矿物质粉体对砂浆及混凝土Cl-渗透性的影响

研究了不同水胶比、不同矿物质粉体掺量的砂浆和混凝土，经标准养护至56天、90天时的导电量。在相同水胶比和相同矿物质粉体掺量下，混凝土的导电量远低于砂浆的导电量。含矿物质粉体的砂浆及混凝土的导电量均低于基准砂浆及混凝土的导电量。导电量随水胶比的降低而降低，也随龄期的增长而降低。     

A modified version of a T‐Cell Algorithm for constrained optimization problems

In this paper, we present a heuristic inspired on the T‐Cell model of the immune system (i.e. an artificial immune system). The proposed approach (called T‐Cell) is used for solving constrained (numerical) optimization problems, and is validated using several test functions taken from the specialized literature on evolutionary optimization. Additionally, several engineering optimization problems are also used for assessing the performance of the proposed approach. The results are compared with respect to approaches representative of the state‐of‐the‐art in constrained evolutionary optimization. Copyright © 2010 John Wiley & Sons, Ltd.     

A new multi-objective evolutionary algorithm: neighbourhood exploring evolution strategy

This article proposes a new multi-objective evolutionary algorithm, called neighbourhood exploring evolution strategy (NEES). This approach incorporates the idea of neighbourhood exploration together with other techniques commonly used in the multi-objective evolutionary optimization literature (namely, non-dominated sorting and diversity preservation mechanisms). The main idea of the proposed approach was derived from a single-objective evolutionary algorithm, called the line-up competition algorithm (LCA), and it consists of assigning neighbourhoods of different sizes to different solutions. Within each neighbourhood, new solutions are generated using a (1+λ)-ES (evolution strategy). This scheme naturally balances the effect of local search (which is performed by the neighbourhood exploration mechanism) with that of the global search performed by the algorithm, and gradually impels the population to progress towards the true Pareto-optimal front of the problem to explore the extent of that front. Three versions of the proposal are studied: a (1+1)-NEES, a (1+2)-NEES and a (1+4)-NEES. Such approaches are validated on a set of standard test problems reported in the specialized literature. Simulation results indicate that, for continuous numerical optimization problems, the proposal (particularly the (1+1)-NEES) is competitive with respect to NSGA-II, which is an algorithm representative of the state-of-the-art in evolutionary multi-objective optimization. Moreover, all the versions of NEES improve on the results of NSGA-II when dealing with a discrete optimization problem. Although preliminary, such results might indicate a potential application area in which the proposed approach could be particularly useful.     

VIS: An artificial immune network for multi-objective optimization

The aim of this work is to propose and validate a novel multi-objective optimization algorithm based on the emulation of the behaviour of the immune system. The rationale of this work is that the artificial immune system has, in its elementary structure, the main features required by other multi-objective evolutionary algorithms described in the literature, such as diversity preservation, memory, adaptivity, and elitism. The proposed approach is compared with three multi-objective evolutionary algorithms that are representative of the state of the art in multi-objective optimization. Algorithms are tested on six standard problems (both unconstrained and constrained) and comparisons are carried out using three different metrics. Results show that the proposed approach has very good performances and can become a valid alternative to standard algorithms for solving multi-objective optimization problems.     

An efficient approach for reliability-based topology optimization

This article presents an efficient approach for reliability-based topology optimization (RBTO) in which the computational effort involved in solving the RBTO problem is equivalent to that of solving a deterministic topology optimization (DTO) problem. The methodology presented is built upon the bidirectional evolutionary structural optimization (BESO) method used for solving the deterministic optimization problem. The proposed method is suitable for linear elastic problems with independent and normally distributed loads, subjected to deflection and reliability constraints. The linear relationship between the deflection and stiffness matrices along with the principle of superposition are exploited to handle reliability constraints to develop an efficient algorithm for solving RBTO problems. Four example problems with various random variables and single or multiple applied loads are presented to demonstrate the applicability of the proposed approach in solving RBTO problems. The major contribution of this article comes from the improved efficiency of the proposed algorithm when measured in terms of the computational effort involved in the finite element analysis runs required to compute the optimum solution. For the examples presented with a single applied load, it is shown that the CPU time required in computing the optimum solution for the RBTO problem is 15–30% less than the time required to solve the DTO problems. The improved computational efficiency allows for incorporation of reliability considerations in topology optimization without an increase in the computational time needed to solve the DTO problem.     

A TABOO SEARCH BASED APPROACH TO FIND THE PARETO OPTIMAL SET IN MULTIPLE OBJECTIVE OPTIMIZATION

Taboo search is a heuristic optimization technique which works with a neighbourhood of solutions to optimize a given objective function. It is generally applied to single objective optimization problems. Taboo search has the potential for solving multiple objective optimization (MOO) problems, because it works with more than one solution at a time, and this gives it the opportunity to evaluate multiple objective functions simultaneously. In this paper, a taboo search based algorithm is developed to find Pareto optimal solutions in multiple objective optimization problems. The developed algorithm has been tested with a number of problems and compared with other techniques. Results obtained from this work have proved that a taboo search based algorithm can find Pareto optimal solutions in MOO effectively.     

Multi-objective hierarchical genetic algorithms for multilevel redundancy allocation optimization

Multilevel redundancy allocation optimization problems (MRAOPs) occur frequently when attempting to maximize the system reliability of a hierarchical system, and almost all complex engineering systems are hierarchical. Despite their practical significance, limited research has been done concerning the solving of simple MRAOPs. These problems are not only NP hard but also involve hierarchical design variables. Genetic algorithms (GAs) have been applied in solving MRAOPs, since they are computationally efficient in solving such problems, unlike exact methods, but their applications has been confined to single-objective formulation of MRAOPs. This paper proposes a multi-objective formulation of MRAOPs and a methodology for solving such problems. In this methodology, a hierarchical GA framework for multi-objective optimization is proposed by introducing hierarchical genotype encoding for design variables. In addition, we implement the proposed approach by integrating the hierarchical genotype encoding scheme with two popular multi-objective genetic algorithms (MOGAs)—the strength Pareto evolutionary genetic algorithm (SPEA2) and the non-dominated sorting genetic algorithm (NSGA-II). In the provided numerical examples, the proposed multi-objective hierarchical approach is applied to solve two hierarchical MRAOPs, a 4- and a 3-level problems. The proposed method is compared with a single-objective optimization method that uses a hierarchical genetic algorithm (HGA), also applied to solve the 3- and 4-level problems. The results show that a multi-objective hierarchical GA (MOHGA) that includes elitism and mechanism for diversity preserving performed better than a single-objective GA that only uses elitism, when solving large-scale MRAOPs. Additionally, the experimental results show that the proposed method with NSGA-II outperformed the proposed method with SPEA2 in finding useful Pareto optimal solution sets.     

Solving constrained optimization problems with a hybrid particle swarm optimization algorithm

This article presents a particle swarm optimization algorithm for solving general constrained optimization problems. The proposed approach introduces different methods to update the particle's information, as well as the use of a double population and a special shake mechanism designed to avoid premature convergence. It also incorporates a simple constraint-handling technique. Twenty-four constrained optimization problems commonly adopted in the evolutionary optimization literature, as well as some structural optimization problems are adopted to validate the proposed approach. The results obtained by the proposed approach are compared with respect to those generated by algorithms representative of the state of the art in the area.     

A constraint consensus memetic algorithm for solving constrained optimization problems

Constraint handling is an important aspect of evolutionary constrained optimization. Currently, the mechanism used for constraint handling with evolutionary algorithms mainly assists the selection process, but not the actual search process. In this article, first a genetic algorithm is combined with a class of search methods, known as constraint consensus methods, that assist infeasible individuals to move towards the feasible region. This approach is also integrated with a memetic algorithm. The proposed algorithm is tested and analysed by solving two sets of standard benchmark problems, and the results are compared with other state-of-the-art algorithms. The comparisons show that the proposed algorithm outperforms other similar algorithms. The algorithm has also been applied to solve a practical economic load dispatch problem, where it also shows superior performance over other algorithms.     

Two efficient algorithms for constructing almost even approximations of the Pareto front in multi-objective optimization problems

In this article, two algorithms are proposed for constructing almost even approximations of the Pareto front of multi-objective optimization problems. The first algorithm is a hybrid of the ε-constraint and Pascoletti–Serafini scalarization methods for solving bi-objective problems. The second is a modification of the successive Pareto optimization (SPO) algorithm for solving three-objective problems. In these algorithms, the MATLAB fmincon solver is used to solve single-objective optimization problems, which returns a local optimal solution. Some metrics are considered to evaluate the quality of approximations obtained by the suggested algorithms on six test problems, and their results are compared with other algorithms (normal constraint, weighted constraint, SPO, differential evolution, multi-objective evolutionary algorithm/decomposition–differential evolution, non-dominated sorting genetic algorithm-II and S-metric selection evolutionary multi-objective algorithm). Experimental results show that the proposed algorithms provide almost even approximations of the whole Pareto front, and better quality of approximation and CPU time compared with established algorithms.     

A highly accurate differential evolution–particle swarm optimization algorithm for the construction of initial value problem solvers

In this work a new evolutionary computation technique is introduced for the construction of initial value solvers based on Runge–Kutta (RK) pairs. The derivation of RK pairs corresponds to solving a nonlinear optimization problem with a multimodal objective function in a high dimensional search space; additional difficulty stems from the fact that only solutions with accuracy at least equal to machine epsilon are acceptable. The proposed approach involves hybridizing a Differential Evolution (DE) strategy with elements from Particle Swarm Optimization (PSO) in order to produce a method for solving optimization problems with high accuracy. The resulting methodology is applied to two different problems of RK pair derivation of orders 5 and 4 and compared with standard DE techniques. Numerical experiments show that the proposed hybrid DE-PSO satisfies the strict accuracy requirements imposed by the particular problem, while outperforming its rivals.     

Function-transformation methods for multi-objective optimization

It is useful with multi-objective optimization (MOO) to transform the objective functions such that they all have similar units and orders of magnitude. This article evaluates various transformation methods using simple example problems. Viewing these methods as different means to restrict function values sheds light on how the methods perform. The weighted sum approach for MOO is used to study how well different methods aid in depicting the Pareto optimal set. Whereas using unrestricted weights is well suited for providing a single solution that reflects preferences, it is found that using a convex combination of functions is desirable when generating the Pareto set. In addition, it is shown that some transformation methods are detrimental to the process of generating a diverse spread of points, and criteria are proposed for determining when the methods fail to generate an accurate representation of the Pareto set. Advantages of using a simple normalization–modification are demonstrated.     

A new multi-objective particle swarm optimizer using empirical movement and diversified search strategies

Most real-world optimization problems involve the optimization task of more than a single objective function and, therefore, require a great amount of computational effort as the solution procedure is designed to anchor multiple compromised optimal solutions. Abundant multi-objective evolutionary algorithms (MOEAs) for multi-objective optimization have appeared in the literature over the past two decades. In this article, a new proposal by means of particle swarm optimization is addressed for solving multi-objective optimization problems. The proposed algorithm is constructed based on the concept of Pareto dominance, taking both the diversified search and empirical movement strategies into account. The proposed particle swarm MOEA with these two strategies is thus dubbed the empirical-movement diversified-search multi-objective particle swarm optimizer (EMDS-MOPSO). Its performance is assessed in terms of a suite of standard benchmark functions taken from the literature and compared to other four state-of-the-art MOEAs. The computational results demonstrate that the proposed algorithm shows great promise in solving multi-objective optimization problems.     

Trajectory planning for multiple unmanned vehicles under reciprocal constraints

In this article, a special class of trajectory optimization problems is formalized and solved. It involves the optimization of different unmanned vehicle (UMV) trajectories that are coupled through reciprocal constraints. It is shown in the article that searching for a solution to the problem at hand may stipulate not just planning a longer than the shortest possible path for each UMV, but also choosing slower travel speeds in order to co-ordinate between the UMVs. Although it seems that solving the problem possesses merits, it has been only partially treated before. Here it is solved by utilizing an evolutionary approach which involves a new algorithmic feature that allows striving towards the desired optimality. The approach is demonstrated and studied through solving and simulating several trajectory planning problems. It is shown that a wide range of problems might be related to that class of problems.     

Self-regulating and self-evolving particle swarm optimizer

In this article, a novel self-regulating and self-evolving particle swarm optimizer (SSPSO) is proposed. Learning from the idea of direction reversal, self-regulating behaviour is a modified position update rule for particles, according to which the algorithm improves the best position to accelerate convergence in situations where the traditional update rule does not work. Borrowing the idea of mutation from evolutionary computation, self-evolving behaviour acts on the current best particle in the swarm to prevent the algorithm from prematurely converging. The performance of SSPSO and four other improved particle swarm optimizers is numerically evaluated by unimodal, multimodal and rotated multimodal benchmark functions. The effectiveness of SSPSO in solving real-world problems is shown by the magnetic optimization of a Halbach-based permanent magnet machine. The results show that SSPSO has good convergence performance and high reliability, and is well matched to actual problems.     

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     

Distributed evolutionary algorithms with hierarchical evaluation

A distributed evolutionary algorithm is presented that is based on a hierarchy of (fitness or cost function) evaluation passes within each deme and is efficient in solving engineering optimization problems. Starting with non-problem-specific evaluations (using surrogate models or metamodels, trained on previously evaluated individuals) and ending up with high-fidelity problem-specific evaluations, intermediate passes rely on other available lower-fidelity problem-specific evaluations with lower CPU cost per evaluation. The sequential use of evaluation models or metamodels, of different computational cost and modelling accuracy, by screening the generation members to get rid of non-promising individuals, leads to reduced overall computational cost. The distributed scheme is based on loosely coupled demes that exchange regularly their best-so-far individuals. Emphasis is put on the optimal way of coupling distributed and hierarchical search methods. The proposed method is tested on mathematical and compressor cascade airfoil design problems.     

Some heuristic approaches for solving extended geometric programming problems

This article introduces an extension of standard geometric programming (GP) problems, called quasi geometric programming (QGP) problems. The idea behind QGP is very simple, it means that a problem becomes a GP problem when some variables are kept constant. The consideration of this particular kind of nonlinear and possibly non-smooth optimization problem is motivated by the fact that many engineering problems can be formulated, or well approximated, as a QGP problem. However, solving a QGP problem remains a difficult task due to its intrinsic nonconvex nature. This is why this article introduces some simple approaches for easily solving this kind of nonconvex problem. The interesting thing is that the proposed methods do not require the development of a customized solver and work well with any existing solver able to solve conventional GP problems. Some considerations on the robustness issue are also presented. Various optimization problems are considered to illustrate the ability of the proposed methods for solving a QGP problem. Comparison with previously published work is also given.     

An orthogonal design based constrained evolutionary optimization algorithm

Solving constrained optimization problems (COPs) via evolutionary algorithms (EAs) has attracted much attention. In this article, an orthogonal design based constrained optimization evolutionary algorithm (ODCOEA) to tackle COPs is proposed. In principle, ODCOEA belongs to a class of steady state evolutionary algorithms. In the evolutionary process, several individuals are chosen from the population as parents and orthogonal design is applied to pairs of parents to produce a set of representative offspring. Then, after combining the offspring generated by different pairs of parents, non-dominated individuals are chosen. Subsequently, from the parent’s perspective, it is decided whether a non-dominated individual replaces a selected parent. Finally, ODCOEA incorporates an improved BGA mutation operator to facilitate the diversity of the population. The proposed ODCOEA is effectively applied to 12 benchmark test functions. The computational experiments show that ODCOEA not only quickly converges to optimal or near-optimal solutions, but also displays a very high performance compared with another two state-of-the-art techniques.     

Use of multi-objective optimization for digital human posture prediction

With sufficient fidelity, the use of virtual humans can save time, money, and lives through improved product design, process design, and understanding of behaviour. Optimization-based posture prediction is a unique tool, and this article presents a study that advances posture prediction with a multi-objective optimization (MOO) approach. MOO is used to both develop and combine the following human performance measures: joint displacement; musculoskeletal discomfort; and a variation on potential energy. The following MOO methods are studied in the context of human modelling: objective sum; min–max; and global criterion. Using MOO yields realistic results. Of the independent performance measures, discomfort generally provides the most accurate postures. Potential energy, however, is not a significant factor in governing human posture and should be combined with other performance measures. The three MOO methods for combining performance measures yield similar results, but the objective sum provides slightly more realistic postures.