基于遗传算法的双目标车辆路线优化研究

本文对车辆路线优化问题建立了双目标多旅行商问题模型，提出一种求解旅行商问题混合遗传算法，并对双目标多旅行商问题提出了解决方案。基于实例的仿真结果表明，文章提出的算法和解决方案是可行而有效的。     

Choquet optimal set in biobjective combinatorial optimization

We study in this paper the generation of the Choquet optimal solutions of biobjective combinatorial optimization problems. Choquet optimal solutions are solutions that optimize a Choquet integral. The Choquet integral is used as an aggregation function, presenting different parameters, and allowing to take into account the interactions between the objectives. We develop a new property that characterizes the Choquet optimal solutions. From this property, a general method to easily generate these solutions in the case of two objectives is defined. We apply the method to two classical biobjective optimization combinatorial optimization problems: the biobjective knapsack problem and the biobjective minimum spanning tree problem. We show that Choquet optimal solutions that are not weighted sum optimal solutions represent only a small proportion of the Choquet optimal solutions and are located in a specific area of the objective space, but are much harder to compute than weighted sum optimal solutions.     

Representation of the non-dominated set in biobjective discrete optimization

This paper introduces several algorithms for finding a representative subset of the non-dominated point set of a biobjective discrete optimization problem with respect to uniformity, coverage and the ϵ-indicator. We consider the representation problem itself as multiobjective, trying to find a good compromise between these quality measures. These representation problems are formulated as particular facility location problems with a special location structure, which allows for polynomial-time algorithms in the biobjective case based on the principles of dynamic programming and threshold approaches. In addition, we show that several multiobjective variants of these representation problems are also solvable in polynomial time. Computational results obtained by these approaches on a wide range of randomly generated point sets are presented and discussed.     

Diagonal bundle method with convex and concave updates for large-scale nonconvex and nonsmooth optimization

Nonsmooth optimization is traditionally based on convex analysis and most solution methods rely strongly on the convexity of the problem. In this paper, we propose an efficient diagonal bundle method for nonconvex large-scale nonsmooth optimization. The novelty of the new method is in different usage of metrics depending on the convex or concave behaviour of the objective at the current iteration point. The usage of different metrics gives us a possibility to better deal with the nonconvexity of the problem than the sole—the most commonly used and quite arbitrary—downward shifting of the piecewise linear model does. The convergence of the proposed method is proved for semismooth functions that are not necessarily differentiable nor convex. The numerical experiments have been made using problems with up to one million variables. The results to be presented confirm the usability of the new method.     

三态协调搜索多目标粒子群优化算法

提出一种三态协调搜索多目标粒子群优化算法. 该算法提出的三态指导粒子选择策略可以很好地协调算法的局部和全局搜索能力, 且算法改进了传统的外部档案保存机制, 同时引入3 种突变因子, 使获得的非劣解具有更好的分散性. 通过对标准测试函数的求解, 并与其他经典多目标优化算法比较, 表明了新算法在收敛性和多样性方面均有较大的优越性. 最后分析了区域划分系数对所提出算法性能的影响.

     

一类新型动态多目标鲁棒进化优化方法

传统动态多目标优化问题（Dynamic multi-objective optimization problems,DMOPs）的求解方法,通常需要在新环境下,通过重新激发寻优过程,获得适应该环境的Pareto最优解.这可能导致较高的计算代价和资源成本,甚至无法在有限时间内执行该优化解.由此,提出一类寻找动态鲁棒Pareto最优解集的进化优化方法.动态鲁棒Pareto解集是指某一时刻下的Pareto较优解可以以一定稳定性阈值,逼近未来多个连续动态环境下的真实前沿,从而直接作为这些环境下的Pareto解集,以减小计算代价.为合理度量Pareto解的环境适应性,给出了时间鲁棒性和性能鲁棒性定义,并将其转化为两类鲁棒优化模型.引入基于分解的多目标进化优化方法和无惩罚约束处理方法,构建了动态多目标分解鲁棒进化优化方法.特别是基于移动平均预测模型实现了未来动态环境下适应值的多维时间序列预测.基于提出的两类新型性能评价测度,针对8个典型动态测试函数的仿真实验,结果表明该方法得到满足决策者精度要求,且具有较长平均生存时间的动态鲁棒Pareto最优解.     

Minimizing distortion and internal forces in truss structures via simulated annealing

Inaccuracies in the length of members and the diameters of joints of large space structures may produce unacceptable levels of surface distortion and internal forces. We formulate two discrete optimization problems, one to minimize surface distortion (DRMS) and the other to minimize internal forces (FRMS). Both of these problems are based on the influence matrices generated by a small deformation linear analysis. Good solutions are obtained for DRMS and FRMS through the use of a simulated annealing heuristic. Results based on two biobjective (DRMS and FRMS) optimization models are discussed     

Speed-up techniques for solving large-scale biobjective TSP

In this paper, we present the Two-Phase Pareto Local Search (2PPLS) method with speed-up techniques for the heuristic resolution of the biobjective traveling salesman problem. The 2PPLS method is a state-of-the-art method for this problem. However, because of its running time that strongly grows with the instances size, the method can be hardly applied to instances with more than 200 cities. We thus adapt some speed-up techniques used in single-objective optimization to the biobjective case. The proposed method is able to solve instances with up to 1000 cities in a reasonable time with no, or very small, reduction of the quality of the generated approximations.     

Improving surrogate-assisted variable fidelity multi-objective optimization using a clustering algorithm

Surrogate-assisted evolutionary optimization has proved to be effective in reducing optimization time, as surrogates, or meta-models can approximate expensive fitness functions in the optimization run. While this is a successful strategy to improve optimization efficiency, challenges arise when constructing surrogate models in higher dimensional function space, where the trade space between multiple conflicting objectives is increasingly complex. This complexity makes it difficult to ensure the accuracy of the surrogates. In this article, a new surrogate management strategy is presented to address this problem. A k-means clustering algorithm is employed to partition model data into local surrogate models. The variable fidelity optimization scheme proposed in the author's previous work is revised to incorporate this clustering algorithm for surrogate model construction. The applicability of the proposed algorithm is illustrated on six standard test problems. The presented algorithm is also examined in a three-objective stiffened panel optimization design problem to show its superiority in surrogate-assisted multi-objective optimization in higher dimensional objective function space. Performance metrics show that the proposed surrogate handling strategy clearly outperforms the single surrogate strategy as the surrogate size increases.     

Performance Metrics and Models for Shared Cache

Performance metrics and models are prerequisites for scientific understanding and optimization. This paper introduces a new footprint-based theory and reviews the research in the past four decades leading to the new theory. The review groups the past work into metrics and their models in particular those of the reuse distance, metrics conversion, models of shared cache, performance and optimization, and other related techniques.     

A Generic Framework for Constrained Optimization Using Genetic Algorithms

In this paper, we propose a generic, two-phase framework for solving constrained optimization problems using genetic algorithms. In the first phase of the algorithm, the objective function is completely disregarded and the constrained optimization problem is treated as a constraint satisfaction problem. The genetic search is directed toward minimizing the constraint violation of the solutions and eventually finding a feasible solution. A linear rank-based approach is used to assign fitness values to the individuals. The solution with the least constraint violation is archived as the elite solution in the population. In the second phase, the simultaneous optimization of the objective function and the satisfaction of the constraints are treated as a biobjective optimization problem. We elaborate on how the constrained optimization problem requires a balance of exploration and exploitation under different problem scenarios and come to the conclusion that a nondominated ranking between the individuals will help the algorithm explore further, while the elitist scheme will facilitate in exploitation. We analyze the proposed algorithm under different problem scenarios using Test Case Generator-2 and demonstrate the proposed algorithm's capability to perform well independent of various problem characteristics. In addition, the proposed algorithm performs competitively with the state-of-the-art constraint optimization algorithms on 11 test cases which were widely studied benchmark functions in literature.     

Bound sets for biobjective combinatorial optimization problems

In this paper we introduce the concept of bound sets for multiobjective discrete optimization. We prove general results on lower and upper bound sets for combinatorial optimization problems with multiple objectives. We present general algorithms for constructing lower and upper bound sets for biobjective problems and provide numerical results on five different problem types.     

New reduction strategy in the biobjective knapsack problem

In this paper, the admissible region of a biobjective knapsack problem is our main interest. Although the reduction of feasible region has been studied by some authors, yet more investigation has to be done in order to deeply explore the domain before solving the problem. We propose, however, a new technique based on extreme supported efficient solutions combined with the dominance relationship between items' efficiency. An illustration of the algorithm by a didactic example is given and some experiments are presented, showing the efficiency of the procedure compared to the previous techniques found in the literature.     

Novel algorithms for the optimization of molecular diversity of combinatorial libraries

Various approaches to measuring and optimizing molecular diversity of combinatorial libraries are presented. The need for different diversity metrics for libraries consisting of discrete molecules ("cherry picking") vs libraries formed from combinatorial R-group enumeration (array-based selection) is discussed. Ideal requirements for diversity metrics applied to array-based selection are proposed, focusing, in particular, on the concept of incremental diversity, i.e., the change in diversity as redundant or nonredundant molecules are added to a compound collection or combinatorial library. Several distance and cell-based diversity functions are presented and analyzed in terms of their ability to satisfy these requirements. These diversity functions are applied to designing diverse libraries for two test cases, and the performance of the diversity functions is assessed. Issues associated with redundant molecules in the virtual library are discussed and analyzed using one of the test examples. The results are compared to reagent-based diversity optimizations, and it is shown that a product-based diversity protocol can result in significant improvements over a reagent-based scheme based on the diversity obtained for the resulting libraries.     

Solving a bi-objective unrelated parallel batch processing machines scheduling problem: A comparison study

Nowadays in competitive markets, production organizations are looking to increase their efficiency and optimize manufacturing operations. In addition, batch processor machines (BPMs) are faster and cheaper to carry out operations; thus the performance of manufacturing systems is increased. This paper studies a production scheduling problem on unrelated parallel BPMs with considering the release time and ready time for jobs as well as batch capacity constraints. In unrelated parallel BPMs, modern machines are used in a production line side by side with older machines that have different purchasing costs; so this factor is introduced as a novel objective to calculate the optimum cost for purchasing various machines due to the budget. Thus, a new bi-objective mathematical model is presented to minimize the makespan (i.e., C_max), tardiness/earliness penalties and the purchasing cost of machines simultaneously. The presented model is first coded and solved by the ε-constraint‌ method. Because of the complexity of the NP-hard problem, exact methods are not able to optimally solve large-sized problems in a reasonable time. Therefore, we propose a multi-objective harmony search (MOHS) algorithm. the results are compared with the multi-objective particle swarm optimization (MOPSO), non-dominated sorting genetic algorithm (NSGA-II), and multi-objective ant colony optimization algorithm (MOACO). To tune their parameters, the Taguchi method is used. The results are compared by five metrics that show the effectiveness of the proposed MOHS algorithm compared with the MOPSO, NSGA-II and MOACO. At last, the sensitivity of the model is analyzed on new parameters and impacts of each parameter are illustrated on bi- objective functions.     

Methodology for validating software metrics

A comprehensive metrics validation methodology is proposed that has six validity criteria, which support the quality functions assessment, control, and prediction, where quality functions are activities conducted by software organizations for the purpose of achieving project quality goals. Six criteria are defined and illustrated: association, consistency, discriminative power, tracking, predictability, and repeatability. The author shows that nonparametric statistical methods such as contingency tables play an important role in evaluating metrics against the validity criteria. Examples emphasizing the discriminative power validity criterion are presented. A metrics validation process is defined that integrates quality factors, metrics, and quality functions     

Implementation of call admission control scheme in next generation mobile communication networks using particle swarm optimization and fuzzy logic systems

In the present and next generation wireless networks, cellular system remains the major method of telecommunication infrastructure. Since the characteristic of the resource constraint, call admission control is required to address the limited resource problem in wireless network. The call dropping probability and call blocking probability are the major performance metrics for quality of service (QoS) in wireless network. Many call admission control mechanisms have been proposed in the literature to decrease connection dropping probability for handoffs and new call blocking probability in cellular communications. In this paper, we proposed an adaptive call admission control and bandwidth reservation scheme using fuzzy logic control concept to reduce the forced termination probability of multimedia handoffs. Meanwhile, we adopt particle swarm optimization (PSO) technique to adjust the parameters of the membership functions in the proposed fuzzy logic systems. The simulation results show that the proposed scheme can achieve satisfactory performance when performance metrics are measured in terms of the forced termination probability for the handoffs, the call blocking probability for the new connections and bandwidth utilization.     

Airfoil shape optimization using improved Multiobjective Territorial Particle Swarm algorithm with the objective of improving stall characteristics

In this paper, a new robust optimization technique with the ability of solving multi-objective constrained design optimization problems in aerodynamics is presented. This new technique is Multi-objective Territorial Particle Swarm Optimization (MOTPSO) algorithm in which diversity is actively preserved by avoiding overcrowded clusters of particles and encouraging broader exploration. Adaptively varying “territories” are formed around promising individuals to prevent many of the lesser individuals from premature clustering and encouraged them to explore new neighborhoods based on a hybrid self-social metric. Also, a new social interaction scheme is introduced which guided particles towards the weighted average of their “elite” neighbors’ best found positions instead of their own personal bests which in turn helps the particles to exploit the candidate local optima more effectively. The MOTPSO algorithm takes into account multiple objective functions using a Pareto-Based approach. The non-dominated solutions found by swarm are stored in an external archive and nearest neighbor density estimator method is used to select a leader for the individual particles in the swarm. Efficiency and robustness of the proposed algorithm is demonstrated using multiple traditional and newly-composed optimization benchmark functions and aerodynamic design problems. In final airfoil designs obtained from the Multi Objective Territorial Particle Swarm Optimization algorithm, separation point is delayed to make the airfoil less susceptible to stall in critical operating conditions and it also reveal an evident improvement over the test case airfoil across all objective functions presented.     

API-Based and Information-Theoretic Metrics for Measuring the Quality of Software Modularization

We present in this paper a new set of metrics that measure the quality of modularization of a non-object-oriented software system. We have proposed a set of design principles to capture the notion of modularity and defined metrics centered around these principles. These metrics characterize the software from a variety of perspectives: structural, architectural, and notions such as the similarity of purpose and commonality of goals. (By structural, we are referring to intermodule coupling-based notions, and by architectural, we mean the horizontal layering of modules in large software systems.) We employ the notion of API (application programming interface) as the basis for our structural metrics. The rest of the metrics we present are in support of those that are based on API. Some of the important support metrics include those that characterize each module on the basis of the similarity of purpose of the services offered by the module. These metrics are based on information-theoretic principles. We tested our metrics on some popular open-source systems and some large legacy-code business applications. To validate the metrics, we compared the results obtained on human-modularized versions of the software (as created by the developers of the software) with those obtained on randomized versions of the code. For randomized versions, the assignment of the individual functions to modules was randomized     

Solving multiobjective problems using cat swarm optimization

This paper proposes a new multiobjective evolutionary algorithm (MOEA) by extending the existing cat swarm optimization (CSO). It finds the nondominated solutions along the search process using the concept of Pareto dominance and uses an external archive for storing them. The performance of our proposed approach is demonstrated using standard test functions. A quantitative assessment of the proposed approach and the sensitivity test of different parameters is carried out using several performance metrics. The simulation results reveal that the proposed approach can be a better candidate for solving multiobjective problems (MOPs).