分组的精确性,提高了算法处理含有大规模变量的多目标优化算法的性能。实验结果表明,该算法在大规模变量多目标问题上明显优于MOEA/D及其它先进算法。     

A new VPS-based algorithm for multi-objective optimization problems

In this paper, a multi-objective variant of the vibrating particles system (MOVPS) is introduced. The new algorithm uses an external archive to keep the non-dominated solutions. Besides, the...     

Entropy-based multi-objective genetic algorithm for design optimization

Obtaining a fullest possible representation of solutions to a multiobjective optimization problem has been a major concern in Multi-Objective Genetic Algorithms (MOGAs). This is because a MOGA, due to its very nature, can only produce a discrete representation of Pareto solutions to a multiobjective optimization problem that usually tend to group into clusters. This paper presents a new MOGA, one that aims at obtaining the Pareto solutions with maximum possible coverage and uniformity along the Pareto frontier. The new method, called an Entropy-based MOGA (or E-MOGA), is based on an application of concepts from the statistical theory of gases to a baseline MOGA. Two demonstration examples, the design of a two-bar truss and a speed reducer, are used to demonstrate the effectiveness of E-MOGA in comparison to the baseline MOGA.     

Interval analysis based robust truss optimization with continuous and discrete variables using mix-coded genetic algorithm

The problem of optimizing truss structures in the presence of uncertain parameters considering both continuous and discrete design variables is studied. An interval analysis based robust optimization method combined with the improved genetic algorithm is proposed for solving the problem. Uncertain parameters are assumed to be bounded in specified intervals. The natural interval extensions are employed to obtain explicitly a conservative approximation of the upper and lower bounds of the structural response, and hereby the bounds of the objective function and the constraint function. This way the uncertainty design may be performed in a very efficient manner in comparison with the probabilistic analysis based method. A mix-coded genetic algorithm (GA), where the discrete variables are coded with binary numbers while the continuous variables are coded with real numbers, is developed to deal with simultaneously the continuous and discrete design variables of the optimization model. An improved differences control strategy is proposed to avoid the GA getting stuck in local optima. Several numerical examples concerning the optimization of plane and space truss structures with continuous, discrete or mixed design variables are presented to validate the method developed in the present paper. Monte Carlo simulation shows that the interval analysis based optimization method gives much more robust designs in comparison with the deterministic optimization method.     

Suspension system performance optimization with discrete design variables

Suspension systems on commercial vehicles have become an important feature meeting the requirements from costumers and legislation. The performance of the suspension system is often limited by available catalogue components. Additionally the suspension performance is restricted by the travel speed which highly influences the ride comfort. In this article a suspension system for an articulated dump truck is optimized in sense of reducing elapsed time for two specified duty cycles without violating a certain comfort threshold level. The comfort threshold level is here defined as a whole-body vibration level calculated by ISO 2631-1. A three-dimensional multibody dynamics simulation model is applied to evaluate the suspension performance. A non-gradient optimization routine is used to find the best possible combination of continuous and discrete design variables including the optimum operational speed without violating a set of side constraints. The result shows that the comfort level converges to the comfort threshold level. Thus it is shown that the operational speed and hence the operator input influences the ride comfort level. Three catalogue components are identified by the optimization routine together with a set of continuous design variables and two operational speeds one for each load case. Thus the work demonstrates handling of human factors in optimization of a mechanical system with discrete and continuous design variables.     

An archive-based artificial bee colony optimization algorithm for multi-objective continuous optimization problem

Neural Computing and Applications - Research on multi-objective optimization (MO) has become one of the hot points of intelligent computation. In this paper, an archive-based multi-objective...     

基于拥挤度与变异的动态微粒群多目标优化算法

提出一种动态微粒群多目标优化算法(DCMOPSO),算法中的惯性权重和加速因子动态变化以增强算法的全局搜索能力,并采用拥挤度的方法对外部档案进行维护以增加非劣解的多样性.在维护过程中,从外部档案中按拥挤度为每个微粒选择全局最好位置,同时使用变异操作避免算法早熟.通过几个典型的多目标测试函数对DCMOPSO算法的性能进行了测试,并与多目标优化算法MOPSO和NSGA-Ⅱ进行对比.结果表明,DCMOPSO算法具有良好的搜索性能.     

基于决策变量关系的动态多目标优化算法

动态多目标优化问题(DMOPs)需要进化算法跟踪不断变化的Pareto最优前沿,从而在检测到环境变化时能够及时有效地做出响应.为了解决上述问题,提出一种基于决策变量关系的动态多目标优化算法.首先,通过决策变量对收敛性和多样性贡献大小的检测机制将决策变量分为收敛性相关决策变量(CV)和多样性相关决策变量(DV),对不同类型决策变量采用不同的优化策略;其次,提出一种局部搜索多样性维护机制,使个体在Pareto前沿分布更加均匀;最后,对两部分产生的组合个体进行非支配排序构成新环境下的种群.为了验证DVR的性能,将DVR与3种动态多目标优化算法在15个基准测试问题上进行比较,实验结果表明, DVR算法相较于其他3种算法表现出更优的收敛性和多样性.     

A new real-coded stochastic Bayesian optimization algorithm for continuous global optimization

Estimation of distribution algorithms are considered to be a new class of evolutionary algorithms which are applied as an alternative to genetic algorithms. Such algorithms sample the new generation from a probabilistic model of promising solutions. The search space of the optimization problem is improved by such probabilistic models. In the Bayesian optimization algorithm (BOA), the set of promising solutions forms a Bayesian network and the new solutions are sampled from the built Bayesian network. This paper proposes a novel real-coded stochastic BOA for continuous global optimization by utilizing a stochastic Bayesian network. In the proposed algorithm, the new Bayesian network takes advantage of using a stochastic structure (that there is a probability distribution function for each edge in the network) and the new generation is sampled from the stochastic structure. In order to generate a new solution, some new structure, and therefore a new Bayesian network is sampled from the current stochastic structure and the new solution will be produced from the sampled Bayesian network. Due to the stochastic structure used in the sampling phase, each sample can be generated based on a different structure. Therefore the different dependency structures can be preserved. Before the new generation is generated, the stochastic network’s probability distributions are updated according to the fitness evaluation of the current generation. The proposed method is able to take advantage of using different dependency structures through the sampling phase just by using one stochastic structure. The experimental results reported in this paper show that the proposed algorithm increases the quality of the solutions on the general optimization benchmark problems.     

A new real-coded quantum-inspired evolutionary algorithm for continuous optimization

This paper presents a recursive deepening hybrid strategy to solve real-parameter optimization problems. It couples a local search technique with a quantum-inspired evolutionary algorithm. In order to adapt the quantum-inspired evolutionary algorithm for continuous optimization without losing the states superposition property, a suitable sampling of the search space that tightens recursively and an integration of a uniformly generated random part after measurement have been utilized. The use of local search provides, for each search window, a good exploitation of the quantum inspired generated solution's neighbourhood. The proposed approach has been tested through the reference black-box optimization benchmarking framework. The comparison of the obtained results with those of some state-of-the-art algorithms has shown its actual effectiveness.     

Direct zigzag search for discrete multi-objective optimization

Multiple objective optimization (MOO) models and solution methods are commonly used for multi-criteria decision making in real-life engineering and management applications. Much research has been conducted for continuous MOO problems, but MOO problems with discrete or mixed integer variables and black-box objective functions arise frequently in practice. For example, in energy industry, optimal development problems of oil gas fields, shale gas hydraulic fracturing, and carbon dioxide geologic storage and enhanced oil recovery, may consider integer variables (number of wells, well drilling blocks), continuous variables (e.g. bottom hole pressures, production rates), and the field performance is typically evaluated by black-box reservoir simulation. These discrete or mixed integer MOO (DMOO) problems with black-box objective functions are more challenging and require new MOO solution techniques. We develop a direct zigzag (DZZ) search method by effectively integrating gradient-free direct search and zigzag search for such DMOO problems. Based on three numerical example problems including a mixed integer MOO problem associated with the optimal development of a carbon dioxide capture and storage (CCS) project, DZZ is demonstrated to be computationally efficient. The numerical results also suggest that DZZ significantly outperforms NSGA-II, a widely used genetic algorithms (GA) method.     

A multi-objective optimization algorithm for feature selection problems

Feature selection (FS) is a critical step in data mining, and machine learning algorithms play a crucial role in algorithms performance. It reduces the processing time and accuracy of the categories. In this paper, three different solutions are proposed to FS. In the first solution, the Harris Hawks Optimization (HHO) algorithm has been multiplied, and in the second solution, the Fruitfly Optimization Algorithm (FOA) has been multiplied, and in the third solution, these two solutions are hydride and are named MOHHOFOA. The results were tested with MOPSO, NSGA-II, BGWOPSOFS and B-MOABC algorithms for FS on 15 standard data sets with mean, best, worst, standard deviation (STD) criteria. The Wilcoxon statistical test was also used with a significance level of 5% and the Bonferroni–Holm method to control the family-wise error rate. The results are shown in the Pareto front charts, indicating that the proposed solutions' performance on the data set is promising.

     

A Pareto-optimal genetic algorithm for warehouse multi-objective optimization

The automated warehouse management requires to fulfill objectives that are usually conflicting with each other. The decisions taken must ensure optimized usage of resources, cost reduction and better customer service. The warehouse replenishment task is a typical example of multi-objective optimization. In this paper, a genetic algorithm with a new crossover operator is developed to solve the replenishment problem. This algorithm is applied to real warehouse data and produces Pareto-optimal permutations of the stored products. A fuzzy rule-base is proposed to increase the diversity of the optimal solutions.     

An orthogonal multi-objective evolutionary algorithm for multi-objective optimization problems with constraints

In this paper, an orthogonal multi-objective evolutionary algorithm (OMOEA) is proposed for multi-objective optimization problems (MOPs) with constraints. Firstly, these constraints are taken into account when determining Pareto dominance. As a result, a strict partial-ordered relation is obtained, and feasibility is not considered later in the selection process. Then, the orthogonal design and the statistical optimal method are generalized to MOPs, and a new type of multi-objective evolutionary algorithm (MOEA) is constructed. In this framework, an original niche evolves first, and splits into a group of sub-niches. Then every sub-niche repeats the above process. Due to the uniformity of the search, the optimality of the statistics, and the exponential increase of the splitting frequency of the niches, OMOEA uses a deterministic search without blindness or stochasticity. It can soon yield a large set of solutions which converges to the Pareto-optimal set with high precision and uniform distribution. We take six test problems designed by Deb, Zitzler et al., and an engineering problem (W) with constraints provided by Ray et al. to test the new technique. The numerical experiments show that our algorithm is superior to other MOGAS and MOEAs, such as FFGA, NSGAII, SPEA2, and so on, in terms of the precision, quantity and distribution of solutions. Notably, for the engineering problem W, it finds the Pareto-optimal set, which was previously unknown.     

A problem reduction based approach to discrete optimization algorithm design

The paper presents a novel approach to formal algorithm design for a typical class of discrete optimization problems. Using a concise set of program calculation rules, our approach reduces a problem into subproblems with less complexity based on function decompositions, constructs the problem reduction graph that describes the recurrence relations between the problem and subproblems, from which a provably correct algorithm can be mechanically derived. Our approach covers a large variety of algorithms and bridges the relationship between conventional methods for designing efficient algorithms (including dynamic programming and greedy) and some effective methods for coping with intractability (including approximation and parameterization).