基于离散差分进化算法雌多维0／1背包问题求解

多维0／1背包问题（MKP）是一种典型的组合优化问题,并且被广泛的应用于各种工程领域。差分进化算法（DE）是一种有效的进化算法,能处理各种复杂的非线性优化问题,但主要是用来解决连续领域的优化问题。提出一种离散差分进化算法,并用来求解MKP问题。在经典测试集上的实验结果表明,提出的算法能更快的求得最优解。     

基于离散差分进化算法的随机车辆路径问题

针对差分进化算法求解组合优化问题存在的局限性,引入计算机语言中的2种按位运算符,对差分进化算法的变异算子进行重新设计,用来求解不确定需求和旅行时间下同时取货和送货的随机车辆路径问题（SVRPSPD）。通过对车辆路径问题的benchmark问题和SVRPSPD问题进行路径优化,并同差分进化算法和遗传算法的计算结果进行比较,验证了离散差分进化算法的性能。结果表明,离散差分进化算法在解决复杂的SVRPSPD问题时,具有较好的优化性能,不仅能得到更好的优化结果,而且具有更快的收敛速度。     

基于改进差分进化算法的运动想象脑机接口频带选择

由于人脑对事件响应频带各不相同,为了准确确定个体最优滤波频带,提出一种多策略变异算子和时变非线性交叉因子差分进化算法对运动想象EEG频带进行处理,采用共空间模式算法提取特征向量,利用线性分类器进行分类识别。使用该方案对BCI competition III-dataset 4a受试者的EEG数据进行了10次5倍交叉分类实验。实验结果表明,该算法稳定性强、耗时少,解决了运动想象BCI特征提取中的最优频带选择问题。     

改进差分进化算法及啤酒灌装机液位控制PID参数整定

目的 针对啤酒液位控制系统存在PID参数整定难、非线性、滞后性问题,提出一种改进基于邻域的改进差分进化算法,应用于PID参数优化整定中,从而提高灌装机的工作效率和啤酒的质量。方法 文中对差分进化算法进行改进,设计一种新型的变异策略,在变异环节引入邻域搜索操作;根据当前种群的分布情况,实时对邻域的个数进行自适应分配,以提升算法全局和局部搜索能力;与2种基本差分进化算法和4种改进差分进化算法对比,用18个测试函数验证文中所提出算法的性能。结果 仿真结果表明,相较于基本差分进化算法,使用改进的差分进化算法整定的PID参数,调节时间减少0.22 s,上升时间减少0.04 s,超调量降低7.63%。结论 通过改进的差分进化算法对啤酒灌装机液位PID参数的优化整定,可以显著改善控制系统的超调量、上升时间和稳态误差等性能,实现了液位的稳定控制。     

进化规划中的变异与收敛

进化规划算法中变异是唯一的操作，因此变异算子对进化规划算法的性能有决定性的影响。文中以高斯变异算子为例，研究了变异算子在进化进程的作用，分析了进化规划算法不收敛的原因以及变异算子与进化代数、收敛精度间的关系。对传统进化规划算法和多群进化规划算法的性能进行了仿真研究，仿真结果表明了分析结果的正确性。     

电力分配系统中的机组组合问题

机组组合问题是在满足多种约束的前提下确定各机组的开关机状态以及开机机组的发电量从而保证发电费用最小的优化问题。广义Benders分解算法(GBD)是一种求解非线性混合整数规划的有效且常见的优化方法。即利用GBD算法求解机组组合问题。     

模糊环境下基于遗传差分协同进化的多阶段投资组合模型

现实经济活动中投资一般是不确定的和随机的,投资者对于风险资产的选择大多情况下是多阶段的。基于该现实因素,在模糊环境下考虑多个摩擦因素,利用交易限制引入资产的基数约束,建立可能性均值–下半方差–熵多阶段投资组合优化模型(V-S-M),该模型是一个多阶段混合整数规划问题。同时,给出了求解该模型的一个遗传差分协同进化算法(GAHDE),并对不同风险态度下的投资组合策略进行了分析,同时将所得数值结果与可能性均值–下半方差模型(V-M)和可能性均值–熵模型(S-M)进行模型对比,与标准的遗传算法和差分进化算法进行了算法对比,结果验证了所建模型和设计算法的优越性与有效性。     

基于混合离散人工蜂群算法的混合零等待柔性流水车间优化研究

从钢铁业等流程工业提炼出一类混合零等待柔性流水车间问题，其中一些加工阶段要求工件连续不断地经过这些工序，对该问题建立了整数规划模型，提出了一种混合离散人工蜂群算法以最小化最大完工时间。采用二维矩阵编码表述染色体以及工件右移调整策略进行解码以获取调度解，改进NEH启发式规则用于生成初始种群。在雇佣蜂阶段，引入了修正粒子群优化算法产生新解；在跟随蜂阶段，设计了迭代贪婪算法中的破坏和构造算子，进一步增强算法的搜索能力；在侦查蜂阶段，利用变邻域搜索算子以替换最差解。对不同规模问题进行了仿真测试并与现有算法进行对比，结果表明所提算法在求解混合零等待柔性流水车间问题方面更加有效。     

基于“两步法”的飞行冲突解脱问题求解策略

本文针对混合整数规划方法求解飞行冲突解脱较慢的问题,提出一种分步求解方法,以此来提升求解效率。该方法在确保解决冲突问题的同时,实现求解效率和解脱成本的优化。具体包括:使用混合整数线性规划方法在角度变量离散化模型中求解得到一个较好的可行解,将此可行解作为非线性模型的初值,再使用非线性规划方法进一步求解。实验结果表明,针对飞行冲突解脱问题,使用混合整数规划和非线性规划的"两步法"求解策略切实可行,实验效果良好。     

混合色彩空间多信息融合的运动目标检测算法

针对传统帧间差分算法存在漏检、空洞和虚假目标等问题,提出一种改进的帧间差分算法。对几种常见色彩空间的运动目标检测效果进行实验对比分析,选取检测效果优良的色彩通道分量构建运动目标检测的混合色彩空间CbVb*。为充分利用帧间信息的相关性,根据CbVb*空间的场景像素变化特性,提出七帧帧间差分算法以获取运动目标的时域帧间差分;采用自适应阈值的Canny算子得到梯度域的运动目标边缘,将时域帧间差分与梯度域目标边缘进行融合,并对融合信息进行腐蚀和膨胀处理得到最终的检测结果。实验结果表明,改进的算法可以更准确地检测出运动目标,并具有较好的鲁棒性、适应性和实时性。     

CO-EVOLUTIONARY HYBRID DIFFERENTIAL EVOLUTION FOR MIXED-INTEGER OPTIMIZATION PROBLEMS

Evolutionary algorithms are promising candidates for obtaining the global optimum. Hybrid differential evolution is one or the evolutionary algorithms, which has been successfully applied to many real-world nonlinear programming problems. This paper proposes a co-evolutionary hybrid differential evolution to solve mixed-integer nonlinear programming (MINLP) problems. The key ingredients of the algorithm consist of an integer-valued variable evolution and a real-valued variable co-evolution, so that the algorithm can be used to solve MINLP problems or pure integer programming problems. Furthermore, the algorithm combines a local search heuristic (called acceleration) and a widespread search heuristic (called migration) to promote the search for a global optimum. Some numerical examples are tested to illustrate the performance of the proposed algorithm. Numerical examples show that the proposed algorithm converges to better solutions than the conventional MINLP optimization methods     

Optimization methods for petroleum fields development and production systems: a review

In this review, we survey the widespread use of numerical optimization or mathematical programming approaches to develop and produce petroleum fields for design and operations; lift gas and rate allocation; and reservoir development, planning, and management. Early applications adopted linear programming alongside heuristics. With continuous advancements in computing speed and algorithms, we have been able to formulate more complex and meaningful models including nonlinear programs and mixed-integer linear and nonlinear programs. Various formulations and solution strategies have been used including continuous and discrete optimization, stochastic programming to handle uncertainty, and metaheuristics such as genetic algorithms to increase solution quality while reducing computational load.     

An Evolutionary Lagrange Method For Mixed-Integer Constrained Optimization Problems

This study proposes a method for solving mixed-integer constrained optimization problems using an evolutionary Lagrange method. In this approach, an augmented Lagrange function is used to transform the mixed-integer constrained optimization problem into an unconstrained min—max problem with decision-variable minimization and Lagrange-multiplier maximization. The mixed-integer hybrid differential evolution (MIHDE) is introduced into the evolutionary min—max algorithm to accomplish the implementation of the evolutionary Lagrange method. MIHDE provides a mixed coding to denote genetic representations of teal and integer variables, and a rounding operation is used to guide the genetic evolution of integer variables. To fulfill global convergence, self-adaptation for penalty parameters is involved in the evolutionary min—max algorithm so that small penalty parameters can be used, not affecting the final search results. Some numerical experiments are tested to evacuate the performance of the proposed method. Numerical experiments demonstrate that the proposed method converges to better solutions than the conventional penalty function method     

Finding multiple optimal solutions of signomial discrete programming problems with free variables

With the increasing reliance on mathematical programming based approaches in various fields, signomial discrete programming (SDP) problems occur frequently in real applications. Since free variables are often introduced to model problems and alternative optima are practical for decision making among multiple strategies, this paper proposes a generalized method to find multiple optimal solutions of SDP problems with free variables. By means of variable substitution and convexification strategies, an SDP problem with free variables is first converted into another convex mixed-integer nonlinear programming problem solvable to obtain an exactly global optimum. Then a general cut is utilized to exclude the previous solution and an algorithm is developed to locate all alternative optimal solutions. Finally, several illustrative examples are presented to demonstrate the effectiveness of the proposed approach.     

Response surface-based robust parameter design optimization with both qualitative and quantitative variables

The response surface-based robust parameter design, with its extensive use of optimization techniques and statistical tools, is known as an effective engineering design methodology for improving production processes, when input variables are quantitative on a continuous scale. In many engineering settings, however, there are situations where both qualitative and quantitative variables are considered. In such situations, traditional response surface designs may not be effective. To rectify this problem, this article lays out a foundation by embedding those input variables into a factorial design with pseudo-centre points. A 0–1 mixed-integer nonlinear programming model is then developed and the solutions found using three optimization tools, namely the outer approximation method, the branch-and-bound technique and the hybrid branch-and-cut algorithm, are compared with traditional counterparts. The numerical example shows that the proposed models result in better robust parameter design solutions than the traditional models.     

A genetic algorithm for optimal unequal-area block layout design

The use of a genetic algorithm (GA) to optimise the binary variables in a mixed-integer linear programming model for the block layout design problem with unequal areas that satisfies area requirements is analysed. The performance of a GA is improved using a local search through the possible binary variables assignment; results encourage the use of this technique to find a set of feasible solutions for the block layout design with more than nine departments.     

An adaptive radial basis algorithm (ARBF) for expensive black-box mixed-integer constrained global optimization

Response surface methods based on kriging and radial basis function (RBF) interpolation have been successfully applied to solve expensive, i.e. computationally costly, global black-box nonconvex optimization problems. In this paper we describe extensions of these methods to handle linear, nonlinear, and integer constraints. In particular, algorithms for standard RBF and the new adaptive RBF (ARBF) are described. Note, however, while the objective function may be expensive, we assume that any nonlinear constraints are either inexpensive or are incorporated into the objective function via penalty terms. Test results are presented on standard test problems, both nonconvex problems with linear and nonlinear constraints, and mixed-integer nonlinear problems (MINLP). Solvers in the TOMLAB Optimization Environment () have been compared, specifically the three deterministic derivative-free solvers rbfSolve, ARBFMIP and EGO with three derivative-based mixed-integer nonlinear solvers, OQNLP, MINLPBB and MISQP, as well as the GENO solver implementing a stochastic genetic algorithm. Results show that the deterministic derivative-free methods compare well with the derivative-based ones, but the stochastic genetic algorithm solver is several orders of magnitude too slow for practical use. When the objective function for the test problems is costly to evaluate, the performance of the ARBF algorithm proves to be superior.     

Application of optimisation techniques in groundwater quantity and quality management

This paper presents the state-of-the-art on application of optimisation techniques in groundwater quality and quantity management. In order to solve optimisation-based groundwater management models, researchers have used various mathematical programming techniques such as linear programming (LP), nonlinear programming (NLP), mixed-integer programming (MIP), optimal control theory-based mathematical programming, differential dynamic programming (DDP), stochastic programming (SP), combinatorial optimisation (CO), and multiple objective programming for multipurpose management. Studies reported in the literature on the application of these methods are reviewed in this paper.     

Extension of the hybrid linear programming method to optimize simultaneously the design and operation of groundwater utilization systems

This article proposes a hybrid linear programming (LP-LP) methodology for the simultaneous optimal design and operation of groundwater utilization systems. The proposed model is an extension of an earlier LP-LP model proposed by the authors for the optimal operation of a set of existing wells. The proposed model can be used to optimally determine the number, configuration and pumping rates of the operational wells out of potential wells with fixed locations to minimize the total cost of utilizing a two-dimensional confined aquifer under steady-state flow conditions. The model is able to take into account the well installation, piping and pump installation costs in addition to the operational costs, including the cost of energy and maintenance. The solution to the problem is defined by well locations and their pumping rates, minimizing the total cost while satisfying a downstream demand, lower/upper bound on the pumping rates, and lower/upper bound on the water level drawdown at the wells. A discretized version of the differential equation governing the flow is first embedded into the model formulation as a set of additional constraints. The resulting mixed-integer highly constrained nonlinear optimization problem is then decomposed into two subproblems with different sets of decision variables, one with a piezometric head and the other with the operational well locations and the corresponding pumping rates. The binary variables representing the well locations are approximated by a continuous variable leading to two LP subproblems. Having started with a random value for all decision variables, the two subproblems are solved iteratively until convergence is achieved. The performance and ability of the proposed method are tested against a hypothetical problem from the literature and the results are presented and compared with those obtained using a mixed-integer nonlinear programming method. The results show the efficiency and effectiveness of the proposed method for solving practical groundwater management problems.     

An integrated location-inventory problem in a closed-loop supply chain with third-party logistics

Third-party logistics (3PL) is a fast growing business. Many large organisations are using 3PL services to reduce operating costs, simplify business processes, and enhance operations and supply chain flexibility. In this paper, we study location-inventory decisions jointly in a closed-loop system with 3PL. First, a model formulation is proposed to develop mixed-integer non-linear programming (MINLP) models for the location-inventory problem under study. Then, a novel heuristics based on differential evolution and the genetic algorithm is designed to solve the MINLP models efficiently. Last, numerical study is presented to illustrate and validate the solution approach.