A simultaneous transit network design and frequency setting: Computing with bees

The transit network design problem belongs to the class of hard combinatorial optimization problem, whose optimal solution is not easy to find out. We consider in this paper the transit network design problem in a way that we simultaneously determine the links to be included in the transit network, assemble chosen links into bus routes, and determine bus frequency on each of the designed routes. Our approach to the transit network design problem is based on the Bee Colony Optimization (BCO) metaheuristic. The BCO algorithm is a stochastic, random-search technique that belongs to the class of population-based algorithms. This technique uses a similarity among the way in which bees in nature look for food, and the way in which optimization algorithms search for an optimum of a combinatorial optimization problem. The numerical experiments are performed on known benchmark problems. We clearly show that our approach, based on the BCO algorithm is competitive with the other approaches in the literature and that can generate high-quality solutions.     

Bee colony optimization for the p-center problem

Bee colony optimization (BCO) is a relatively new meta-heuristic designed to deal with hard combinatorial optimization problems. It is biologically inspired method that explores collective intelligence applied by the honey bees during nectar collecting process. In this paper we apply BCO to the p-center problem in the case of symmetric distance matrix. On the contrary to the constructive variant of the BCO algorithm used in recent literature, we propose variant of BCO based on the improvement concept (BCOi). The BCOi has not been significantly used in the relevant BCO literature so far. In this paper it is proved that BCOi can be a very useful concept for solving difficult combinatorial problems. The numerical experiments performed on well-known benchmark problems show that the BCOi is competitive with other methods and it can generate high-quality solutions within negligible CPU times.     

Very large-scale neighborhood search

Neighborhood search algorithms are often the most effective approaches available for solving partitioning problems, a difficult class of combinatorial optimization problems arising in many application domains including vehicle routing, telecommunications network design, parallel machine scheduling, location theory, and clustering. A critical issue in the design of a neighborhood search algorithm is the choice of the neighborhood structure, that is, the manner in which the neighborhood is defined. Currently, the two-exchange neighborhood is the most widely used neighborhood for solving partitioning problems. The paper describes the cyclic exchange neighborhood , which is a generalization of the two-exchange neighborhood in which a neighbor is obtained by performing a cyclic exchange . The cyclic exchange neighborhood has substantially more neighbors compared to the two-exchange neighborhood. This paper outlines a network optimization based methodology to search the neighborhood efficiently and presents a proof of concept by applying it to the capacitated minimum spanning tree problem, an important problem in telecommunications network design.     

离散Jaya算法的复杂网络社区发现

社区结构是复杂网络的重要特性之一, 基于模块度的复杂网络社区发现问题是一个NP难度的组合优化问题, 常用启发式算法求解. 最近出现的Jaya算法是求解连续优化问题的一种简单有效的元启发式方法. 本文在遵循Jaya算法按靠近最好解、远离最差解的方式更新种群个体的基础上, 针对复杂网络社区发现问题给出了Jaya算法离散化的策略, 提出一种复杂网络社区发现的离散Jaya算法. 实验表明, 在几个典型真实网络实例和一类人造网络实例上, 与几个经典算法和元启发式算法相比, 本文算法具有求解精度高、能自动确定社区数目等优点.     

A new real-coded Bayesian optimization algorithm based on a team of learning automata for continuous optimization

Estimation of distribution algorithms have evolved as a technique for estimating population distribution in evolutionary algorithms. They estimate the distribution of the candidate solutions and then sample the next generation from the estimated distribution. Bayesian optimization algorithm is an estimation of distribution algorithm, which uses a Bayesian network to estimate the distribution of candidate solutions and then generates the next generation by sampling from the constructed network. The experimental results show that the Bayesian optimization algorithms are capable of identifying correct linkage between the variables of optimization problems. Since the problem of finding the optimal Bayesian network belongs to the class of NP-hard problems, typically Bayesian optimization algorithms use greedy algorithms to build the Bayesian network. This paper proposes a new real-coded Bayesian optimization algorithm for solving continuous optimization problems that uses a team of learning automata to build the Bayesian network. This team of learning automata tries to learn the optimal Bayesian network structure during the execution of the algorithm. The use of learning automaton leads to an algorithm with lower computation time for building the Bayesian network. The experimental results reported here show the preference of the proposed algorithm on both uni-modal and multi-modal optimization problems.     

求解混杂生产调度问题的嵌套混合蚁群算法

蚁群算法作为解决优化问题的有力工具,它的有效性已经得到了证明.由于其生物学背 景,基本蚁群算法被设计来求解复杂的排序类型组合优化问题,在连续空间优化问题的求解方面 研究很少.本文提出一种嵌套混合蚁群算法,用于解决具有混杂变量类型的复杂生产调度问题, 在一种新的最佳路径信息素更新算法的基础上,提高了搜索效率.计算机仿真结果表明,本文提 出的方法在求解此类问题上性能优于另一种基于进化计算的有效方法--遗传算法.     

基于遗传禁忌算法的多目的间歇过程调度问题求解

由于组合爆炸特性,多目的厂的调度问题很难求解大规模甚至中等规模的问题,本文采用一种新的随机性优化技术一基于禁忌技术的遗传算法点(Tabu-genetic algorithm,TGA)来对该问题进行求解,引入新的选择策略和变异方法．并以零等待的多目的间歇过程调度为实例,计算表明同已有的方法相比,该方法求解效率高、收敛速度快、使用简单方便,可有效的克服计算负荷和求解质量之间的冲突,是一种求解多目的厂间歇过程调度问题的有效算法。     

带平衡约束矩形布局优化问题的深度强化学习算法

带平衡约束的矩形布局问题源于卫星舱设备布局设计,属于组合优化问题。深度强化学习利用奖赏机制,通过数据训练实现高性能决策优化。针对布局优化问题,提出一种基于深度强化学习的新算法DAR及其扩展算法IDAR。DAR用指针网络输出定位顺序,再利用定位机制给出布局结果,算法的时间复杂度是O（n³）;IDAR算法在DAR的基础上引入迭代机制,算法时间复杂度是O（n⁴）,但能给出更好的结果。测试表明DAR算法具有较好的学习能力,用小型布局问题进行求解训练所获得的模型,能有效应用在大型问题上。在两个大规模典型算例的对照实验中,提出算法分别超出和接近目前最优解,具有时间和质量上的优势。     

Hybrid particle swarm optimization and differential evolution for optimal design of water distribution systems

Water distribution system design belongs to a class of large combinatorial non-linear optimization problems, involving complex implicit constraints, such as conservation of mass and energy equations, which are commonly satisfied through the use of hydraulic simulation solvers. Recently, many researchers have shifted the focus from traditional optimization methods to the use of meta-heuristic approaches for handling this complexity. This paper proposes a hybrid particle swarm optimization (PSO) and differential evolution (DE) method, linked to the hydraulic simulator, EPANET, for minimizing the cost design of water distribution systems. The performance of the proposed PSO-DE algorithm is demonstrated using three well-known benchmark water distribution system problems, the two-loop network, the Hanoi network and the New York Tunnels network. The results are compared to that of standard PSO and previously applied optimization methods. It is found that PSO-DE is a promising method for solving water distribution system design problems as it outperforms standard PSO and other algorithms previously presented in the literature for the three case studies considered.     

Solving fuzzy assembly-line balancing problem with genetic algorithms

Assembly-line balancing problem is known as one of difficult combinatorial optimization problems. This problem has been solved with linear programming, dynamic programming approaches, but unfortunately these approaches do not lead to efficient algorithms. Recently, genetic algorithm has been recognized as an efficient and usefull procedure for solving large and hard combinatorial optimization problems, such as scheduling problems, travelling salesman problems, transportation problems, and so on. Fuzzy sets theory is frequently used to represent uncertainty of information. In this paper, to treat the data of real-world problems we use a fuzzy number to represent the processing time and show that we can get a good performance in solving this problem using genetic algorithms.     

A modified genetic algorithm with fuzzy roulette wheel selection for job-shop scheduling problems

The job-shop scheduling problem is one of the most difficult production planning problems. Since it is in the NP-hard class, a recent trend in solving the job-shop scheduling problem is shifting towards the use of heuristic and metaheuristic algorithms. This paper proposes a novel metaheuristic algorithm, which is a modification of the genetic algorithm. This proposed algorithm introduces two new concepts to the standard genetic algorithm: (1) fuzzy roulette wheel selection and (2) the mutation operation with tabu list. The proposed algorithm has been evaluated and compared with several state-of-the-art algorithms in the literature. The experimental results on 53 JSSPs show that the proposed algorithm is very effective in solving the combinatorial optimization problems. It outperforms all state-of-the-art algorithms on all benchmark problems in terms of the ability to achieve the optimal solution and the computational time.     

Towards hybrid evolutionary algorithms

Metaheuristics have received considerable interest these recent years in the field of combinatorial optimization. However, the choice of a particular algorithm to optimize a certain problem is still mainly driven by some sort of devotion of its author to a certain technique rather than by a rationalistic choice driven by reason. Hybrid algorithms have shown their ability to provide local optima of high quality. Hybridization of algorithms is still in its infancy: certain combinations of algorithms have experimentally shown their performance, though the reasons of their success is not always really clear. In order to add some rational to these issues, we study the structure of search spaces and attempt to relate it to the performance of algorithms. We wish to explain the behavior of search algorithms with this knowledge and provide guidelines in the design of hybrid algorithms. This paper briefly reviews the current knowledge we have on search spaces of combinatorial optimization problems. Then, we discuss hybridization and present a general classification of the way hybridization can be conducted in the light of our knowledge of the structure of search spaces.     

基于蚁群算法的电梯群控调度优化策略研究

为了研究多台电梯的群控调度问题,并根据现有电梯调度策略的不足,建立以服务间和运行能耗为优化目标函数的调度模型,提出将电梯群控调度问题转化为离散组合优化问题,并利用蚁群优化算法求解。算法在接受众多乘客的随机请求下,能根据各电梯的运行现状,将不同层的乘客请求组合分配到相应电梯进行服务的最优调度方案,优化了群控电梯的运行模式,仿真实验证明算法能大幅度减少乘客的平均侯梯时间及缩短运行路径,证明了算法的有效性。     

An approximation algorithm for interval data minmax regret combinatorial optimization problems

The general problem of minimizing the maximal regret in combinatorial optimization problems with interval data is considered. In many cases, the minmax regret versions of the classical, polynomially solvable, combinatorial optimization problems become NP-hard and no approximation algorithms for them have been known. Our main result is a polynomial time approximation algorithm with a performance ratio of 2 for this class of problems.     

AAO as a new strategy in modeling and simulation of constructional problems optimization

The article presents a new multi-criteria optimization method called Artificial Acari Optimization (AAO). AAO method was tested with five well-known benchmark structural problems i.e.: welded beam, pressure vessel, speed reducer, spring design and gear train problem. The results were compared on other representatives of Swarm Intelligence mainstream which are bee algorithms MBO, BCO and ABC. Numerous references show dominance of ABC over MBO and BCO. To check this, a detailed comparisons of AAO results were made and introduced together with the results of the ABC algorithm.     

Immigrant Population Search Algorithm for Solving Constrained Optimization Problems

This article introduces the Immigrant Population Search Algorithm (IPSA) inspired by the pattern of human population migration to find better habitats. The algorithm is viewed as a new optimization method for solving constrained optimization problems, and it belongs to the set of population-based algorithms that are proposed for combinatorial optimization. In this algorithm, the life environment is the solution space of the problem. Every point of this space is a solution for the problem, which may be feasible or infeasible, and the quality of life at that point is the value of fitness function for that solution. Each population group tries to investigate feasible and better habitats. In other words, it tries to optimize the problem. After the algorithm steps are described, the efficiency of the algorithm is compared to that of three other metaheuristic algorithms that are used to optimize some mathematic problems. The results show that the proposed algorithm performs better than the other three methods.     

A learning automata-based algorithm for determination of the number of hidden units for three-layer neural networks

There is no method to determine the optimal topology for multi-layer neural networks for a given problem. Usually the designer selects a topology for the network and then trains it. Since determination of the optimal topology of neural networks belongs to class of NP-hard problems, most of the existing algorithms for determination of the topology are approximate. These algorithms could be classified into four main groups: pruning algorithms, constructive algorithms, hybrid algorithms and evolutionary algorithms. These algorithms can produce near optimal solutions. Most of these algorithms use hill-climbing method and may be stuck at local minima. In this article, we first introduce a learning automaton and study its behaviour and then present an algorithm based on the proposed learning automaton, called survival algorithm, for determination of the number of hidden units of three layers neural networks. The survival algorithm uses learning automata as a global search method to increase the probability of obtaining the optimal topology. The algorithm considers the problem of optimization of the topology of neural networks as object partitioning rather than searching or parameter optimization as in existing algorithms. In survival algorithm, the training begins with a large network, and then by adding and deleting hidden units, a near optimal topology will be obtained. The algorithm has been tested on a number of problems and shown through simulations that networks generated are near optimal.     

A genetic algorithm-based solution methodology for modular design

Combinatorial optimization problems usually have a finite number of feasible solutions. However, the process of solving these types of problems can be a very long and tedious task. Moreover, the cost and time for getting accurate and acceptable results is usually quite large. As the complexity and size of these problems grow, the current methods for solving problems such as the scheduling problem or the classification problem have become obsolete, and the need for an efficient method that will ensure good solutions for these complicated problems has increased. This paper presents a genetic algorithm (GA)-based method used in the solution of a set of combinatorial optimization problems. A definition of a combinatorial optimization problem is first given. The definition is followed by an introduction to genetic algorithms and an explanation of their role in solving combinatorial optimization problems such as the traveling salesman problem. A heuristic GA is then developed and used as a tool for solving various combinatorial optimization problems such as the modular design problem. A modularity case study is used to test and measure the performance of the developed algorithm.     

基于细菌觅食优化算法的城市轨道交通调度优化

为了合理高效地制定城市轨道交通调度方案,实现客流与车次的优化配置,提出了一种基于细菌觅食优化算法的城市轨道交通调度优化策略。兼顾乘客与运营企业双方利益,以发车间隔为决策变量,乘客平均候车时间最短和发车次数最少为优化目标,建立调度优化模型,并对细菌觅食优化算法求解该调度模型的过程进行分析。结合某城市轨道交通一号线实际运营数据进行仿真实验,并与其他算法的优化结果进行对比分析,实验表明该算法和模型能有效解决城市轨道交通调度优化问题。     

基于改进模拟退火算法的登机口分配问题

为研究新建卫星厅对中转旅客的航班衔接的影响,分析中转旅客的换乘紧张程度,提高机场资源利用效率,本文对登机口分配问题进行研究.在最小化登机口使用个数的前提下,考虑了中转旅客的换乘紧张度,建立了飞机-登机口分配0-1整数规划模型.为改善传统启发式算法的搜索能力,本文结合变邻域搜索的邻域构造思想,综合利用集束搜索和模拟退火算法的优势,提出了基于集束搜索的改进型模拟退火算法,并借助Java语言进行编程求解.结果表明:与禁忌搜索算法、变邻域搜索算法和经典蚁群算法相比,本文所提出算法的优化效果较好.