Multi-objective simulation-based evolutionary algorithm for an aircraft spare parts allocation problem

Simulation optimization has received considerable attention from both simulation researchers and practitioners. In this study, we develop a solution framework which integrates multi-objective evolutionary algorithm (MOEA) with multi-objective computing budget allocation (MOCBA) method for the multi-objective simulation optimization problem. We apply it on a multi-objective aircraft spare parts allocation problem to find a set of non-dominated solutions. The problem has three features: huge search space, multi-objective, and high variability. To address these difficulties, the solution framework employs simulation to estimate the performance, MOEA to search for the more promising designs, and MOCBA algorithm to identify the non-dominated designs and efficiently allocate the simulation budget. Some computational experiments are carried out to test the effectiveness and performance of the proposed solution framework.     

An interactive evolutionary multi-objective optimization algorithm with a limited number of decision maker calls

This paper presents a preference-based method to handle optimization problems with multiple objectives. With an increase in the number of objectives the computational cost in solving a multi-objective optimization problem rises exponentially, and it becomes increasingly difficult for evolutionary multi-objective techniques to produce the entire Pareto-optimal front. In this paper, an evolutionary multi-objective procedure is combined with preference information from the decision maker during the intermediate stages of the algorithm leading to the most preferred point. The proposed approach is different from the existing approaches, as it tries to find the most preferred point with a limited budget of decision maker calls. In this paper, we incorporate the idea into a progressively interactive technique based on polyhedral cones. The idea is also tested on another progressively interactive approach based on value functions. Results are provided on two to five-objective unconstrained as well as constrained test problems.     

Interactive evolutionary multi-objective optimization for quasi-concave preference functions

We present a new hybrid approach to interactive evolutionary multi-objective optimization that uses a partial preference order to act as the fitness function in a customized genetic algorithm. We periodically send solutions to the decision maker (DM) for her evaluation and use the resulting preference information to form preference cones consisting of inferior solutions. The cones allow us to implicitly rank solutions that the DM has not considered. This technique avoids assuming an exact form for the preference function, but does assume that the preference function is quasi-concave. This paper describes the genetic algorithm and demonstrates its performance on the multi-objective knapsack problem.     

A new mechanism to maintain diversity in multi-objective metaheuristics

In this article, a new mechanism to spread the solutions generated by a multi-objective evolutionary algorithm is proposed. This approach is based on the use of stripes that are applied in objective function space and is independent of the search engine adopted. Additionally, it overcomes some of the drawbacks of other previous proposals such as the ?-dominance method. In order to validate the proposed approach, it is coupled to a multi-objective particle swarm optimizer and its performance is assessed with respect to that of state-of-the-art algorithms, using standard test problems and performance measures taken from the specialized literature. The results indicate that the proposed approach is a viable diversity maintenance mechanism that can be incorporated to any multi-objective metaheuristic used for multi-objective optimization.     

Expected runtimes of a simple evolutionary algorithm for the multi-objective minimum spanning tree problem

Evolutionary algorithms are applied to problems that are not well understood as well as to problems in combinatorial optimization. The analysis of these search heuristics has been started for some well-known polynomial solvable problems. Such analyses are starting points for the analysis of evolutionary algorithms on difficult problems. We present the first runtime analysis of a multi-objective evolutionary algorithm on a NP-hard problem. The subject of our analysis is the multi-objective minimum spanning tree problem for which we give upper bounds on the expected time until a simple evolutionary algorithm has produced a population including for each extremal point of the Pareto front a corresponding spanning tree. These points are of particular interest as they give a 2-approximation of the Pareto front. We show that in expected pseudopolynomial time a population is produced that includes for each extremal point a corresponding spanning tree.     

An evolutionary algorithm for the vehicle routing problem with route balancing

In this paper, we address a bi-objective vehicle routing problem in which the total length of routes is minimized as well as the balance of routes, i.e. the difference between the maximal route length and the minimal route length. We propose a meta-heuristic method based on an evolutionary algorithm involving classical multi-objective operators. To improve its efficiency, two mechanisms, which favor the diversification of the search, have been added. First, an elitist diversification mechanism is used in cooperation with classical diversification methodologies. Second, a parallel model designed to take into account the elitist diversification is proposed. Our method is tested on standard benchmarks for the vehicle routing problem. The contribution of the introduced mechanisms is evaluated by different performance metrics. All the experimentations indicate a strict improvement of the generated Pareto set.     

A simulated annealing technique for multi-objective simulation optimization

In this paper, we present a simulated annealing algorithm for solving multi-objective simulation optimization problems. The algorithm is based on the idea of simulated annealing with constant temperature, and uses a rule for accepting a candidate solution that depends on the individual estimated objective function values. The algorithm is shown to converge almost surely to an optimal solution. It is applied to a multi-objective inventory problem; the numerical results show that the algorithm converges rapidly.     

Local models—an approach to distributed multi-objective optimization

When solving real-world optimization problems, evolutionary algorithms often require a large number of fitness evaluations in order to converge to the global optima. Attempts have been made to find techniques to reduce the number of fitness function evaluations. We propose a novel framework in the context of multi-objective optimization where fitness evaluations are distributed by creating a limited number of adaptive spheres spanning the search space. These spheres move towards the global Pareto front as components of a swarm optimization system. We call this process localization. The contribution of the paper is a general framework for distributed evolutionary multi-objective optimization, in which the individuals in each sphere can be controlled by any existing evolutionary multi-objective optimization algorithm in the literature.     

Portfolio optimization with an envelope-based multi-objective evolutionary algorithm

The problem of portfolio selection is a standard problem in financial engineering and has received a lot of attention in recent decades. Classical mean–variance portfolio selection aims at simultaneously maximizing the expected return of the portfolio and minimizing portfolio variance. In the case of linear constraints, the problem can be solved efficiently by parametric quadratic programming (i.e., variants of Markowitz’ critical line algorithm). However, there are many real-world constraints that lead to a non-convex search space, e.g., cardinality constraints which limit the number of different assets in a portfolio, or minimum buy-in thresholds. As a consequence, the efficient approaches for the convex problem can no longer be applied, and new solutions are needed.In this paper, we propose to integrate an active set algorithm optimized for portfolio selection into a multi-objective evolutionary algorithm (MOEA). The idea is to let the MOEA come up with some convex subsets of the set of all feasible portfolios, solve a critical line algorithm for each subset, and then merge the partial solutions to form the solution of the original non-convex problem. We show that the resulting envelope-based MOEA significantly outperforms existing MOEAs.     

Multi-objective Meta-heuristics for the Traveling Salesman Problem with Profits

We introduce and test a new approach for the bi-objective routing problem known as the traveling salesman problem with profits. This problem deals with the optimization of two conflicting objectives: the minimization of the tour length and the maximization of the collected profits. This problem has been studied in the form of a single objective problem, where either the two objectives have been combined or one of the objectives has been treated as a constraint. The purpose of our study is to find solutions to this problem using the notion of Pareto optimality, i.e. by searching for efficient solutions and constructing an efficient frontier. We have developed an ejection chain local search and combined it with a multi-objective evolutionary algorithm which is used to generate diversified starting solutions in the objective space. We apply our hybrid meta-heuristic to synthetic data sets and demonstrate its effectiveness by comparing our results with a procedure that employs one of the best single-objective approaches.      

A hybrid multi-objective evolutionary algorithm based on NSGA-II for practical scheduling with release times in steel plants

The hot metal is produced from the blast furnaces in the iron plant and should be processed as soon as possible in the subsequent steel plant for energy saving. Therefore, the release times of hot metal have an influence on the scheduling of a steel plant. In this paper, the scheduling problem with release times for steel plants is studied. The production objectives and constraints related to the release times are clarified, and a new multi-objective scheduling model is built. For the solving of the multi-objective optimization, a hybrid multi-objective evolutionary algorithm based on non-dominated sorting genetic algorithm-II (NSGA-II) is proposed. In the hybrid multi-objective algorithm, an efficient decoding heuristic (DH) and a non-dominated solution construction method (NSCM) are proposed based on the problem-specific characteristics. During the evolutionary process, individuals with different solutions may have a same chromosome because the NSCM constructs non-dominated solutions just based on the solution found by DH. Therefore, three operations in the original NSGA-II process are modified to avoid identical chromosomes in the evolutionary operations. Computational tests show that the proposed hybrid algorithm based on NSGA-II is feasible and effective for the multi-objective scheduling with release times.     

Solving a new stochastic multi-mode p-hub covering location problem considering risk by a novel multi-objective algorithm

In this paper, we develop a novel stochastic multi-objective multi-mode transportation model for hub covering location problem under uncertainty. The transportation time between each pair of nodes is an uncertain parameter and also is influenced by a risk factor in the network. We extend the traditional comprehensive hub location problem by considering two new objective functions. So, our multi-objective model includes (i) minimization of total current investment costs and (ii) minimization of maximum transportation time between each origin–destination pair in the network. Besides, a novel multi-objective imperialist competitive algorithm (MOICA) is proposed to obtain the Pareto-optimal solutions of the problem. The performance of the proposed solution algorithm is compared with two well-known meta-heuristics, namely, non-dominated sorting genetic algorithm (NSGA-II) and Pareto archive evolution strategy (PAES). Computational results show that MOICA outperforms the other meta-heuristics.     

基于拟态物理学的约束多目标共轭梯度混合算法

在拟态物理学优化算法APO的基础上,将一种基于序值的无约束多目标算法RMOAPO的思想引入到约束多目标优化领域中.提出一种基于拟态物理学的约束多目标共轭梯度混合算法CGRMOAPA.算法采取外点罚函数法作为约束问题处理技术,并借鉴聚集函数法的思想,将约束多目标优化问题转化为单目标无约束优化问题,最终利用共轭梯度法进行求解.通过与CRMOAPO、MOGA、NSGA-II的实验对比,表明了算法CGRMOAPA具有较好的分布性能,也为约束多目标优化问题的求解提供了一种新的思路.     

On a high-dimensional objective genetic algorithm and its nonlinear dynamic properties

The revival of multi-objective optimization is mainly resulted from the recent development of multi-objective evolutionary optimization that allows the generation of the overall Pareto front. This paper presents an algorithm called HOGA (High-dimensional Objective Genetic Algorithm) for high-dimensional objective optimization on the basis of evolutionary computing. It adopts the principle of Shannon entropy to calculate the weight for each object since the well-known multi-objective evolutionary algorithms work poorly on the high-dimensional optimization problem. To further discuss the nonlinear dynamic property of HOGA, a martingale analysis approach is then employed; some mathematical derivations of the convergent theorems are obtained. The obtained results indicate that this new algorithm is indeed capable of achieving convergence and the suggested martingale analysis approach provides a new methodology for nonlinear dynamic analysis of evolutionary algorithms.     

基于种群自适应调整的多目标差分进化算法

为提高已有多目标进化算法在求解复杂多目标优化问题上的收敛性和解集分布性,提出一种基于种群自适应调整的多目标差分进化算法。该算法设计一个种群扩增策略,它在决策空间生成一些新个体帮助搜索更优的非支配解;设计了一个种群收缩策略,它依据对非支配解集的贡献程度淘汰较差的个体以减少计算负荷,并预留一些空间给新的带有种群多样性的扰动个体;引入精英学习策略,防止算法陷入局部收敛。通过典型的多目标优化函数对算法进行测试验证,结果表明所提算法相对于其他算法具有明显的优势,其性能优越,能够在保证良好收敛性的同时,使获得的Pareto最优解集具有更均匀的分布性和更广的覆盖范围,尤其适合于高维复杂多目标优化问题的求解。     

A simulated annealing based genetic local search algorithm for multi-objective multicast routing problems

This paper presents a new hybrid evolutionary algorithm to solve multi-objective multicast routing problems in telecommunication networks. The algorithm combines simulated annealing based strategies and a genetic local search, aiming at a more flexible and effective exploration and exploitation in the search space of the complex problem to find more non-dominated solutions in the Pareto Front. Due to the complex structure of the multicast tree, crossover and mutation operators have been specifically devised concerning the features and constraints in the problem. A new adaptive mutation probability based on simulated annealing is proposed in the hybrid algorithm to adaptively adjust the mutation rate according to the fitness of the new solution against the average quality of the current population during the evolution procedure. Two simulated annealing based search direction tuning strategies are applied to improve the efficiency and effectiveness of the hybrid evolutionary algorithm. Simulations have been carried out on some benchmark multi-objective multicast routing instances and a large amount of random networks with five real world objectives including cost, delay, link utilisations, average delay and delay variation in telecommunication networks. Experimental results demonstrate that both the simulated annealing based strategies and the genetic local search within the proposed multi-objective algorithm, compared with other multi-objective evolutionary algorithms, can efficiently identify high quality non-dominated solution set for multi-objective multicast routing problems and outperform other conventional multi-objective evolutionary algorithms in the literature.     

Multi-Objective Biclustering: When Non-dominated Solutions are not Enough

The biclustering technique was developed to avoid some of the drawbacks presented by standard clustering techniques, such as their impossibility of finding correlating data under a subset of features, and, consequently, to allow the extraction of more accurate information from datasets. Given that biclustering requires the optimization of at least two conflicting objectives (residue and volume) and that multiple independent solutions are desirable as the outcome, a few multi-objective evolutionary algorithms for biclustering were proposed in the literature. However, these algorithms only focus their search in the generation of a global set of non-dominated biclusters, which may be insufficient for most of the problems as the coverage of the dataset can be compromised. In order to overcome such problem, a multi-objective artificial immune system capable of performing a multipopulation search, named MOM-aiNet, was proposed. In this work, the MOM-aiNet algorithm will be described in detail, and an extensive set of experimental comparisons will be performed, with the obtained results of MOM-aiNet being confronted with those produced by the popular CC algorithm, by another immune-inspired approach for biclustering (BIC-aiNet), and by the multi-objective approach for biclustering proposed by Mitra & Banka.     

多目标应急物流中心选址的鲁棒优化模型

针对重大突发事件的应急物资救援,研究了应急物流中心的选址及应急物资的调运问题。利用离散的情景集合描述受灾点应急物资需求的不确定性以及应急物资运输成本和运输时间的不确定性,同时考虑应急救援成本和应急救援时间两个目标,建立了多目标应急物流中心选址的确定型模型和鲁棒优化模型。为将多目标问题转化为单目标问题,利用成本单目标和时间单目标的最优结果将多目标转化为相对值再加权处理,该方法既可消除多个目标之间的单位及数量级差异,还可以根据问题的数据变化进行动态调整。以提供应急物资救援服务的设施作为编码,设计了一种通用的混合蛙跳算法。为检验模型和算法的有效性,设计了一个多情景的算例,结果表明两个模型和算法具备良好的可行性和有效性,且鲁棒优化模型能较好地保持对各种不确定性的抗干扰能力;最后,讨论分析了成本偏好权重和鲁棒约束系数的影响,结果表明可根据成本偏好权重的取值范围来区分各种应急救援阶段,体现不同救援阶段的救援要求及特征,并给出了成本偏好权重和鲁棒约束系数的取值建议。     

The hypervolume based directed search method for multi-objective optimization problems

We present a new hybrid evolutionary algorithm for the effective hypervolume approximation of the Pareto front of a given differentiable multi-objective optimization problem. Starting point for the local search (LS) mechanism is a new division of the decision space as we will argue that in each of these regions a different LS strategy seems to be most promising. For the LS in two out of the three regions we will utilize and adapt the Directed Search method which is capable of steering the search into any direction given in objective space and which is thus well suited for the problem at hand. We further on integrate the resulting LS mechanism into SMS-EMOA, a state-of-the-art evolutionary algorithm for hypervolume approximations. Finally, we will present some numerical results on several benchmark problems with two and three objectives indicating the strength and competitiveness of the novel hybrid.     

A hybrid heuristic for the maximum clique problem

In this paper we present a heuristic based steady-state genetic algorithm for the maximum clique problem. The steady-state genetic algorithm generates cliques, which are then extended into maximal cliques by the heuristic. We compare our algorithm with three best evolutionary approaches and the overall best approach, which is non-evolutionary, for the maximum clique problem and find that our algorithm outperforms all the three evolutionary approaches in terms of best and average clique sizes found on majority of DIMACS benchmark instances. However, the obtained results are much inferior to those obtained with the best approach for the maximum clique problem.