Multi-strategy ensemble evolutionary algorithm for dynamic multi-objective optimization

Dynamic optimization and multi-objective optimization have separately gained increasing attention from the research community during the last decade. However, few studies have been reported on dynamic multi-objective optimization (dMO) and scarce effective dMO methods have been proposed. In this paper, we fulfill these gabs by developing new dMO test problems and new effective dMO algorithm. In the newly designed dMO problems, Pareto-optimal decision values (i.e., Pareto-optimal solutions: POS) or both POS and Pareto-optimal objective values (i.e., Pareto-optimal front: POF) change with time. A new multi-strategy ensemble multi-objective evolutionary algorithm (MS-MOEA) is proposed to tackle the challenges of dMO. In MS-MOEA, the convergence speed is accelerated by the new offspring creating mechanism powered by adaptive genetic and differential operators (GDM); a Gaussian mutation operator is employed to cope with premature convergence; a memory like strategy is proposed to achieve better starting population when a change takes place. In order to show the advantages of the proposed algorithm, we experimentally compare MS-MOEA with several algorithms equipped with traditional restart strategy. It is suggested that such a multi-strategy ensemble approach is promising for dealing with dMO problems.     

Shape functional optimization with restrictions boosted with machine learning techniques

Shape optimization is a widely used technique in the design phase of a product. Current ongoing improvement policies require a product to fulfill a series of conditions from the perspective of mechanical resistance, fatigue, natural frequency, impact resistance, etc. All these conditions are translated into equality or inequality restrictions which must be satisfied during the optimization process that is necessary in order to determine the optimal shape. This article describes a new method for shape optimization that considers any regular shape as a possible shape, thereby improving on traditional methods limited to straight profiles or profiles established a priori. Our focus is based on using functional techniques and this approach is, based on representing the shape of the object by means of functions belonging to a finite-dimension functional space. In order to resolve this problem, the article proposes an optimization method that uses machine learning techniques for functional data in order to represent the perimeter of the set of feasible functions and to speed up the process of evaluating the restrictions in each iteration of the algorithm. The results demonstrate that the functional approach produces better results in the shape optimization process and that speeding up the algorithm using machine learning techniques ensures that this approach does not negatively affect design process response times.     

New approaches to multi-objective optimization

A natural way to deal with multiple, partially conflicting objectives is turning all the objectives but one into budget constraints. Many classical optimization problems, such as maximum spanning tree and forest, shortest path, maximum weight (perfect) matching, maximum weight independent set (basis) in a matroid or in the intersection of two matroids, become NP-hard even with one budget constraint. Still, for most of these problems efficient deterministic and randomized approximation schemes are known. Not much is known however about the case of two or more budgets: filling this gap, at least partially, is the main goal of this paper. In more detail, we obtain the following main results: Using iterative rounding for the first time in multi-objective optimization, we obtain multi-criteria PTASs (which slightly violate the budget constraints) for spanning tree, matroid basis, and bipartite matching with \(k=O(1)\) budget constraints. We present a simple mechanism to transform multi-criteria approximation schemes into pure approximation schemes for problems whose feasible solutions define an independence system. This gives improved algorithms for several problems. In particular, this mechanism can be applied to the above bipartite matching algorithm, hence obtaining a pure PTAS. We show that points in low-dimensional faces of any matroid polytope are almost integral, an interesting result on its own. This gives a deterministic approximation scheme for \(k\) -budgeted matroid independent set. We present a deterministic approximation scheme for \(k\) -budgeted matching (in general graphs), where \(k=O(1)\) . Interestingly, to show that our procedure works, we rely on a non-constructive result by Stromquist and Woodall, which is based on the Ham Sandwich Theorem.     

Branch-and-bound approaches to standard quadratic optimization problems

This paper explores several possibilities for applying branch-and-bound techniques to a central problem class in quadratic programming, the so-called Standard Quadratic Problems (StQPs), which consist of finding a (global) minimizer of a quadratic form over the standard simplex. Since a crucial part of the procedures is based on efficient local optimization, different procedures to obtain local solutions are discussed, and a new class of ascent directions is proposed, for which a convergence result is established. Main emphasis is laid upon a d.c.-based branch-and-bound algorithm, and various strategies for obtaining an efficient d.c. decomposition are discussed.     

Convex optimization approaches to maximally predictable portfolio selection

In this article we propose a simple heuristic algorithm for approaching the maximally predictable portfolio, which is constructed so that return model of the resulting portfolio would attain the largest goodness-of-fit. It is obtained by solving a fractional program in which a ratio of two convex quadratic functions is maximized, and the number of variables associated with its nonconcavity has been a bottleneck in spite of continuing endeavour for its global optimization. The proposed algorithm can be implemented by simply solving a series of convex quadratic programs, and computational results show that it yields within a few seconds a (near) Karush–Kuhn–Tucker solution to each of the instances which were solved via a global optimization method in [H. Konno, Y. Takaya and R. Yamamoto, A maximal predictability portfolio using dynamic factor selection strategy, Int. J. Theor. Appl. Fin. 13 (2010) pp. 355–366]. In order to confirm the solution accuracy, we also pose a semidefinite programming relaxation approach, which succeeds in ensuring a near global optimality of the proposed approach. Our findings through computational experiments encourage us not to employ the global optimization approach, but to employ the local search algorithm for solving the fractional program of much larger size.     

Fuzzy approaches for multiple objective linear fractional optimization

The problem of finding a solution to a multiple objective linear fractional program arises in several real world situations.In this paper we advocate that fuzzy sets theory provides a basis for solving this problem with sufficient consistency and rigorousness.After representing imprecise aspirations of the decision maker by structured linguistic variables or converting the original problem via approximations or change of variables into a multiple objective linear program, techniques of fuzzy linear programming may be used to reach a satisfactory solution.It is shown that under reasonable restrictions, this solution is efficient (Pareto optimal) for the original problem. Numerical examples are also included for illustration.     

A new chaos optimization algorithm based on symmetrization and levelling approaches for global optimization

Chaos optimization algorithm is a recently developed method for global optimization based on chaos theory. It has many good features such as easy implementation, short execution time and robust mechanisms for escaping from local minima compared with existing stochastic searching algorithms. In the present paper, we propose a new chaos optimization algorithm (COA) approach called SLC (symmetric levelled chaos) based on new strategies including symmetrization and levelling: the proposed SLC method is, to our knowledge, the first chaos approach that can efficiently and successfully operates in higher-dimensional spaces. The proposed method is tested on a number of benchmark functions, and its performance comparisons are provided against previous COAs. The experiment results show that the proposed method has a marked improvement in performance over the classical COA approaches. Moreover, among all COA approaches, SLC is the only one to work efficiently in higher-dimensional spaces.     

Performance analysis of distributed solution approaches in simulation-based optimization

Applying computationally expensive simulations in design or process optimization results in long-running solution processes even when using a state-of-the-art distributed algorithm and hardware. Within these simulation-based optimization problems the optimizer has to treat the simulation systems as black-boxes. The distributed solution of this kind of optimization problem demands efficient utilization of resources (i.e. processors) and evaluation of the solution quality. Analyzing the parallel performance is therefore an important task in the development of adequate distributed approaches taking into account the numerical algorithm, its implementation, and the used hardware architecture. In this paper, simulation-based optimization problems are characterized and a distributed solution algorithm is presented. Different performance analysis techniques (e.g. scalability analysis, computational complexity) are discussed and a new approach integrating parallel performance and solution quality is developed. This approach combines a priori and a posteriori techniques and can be applied in early stages of the solution process. The feasibility of the approach is demonstrated by applying it to three different classes of simulation-based optimization problems from groundwater management.     

High-resolution boosted deconvolution of spectroscopic data

The quality of the analysis of spectrometric data consists in correct identification of the existence of peaks and subsequently in good estimation of their positions. In this paper we present high-resolution deconvolution algorithms. We propose an improvement in the efficiency by introducing a boosting operation into the deconvolution process.     

DC programming approaches for discrete portfolio optimization under concave transaction costs

The paper investigates DC programming and DCA for both modeling discrete portfolio optimization under concave transaction costs as DC programs, and their solution. DC reformulations are established by using penalty techniques in DC programming. A suitable global optimization branch and bound technique is also developed where a DC relaxation technique is used for lower bounding. Numerical simulations are reported that show the efficiency of DCA and the globality of its computed solutions, compared to standard algorithms for nonconvex nonlinear integer programs.     

Heuristic and optimization approaches to extending the Kohonen self organizing algorithm

The Kohonen self organizing neural network has been applied to an increasingly wider range of application problems that traditionally have been the domain of statistical and operational research techniques, such as data clustering and classification, and optimization and control. This Kohonen network is bestowed with a number of unique strengths which are, unfortunately, matched by an equally formidable set of limitations due its learning algorithm. There have been extensive studies over the last decade to extend the Kohonen neural network using heuristic and optimization approaches. This paper provides a comprehensive survey of the research efforts directed to enhancing the Kohonen self organizing neural network and its learning algorithm. We also point out some research directions for pursuing further improvements.     

一种求解TSP问题的多策略改进蚁群算法

蚁群算法是一种求解复杂组合优化问题的启发式仿生进化算法,并是求解TSP问题行之有效的一种随机算法.但此算法仍存在求解精度低、易陷入局部最优及求解效率低的问题,针对该问题提出一种多策略改进蚁群算法.采用最近邻法影响初始信息素的分布,达到降低算法初期较短路径上信息素浓度的目的,并在转移规则变异调整的基础上,结合路径的均值交叉进化策略,增强算法探索全局解空间和避免陷入局部最优的能力.然后,结合迭代和精英策略对信息素更新机制进行改进,进一步提高化算法的求解性能及求解效率,最后,对从TSPLIB数据库选出的8个实例进行求解并与其他算法进行对比,实验结果表明,改进算法在求解旅行商问题时的高效性,且具有较高的运算性能.     

一种多策略引导的电磁场优化算法求解作业车间调度问题

电磁场优化算法是目前一种比较新颖的群智能优化算法,其利用不同极性电磁场所产生的引斥力,使电磁粒子朝最优解移动。针对标准电磁场优化算法在求解作业车间调度问题时容易陷入局部极值点、收敛精度差等问题,提出了一种多策略引导的电磁场优化算法。算法中粒子受到三种不同来源的引斥力,在迭代过程中通过计算每种移动策略的临代电差、累计电差和综合电差来决定粒子的引导方式,并通过概率变异算法来避免陷入局部最优解。通过作业车间调度问题FT、LA系列测试实例仿真实验,对新算法与其他算法的测试结果进行比较分析,研究表明该算法具有更高的求解精度和更快的计算速度。     

A survey on the global optimization problem: General theory and computational approaches

Several different approaches have been suggested for the numerical solution of the global optimization problem: space covering methods, trajectory methods, random sampling, random search and methods based on a stochastic model of the objective function are considered in this paper and their relative computational effectiveness is discussed. A closer analysis is performed of random sampling methods along with cluster analysis of sampled data and of Bayesian nonparametric stopping rules.     

The prize collecting Steiner tree problem: models and Lagrangian dual optimization approaches

We propose a generalized version of the Prize Collecting Steiner Tree Problem (PCSTP), which offers a fundamental unifying model for several well-known -hard tree optimization problems. The PCSTP also arises naturally in a variety of network design applications including cable television and local access networks. We reformulate the PCSTP as a minimum spanning tree problem with additional packing and knapsack constraints and we explore various nondifferentiable optimization algorithms for solving its Lagrangian dual. We report computational results for nine variants of deflected subgradient strategies, the volume algorithm (VA), and the variable target value method used in conjunction with the VA and with a generalized Polyak–Kelley cutting plane technique. The performance of these approaches is also compared with an exact stabilized constraint generation procedure.     

Decomposition based and branch and bound global optimization approaches for the phase equilibrium problem

An increasingly popular approach when solving the phase and chemical equilibrium problem is to pose it as an optimization problem. However, difficulties are encountered due to the highly nonlinear nature of the models used to represent the behavior of the fluids, and because of the existence of multiple local solutions. This work shows how it is possible to guarantee -global solutions for a certain important class of the phase and chemical equilibrium problem, namely when the liquid phase can be modeled using neither the Non-Random Two-Liquid (NRTL) equation, or the UNIversal QUAsi Chemical (UNIQUAC) equation. Ideal vapor phases are easily incorporated into the global optimization framework. A numberof interesting properties are described which drastically alter the structure of the respective problems. For the NRTL equation, it is shown that the formulation can be converted into a biconvex optimization problem. The GOP algorithm of Floudas and Visweswaran [8, 9] can then be used to obtain -global solutions in this case. For the UNIQUAC equation, the new properties show how the objective function can be transformed into the difference of two convex functions (i.e. a D.C. programming problem is obtained), where the concave portion is separable. A branch and bound algorithm based on that of Falk and Soland [6] is used to guarantee convergence to an -global solution. Examples are presented which demonstrate the performance of both algorithms.     

Neighborhood search approaches to non-coplanar beam orientation optimization for total marrow irradiation using IMRT

We consider the beam orientation optimization (BOO) problem for total marrow irradiation (TMI) treatment planning using intensity modulated radiation therapy (IMRT). Currently, IMRT is not widely used in TMI treatment delivery; furthermore, the effect of using non-coplanar beam orientations is not known. We propose and implement several variations of a single neighborhood search algorithm that solves the BOO problem effectively when gantry angles and couch translations are considered. Our work shows that the BOO problem for TMI cases can be solved in a clinically acceptable amount of time and leads to treatment plans that are more effective than the conventional approach to TMI.     

Neighborhood search approaches to beam orientation optimization in intensity modulated radiation therapy treatment planning

The intensity modulated radiation therapy (IMRT) treatment planning problem consists of several subproblems which are typically solved sequentially. We seek to combine two of the subproblems: the beam orientation optimization (BOO) problem and the fluence map optimization (FMO) problem. The BOO problem is the problem of selecting the beam orientations to deliver radiation to the patient. The FMO problem is the problem of determining the amount of radiation intensity, or fluence, of each beamlet in each beam. The solution to the FMO problem measures the quality of a beam set, but the majority of previous BOO studies rely on heuristics and approximations to gauge the quality of the beam set. In contrast with these studies, we use an exact measure of the treatment plan quality attainable using a given beam set, which ensures convergence to a global optimum in the case of our simulated annealing algorithm and a local optimum in the case of our local search algorithm. We have also developed a new neighborhood structure that allows for faster convergence using our simulated annealing and local search algorithms, thus reducing the amount of time required to obtain a good solution. Finally, we show empirically that we can generate clinically acceptable treatment plans that require fewer beams than in current practice. This may reduce the length of treatment time, which is an important clinical consideration in IMRT.     

Electricity swing option pricing by stochastic bilevel optimization: A survey and new approaches

We demonstrate how the problem of determining the ask price for electricity swing options can be considered as a stochastic bilevel program with asymmetric information. Unlike as for financial options, there is no way for basing the pricing method on no-arbitrage arguments. Two main situations are analyzed: if the seller has strong market power he/she might be able to maximize his/her utility, while in fully competitive situations he/she will just look for a price which makes profit and has acceptable risk. In both cases the seller has to consider the decision problem of a potential buyer – the valuation problem of determining a fair value for a specific option contract – and anticipate the buyer’s optimal reaction to any proposed strike price. We also discuss some methods for finding numerical solutions of stochastic bilevel problems with a special emphasis on using duality gap penalizations.