Chaotic particle swarm optimization for assembly sequence planning

Assembly sequence planning of complex products is difficult to be tackled, because the size of the search space of assembly sequences is exponentially proportional to the number of parts or components of the products. Contrasted with the conventional methods, the intelligent optimization algorithms display their predominance in escaping from the vexatious trap. This paper proposes a chaotic particle swarm optimization (CPSO) approach to generate the optimal or near-optimal assembly sequences of products. Six kinds of assembly process constraints affecting the assembly cost are concerned and clarified at first. Then, the optimization model of assembly sequences is presented. The mapping rules between the optimization model and the traditional PSO model are given. The variable velocity in the traditional PSO algorithm is changed to the velocity operator (vo) which is used to rearrange the parts in the assembly sequences to generate the optimal or near-optimal assembly sequences. To improve the quality of the optimal assembly sequence and increase the convergence rate of the traditional PSO algorithm, the chaos method is proposed to provide the preferable assembly sequences of each particle in the current optimization time step. Then, the preferable assembly sequences are considered as the seeds to generate the optimal or near-optimal assembly sequences utilizing the traditional PSO algorithm. The proposed method is validated with an illustrative example and the results are compared with those obtained using the traditional PSO algorithm under the same assembly process constraints.     

An interval space reducing method for constrained problems with particle swarm optimization

In this paper, we propose a method for solving constrained optimization problems using interval analysis combined with particle swarm optimization. A set inverter via interval analysis algorithm is used to handle constraints in order to reduce constrained optimization to quasi unconstrained one. The algorithm is useful in the detection of empty search spaces, preventing useless executions of the optimization process. To improve computational efficiency, a space cleaning algorithm is used to remove solutions that are certainly not optimal. As a result, the search space becomes smaller at each step of the optimization procedure. After completing pre-processing, a modified particle swarm optimization algorithm is applied to the reduced search space to find the global optimum. The efficiency of the proposed approach is demonstrated through comprehensive experimentation involving 100 000 runs on a set of well-known benchmark constrained engineering design problems. The computational efficiency of the new method is quantified by comparing its results with other PSO variants found in the literature.     

An investigation on a two-agent single-machine scheduling problem with unequal release dates

This paper addresses a two-agent scheduling problem on a single machine with arbitrary release dates, where the objective is to minimize the tardiness of one agent, while keeping the lateness of the other agent below or at a fixed level Q. A mixed integer programming model is first presented for its optimal solution, admittedly not to be practical or useful in the most cases, but theoretically interesting since it models the problem. Thus, as an alternative, a branch-and-bound algorithm incorporating with several dominance properties and a lower bound is provided to derive the optimal solution and a marriage in honey-bees optimization algorithm (MBO) is developed to derive the near-optimal solutions for the problem. Computational results are also presented to evaluate the performance of the proposed algorithms.     

A linear programming based heuristic framework for min-max regret combinatorial optimization problems with interval costs

This work deals with a class of problems under interval data uncertainty, namely interval robust-hard problems, composed of interval data min-max regret generalizations of classical NP-hard combinatorial problems modeled as 0-1 integer linear programming problems. These problems are more challenging than other interval data min-max regret problems, as solely computing the cost of any feasible solution requires solving an instance of an NP-hard problem. The state-of-the-art exact algorithms in the literature are based on the generation of a possibly exponential number of cuts. As each cut separation involves the resolution of an NP-hard classical optimization problem, the size of the instances that can be solved efficiently is relatively small. To smooth this issue, we present a modeling technique for interval robust-hard problems in the context of a heuristic framework. The heuristic obtains feasible solutions by exploring dual information of a linearly relaxed model associated with the classical optimization problem counterpart. Computational experiments for interval data min-max regret versions of the restricted shortest path problem and the set covering problem show that our heuristic is able to find optimal or near-optimal solutions and also improves the primal bounds obtained by a state-of-the-art exact algorithm and a 2-approximation procedure for interval data min-max regret problems.     

基于泛化竞争和局部渗透机制的自组织网TSP问题求解方法

旅行商问题(TSP)是组合优化中最典型的NP完全问题之一,具有很强的工程背景和应用价值.文章在分析了标准SOM(Self-Organizing Map)算法在求解TSP问题的不足和在寻求总体最优解的潜力的基础上,引入泛化竞争和局部渗透这两个新的学习机制,提出了一种新的SOM算法---渗透的SOM(Infiltrative SOM,ISOM)算法.通过泛化竞争和局部渗透策略的协同作用:总体竞争和局部渗透并举、先倾向总体竞争后倾向局部渗透、在总体竞争基础上的局部渗透,实现了在总体路径寻优指导下的局部路径优化,从而使所得路径尽可能接近最优解.通过对TSPLIB中14组TSP实例的测试结果及与KNIES、SETSP、Budinich和ESOM等类SOM算法的比较,表明该算法既简单又能使解的质量得到很大提高,同时还保持了解的良好的稳健特性.     

A filter-and-fan algorithm for the capacitated minimum spanning tree problem

The capacitated minimum spanning tree (CMST) is a notoriously difficult problem in combinatorial optimization. Extensive investigation has been devoted to developing efficient algorithms to find optimal or near-optimal solutions. This paper proposes a new CMST heuristic algorithm that effectively combines the classical node-based and tree-based neighborhoods embodied in a filter-and-fan (F&F) approach, a local search procedure that generates compound moves in a tree search fashion. The overall algorithm is guided by a multi-level oscillation strategy used to trigger each type of neighborhood while allowing the search to cross feasibility boundaries. Computational results carried out on a standard set of 135 benchmark problems show that a simple F&F design competes effectively with prior CMST metaheuristics, rivaling the best methods, which are significantly more complex.     

On the sizing of a solar thermal electricity plant for multiple objectives using evolutionary optimization

Design, implementation and operation of solar thermal electricity plants are no more an academic task, rather they have become a necessity. In this paper, we work with power industries to formulate a multi-objective optimization model and attempt to solve the resulting problem using classical as well as evolutionary optimization techniques. On a set of four objectives having complex trade-offs, our proposed procedure first finds a set of trade-off solutions showing the entire range of optimal solutions. Thereafter, the evolutionary optimization procedure is combined with a multiple criterion decision making (MCDM) approach to focus on preferred regions of the trade-off frontier. Obtained solutions are compared with a classical generating method. Eventually, a decision-maker is involved in the process and a single preferred solution is obtained in a systematic manner. Starting with generating a wide spectrum of trade-off solutions to have a global understanding of feasible solutions, then concentrating on specific preferred regions for having a more detailed understanding of preferred solutions, and then zeroing on a single preferred solution with the help of a decision-maker demonstrates the use of multi-objective optimization and decision making methodologies in practice. As a by-product, useful properties among decision variables that are common to the obtained solutions are gathered as vital knowledge for the problem. The procedures used in this paper are ready to be used to other similar real-world problem solving tasks.     

Coupling the cross-entropy with the line sampling method for risk-based design optimization

An algorithm for risk-based optimization (RO) of engineering systems is proposed, which couples the Cross-entropy (CE) optimization method with the Line Sampling (LS) reliability method. The CE-LS algorithm relies on the CE method to optimize the total cost of a system that is composed of the design and operation cost (e.g., production cost) and the expected failure cost (i.e., failure risk). Guided by the random search of the CE method, the algorithm proceeds iteratively to update a set of random search distributions such that the optimal or near-optimal solution is likely to occur. The LS-based failure probability estimates are required to evaluate the failure risk. Throughout the optimization process, the coupling relies on a local weighted average approximation of the probability of failure to reduce the computational demands associated with RO. As the CE-LS algorithm proceeds to locate a region of design parameters with near-optimal solutions, the local weighted average approximation of the probability of failure is refined. The adaptive refinement procedure is repeatedly applied until convergence criteria with respect to both the optimization and the approximation of the failure probability are satisfied. The performance of the proposed optimization heuristic is examined empirically on several RO problems, including the design of a monopile foundation for offshore wind turbines.     

A <Emphasis Type="Italic">Q</Emphasis>-learning-based swarm optimization algorithm for economic dispatch problem

In this paper, we treat optimization problems as a kind of reinforcement learning problems regarding an optimization procedure for searching an optimal solution as a reinforcement learning procedure for finding the best policy to maximize the expected rewards. This viewpoint motivated us to propose a Q-learning-based swarm optimization (QSO) algorithm. The proposed QSO algorithm is a population-based optimization algorithm which integrates the essential properties of Q-learning and particle swarm optimization. The optimization procedure of the QSO algorithm proceeds as each individual imitates the behavior of the global best one in the swarm. The best individual is chosen based on its accumulated performance instead of its momentary performance at each evaluation. Two data sets including a set of benchmark functions and a real-world problem—the economic dispatch (ED) problem for power systems—were used to test the performance of the proposed QSO algorithm. The simulation results on the benchmark functions show that the proposed QSO algorithm is comparable to or even outperforms several existing optimization algorithms. As for the ED problem, the proposed QSO algorithm has found solutions better than all previously found solutions.     

A branch-and-bound procedure for a single-machine earliness scheduling problem with two agents

This paper addresses a two-agent scheduling problem on a single machine where the objective is to minimize the total weighted earliness cost of all jobs, while keeping the earliness cost of one agent below or at a fixed level Q. A mixed-integer programming (MIP) model is first formulated to find the optimal solution which is useful for small-size problem instances. To solve medium- to large-size problem instances, a branch-and-bound algorithm incorporating with several dominance properties and a lower bound is then provided to derive the optimal solution. A simulated annealing heuristic algorithm incorporating with a heuristic procedure is developed to derive the near-optimal solutions for the problem. A computational experiment is also conducted to evaluate the performance of the proposed algorithms.     

A probabilistic approach for designing nonlinear optimal robust tracking controllers for unmanned aerial vehicles

In this study, we propose a probabilistic approach for designing nonlinear optimal robust tracking controllers for unmanned aerial vehicles. The controller design is formulated in terms of a multi-objective optimization problem that is solved by using a bio-inspired optimization algorithm, offering high likelihood of finding an optimal or near-optimal global solution. The process of tuning the controller minimizes differences between system outputs and optimal specifications given in terms of rising time, overshoot and steady-state error, and the controller succeed in fitting the performance requirements even considering parametric uncertainties and the nonlinearities of the aircraft. The stability of the controller is proved for the nominal case and its robustness is carefully verified by means of Monte Carlo simulations.     

云计算环境中面向DAG任务的多目标调度算法

为了实现任务执行效率与执行代价的同步优化,提出了一种云计算环境中的DAG任务多目标调度优化算法。算法将多目标最优化问题以满足Pareto最优的均衡最优解集合的形式进行建模,以启发式方式对模型进行求解;同时,为了衡量多目标均衡解的质量,设计了基于hypervolume方法的评估机制,从而可以得到相互冲突目标间的均衡调度解。通过配置云环境与三种人工合成工作流和两种现实科学工作流的仿真实验测试,结果表明,比较同类单目标算法和多目标启发式算法,算法不仅求解质量更高,而且解的均衡度更好,更加符合现实云的资源使用特征与工作流调度模式。     

Constrained multi-objective optimization algorithms: Review and comparison with application in reinforced concrete structures

Engineering design problems are often multi-objective in nature, which means trade-offs are required between conflicting objectives. In this study, we examine the multi-objective algorithms for the optimal design of reinforced concrete structures. We begin with a review of multi-objective optimization approaches in general and then present a more focused review on multi-objective optimization of reinforced concrete structures. We note that the existing literature uses metaheuristic algorithms as the most common approaches to solve the multi-objective optimization problems. Other efficient approaches, such as derivative-free optimization and gradient-based methods, are often ignored in structural engineering discipline. This paper presents a multi-objective model for the optimal design of reinforced concrete beams where the optimal solution is interested in trade-off between cost and deflection. We then examine the efficiency of six established multi-objective optimization algorithms, including one method based on purely random point selection, on the design problem. Ranking and consistency of the result reveals a derivative-free optimization algorithm as the most efficient one.     

Optimal sequencing of warm standby elements

Warm standby redundancy has been used as an effective design technique for improving the reliability of a system while achieving the compromise between restoration cost and operation cost of standby elements. This paper considers the optimal standby element sequencing problem (SESP) for 1-out-of-N: G heterogeneous warm-standby systems. Given the desired redundancy level and a fixed set of element choices, the objective of the optimal system design is to select the initiation sequence of the system elements so as to minimize the expected mission cost of the system while providing a certain level of system reliability. Based on a discrete approximation of time-to-failure distributions of the system elements, the system reliability and expected mission cost are evaluated using an iterative procedure. A genetic algorithm is used as an optimization tool for solving the formulated SESP problem for 1-out-of-N: G warm-standby systems with non-identical elements. As illustrated through examples, results generated using the suggested methodology can facilitate the system reliability versus cost trade-off study, which can further assist in the decision making about the best standby policy for fault-tolerant system designs.     

Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization

The performance of an optimization tool is largely determined by the efficiency of the search algorithm used in the process. The fundamental nature of a search algorithm will essentially determine its search efficiency and thus the types of problems it can solve. Modern metaheuristic algorithms are generally more suitable for global optimization. This paper carries out extensive global optimization of unconstrained and constrained problems using the recently developed eagle strategy by Yang and Deb in combination with the efficient differential evolution. After a detailed formulation and explanation of its implementation, the proposed algorithm is first verified using twenty unconstrained optimization problems or benchmarks. For the validation against constrained problems, this algorithm is subsequently applied to thirteen classical benchmarks and three benchmark engineering problems reported in the engineering literature. The performance of the proposed algorithm is further compared with various, state-of-the-art algorithms in the area. The optimal solutions obtained in this study are better than the best solutions obtained by the existing methods. The unique search features used in the proposed algorithm are analyzed, and their implications for future research are also discussed in detail.     

Reliability evaluation and optimal design in heterogeneous multi-state series-parallel systems

This paper addresses the heterogeneous redundancy allocation problem in multi-state series-parallel reliability structures with the objective to minimize the total cost of system design satisfying the given reliability constraint and the consumer load demand. The demand distribution is presented as a piecewise cumulative load curve and each subsystem is allowed to consist of parallel redundant components of not more than three types. The system uses binary capacitated components chosen from a list of available products to provide redundancy so as to increase system performance and reliability. The components are characterized by their feeding capacity, reliability and cost. A system that consists of elements with different reliability and productivity parameters has the capacity strongly dependent upon the selection of constituent components. A binomial probability based method to compute exact system reliability index is suggested. To analyze the problem and suggest an optimal/near-optimal system structure, an ant colony optimization algorithm has been presented. The solution approach consists of a series of simple steps as used in early ant colony optimization algorithms dealing with other optimization problems and offers straightforward analysis. Four multi-state system design problems have been solved for illustration. Two problems are taken from the literature and solved to compare the algorithm with the other existing methods. The other two problems are based upon randomly generated data. The results show that the method can be appealing to many researchers with regard to the time efficiency and yet without compromising over the solution quality.     

Optimizing thermal design of data center cabinets with a new multi-objective genetic algorithm

There is an ever increasing need to use optimization methods for thermal design of data centers and the hardware populating them. Airflow simulations of cabinets and data centers are computationally intensive and this problem is exacerbated when the simulation model is integrated with a design optimization method. Generally speaking, thermal design of data center hardware can be posed as a constrained multi-objective optimization problem. A popular approach for solving this kind of problem is to use Multi-Objective Genetic Algorithms (MOGAs). However, the large number of simulation evaluations needed for MOGAs has been preventing their applications to realistic engineering design problems. In this paper, details of a substantially more efficient MOGA are formulated and demonstrated through a thermal analysis simulation model of a data center cabinet. First, a reduced-order model of the cabinet problem is constructed using the Proper Orthogonal Decomposition (POD). The POD model is then used to form the objective and constraint functions of an optimization model. Next, this optimization model is integrated with the new MOGA. The new MOGA uses a “kriging” guided operation in addition to conventional genetic algorithm operations to search the design space for global optimal design solutions. This approach for optimal design is essential to handle complex multi-objective situations, where the optimal solutions may be non-obvious from simple analyses or intuition. It is shown that in optimizing the data center cabinet problem, the new MOGA outperforms a conventional MOGA by estimating the Pareto front using 50% fewer simulation calls, which makes its use very promising for complex thermal design problems. Recommended by: Monem Beitelmal     

On the use of genetic algorithms to solve location problems

This paper seeks to evaluate the performance of genetic algorithms (GA) as an alternative procedure for generating optimal or near-optimal solutions for location problems. The specific problems considered are the uncapacitated and capacitated fixed charge problems, the maximum covering problem, and competitive location models. We compare the performance of the GA-based heuristics developed against well-known heuristics from the literature, using a test base of publicly available data sets.Scope and purposeGenetic algorithms are a potentially powerful tool for solving large-scale combinatorial optimization problems. This paper explores the use of this category of algorithms for solving a wide class of location problems. The purpose is not to “prove” that these algorithms are superior to procedures currently utilized to solve location problems, but rather to identify circumstances where such methods can be useful and viable as an alternative/superior heuristic solution method.     

Flow-shop sequencing using hybrid simulated annealing

Simulated annealing (SA) heuristics have been successfully applied on a variety of complex optimization problems. This paper presents a new hybrid SA approach for the permutation flow-shop scheduling (FSS) problem. FSS is known to be NP-hard, and thus the right way to proceed is through the use of heuristics techniques. The proposed approach combines the characteristics of a canonical SA procedure together with features borrowed from the field of genetic algorithms (GAs), such as the use of a population of individuals and the use of a novel, non-standard recombination operator for generating solutions. The approach is easily implemented and performs near-optimal schedules in a rather short computation time. Experiments over multiple benchmarks test problems show that the developed approach has higher performance than that of other FSS meta-heuristic approaches, generating schedules of shorter makespans faster. The experiments include comparisons between the proposed hybrid model, a genetic algorithm, and two other standard simulated annealing approaches. The final solutions obtained by the method are within less than 1% in average from the optimal solutions obtained so far.     

基于广义凸下界估计的多模态差分进化算法

针对多模态优化问题,提出了基于广义凸下界估计模型的改进差分进化算法。首先,基于模型变换方法将原优化问题转变为单位单纯形约束条件下的严格递增射线凸优化问题;其次,基于广义凸理论,利用差分进化算法中更新个体的适应度知识,建立原优化问题广义凸下界估计模型,设计实现了基于 N-叉树的估计模型快速计算方法;进而,综合考虑原问题目标值与其估计值之间的差异,提出一种基于有偏采样的小生境指标,并设计区域进化树更新策略来保证算法的局部搜索能力。数值实验结果表明,提出的算法能够有效地发现并维持一定数量的满意解模态,动态地实现全局模态搜索到模态内局部增强的自适应平滑过渡。对于给出的测试问题,能够发现所有的全局最优解以及一些较好的局部极值解。