Evolutionary structural optimisation using an additive algorithm

The evolutionary structural optimisation (ESO) method has been under continuous development since 1992. Traditionally, the method was conceived from the engineering perspective that the topology and shape of structures were naturally conservative for safety reasons and therefore contained an excess of material. To move from the conservative design to a more optimum design would therefore involve the removal of material. Thus the ESO method started from a design space much bigger than the optimum and the final topology or shape emerged by a process of removal of unwanted/inefficient/lowly stresses material. The original algorithms allowed for two forms of evolution. One was there the understressed material could be removed from anywhere in the allowable design space, and with compensation for checker-boarding this produces an optimum topology under the prescribed environments. The second form only allows removal from the surface or parts of the surface (called nibbling in the ESO lexicon); this produces a Min–Max situation where the maximum surface stress is reduced to a minimum. It has been demonstrated that the ESO process produces a surface that is an iso-stress contour thus satisfying the Min–Max optimality criterion. The present paper addresses the opposite evolutionary process whereby the structure evolves from a base which is the minimum structural form required to carry the load regardless of the magnitude of the stress levels. Material is added in the proximity of high stress to ameliorate its effect and hence the final structural form emerges. Only singly connected regions are formed in the present analysis and thus the additive ESO process is the opposite of the nibbling SO, mentioned above, that produces optimum surface shapes. The paper presents a brief background to the current state of structural optimisation research. This is followed by a discussion of the strategies for the additive ESO (AESO) algorithm and two examples are presented.     

Sequential stopping rules for the multistart algorithm in global optimisation

In this paper a sequential stopping rule is developed for the Multistart algorithm. A statistical model for the values of the observed local maxima of an objective function is introduced in the framework of Bayesian non-parametric statistics. A suitablea-priori distribution is proposed which is general enough and which leads to computationally manageable expressions for thea-posteriori distribution. Sequential stopping rules of thek-step look-ahead kind are then explicitly derived, and their numerical effectiveness compared.     

An improved ant colony optimisation heuristic for graph colouring

The focus of this paper is an ant colony optimisation heuristic for the graph colouring problem. We start by showing how a series of improvements enhance the performance of an existing ant colony approach to the problem and then go on to demonstrate that a further strengthening of the construction phase, combined with a tabu search improvement phase, raise the performance to the point where it is able to compete with some of the best-known approaches on a series of benchmark problems.     

Efficient microwave-assisted synthesis of 4-amino-2-benzazepin-3-ones as conformationally restricted dipeptide mimetics

In this paper, we describe the synthesis of conformationally constrained dipeptide mimetic derivatives. Microwave flash heating was used in several synthetic steps providing the opportunity to perform the reactions in dramatically shortened time as well as to increase the obtained yields. The efficiency of the methodology makes it useful in order to prepare other dipeptides containing the 4-amino-tetrahydro-2-benzazepin-3-one motif.     

A superlinearly convergent norm-relaxed SQP method of strongly sub-feasible directions for constrained optimization without strict complementarity

In this paper, a kind of optimization problems with nonlinear inequality constraints is discussed. Combined the ideas of norm-relaxed SQP method and strongly sub-feasible direction method as well as a pivoting operation, a new fast algorithm with arbitrary initial point for the discussed problem is presented. At each iteration of the algorithm, an improved direction is obtained by solving only one direction finding subproblem which possesses small scale and always has an optimal solution, and to avoid the Maratos effect, another correction direction is yielded by a simple explicit formula. Since the line search technique can automatically combine the initialization and optimization processes, after finite iterations, the iteration points always get into the feasible set. The proposed algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Finally, some numerical tests are reported.     

Two phase algorithms for the bi-objective assignment problem

In this paper, we present several algorithms for the bi-objective assignment problem. The algorithms are based on the two phase method, which is a general technique to solve multi-objective combinatorial optimisation (MOCO) problems.     

解非线性约束方程的拉格朗日全局投影方法

基于最优化方法求解约束非线性方程组的一个突出困难是计算 得到的仅是该优化问题的稳定点或局部极小点,而非方程组的解点.由此引出的问题是如何从一个稳定点出发得到一个相对于方程组解更好的点. 该文采用投影型算法,推广了Nazareth-Qi$^{[8,9]}$ 求解无约束非线性方程组的拉格朗日全局算法(Lagrangian Global-LG)于约束方程上; 理论上证明了从优化问题的稳定点出发,投影LG方法可寻找到一个更好的点. 数值试验证明了LG方法的有效性.     

Efficient interval partitioning for constrained global optimization

A new efficient interval partitioning approach to solve constrained global optimization problems is proposed. This involves a new parallel subdivision direction selection method as well as an adaptive tree search. The latter explores nodes (intervals in variable domains) using a restricted hybrid depth-first and best-first branching strategy. This hybrid approach is also used for activating local search to identify feasible stationary points. The new tree search management technique results in improved performance across standard solution and computational indicators when compared to previously proposed techniques. On the other hand, the new parallel subdivision direction selection rule detects infeasible and suboptimal boxes earlier than existing rules, and this contributes to performance by enabling earlier reliable deletion of such subintervals from the search space.     

Coordinated control of distribution supply chains in the presence of fuzzy customer demand

This paper considers a single product inventory control in a Distribution Supply Chain (DSC). The DSC operates in the presence of uncertainty in customer demands. The demands are described by imprecise linguistic expressions that are modelled by discrete fuzzy sets. Inventories at each facility within the DSC are replenished by applying periodic review policies with optimal order up-to-quantities. Fuzzy customer demands imply fuzziness in inventory positions at the end of review intervals and in incurred relevant costs per unit time interval. The determination of the minimum of defuzzified total cost of the DSC is a complex problem which is solved by applying decomposition; the original problem is decomposed into a number of simpler independent optimisation subproblems, where each retailer and the warehouse determine their optimum periodic reviews and order up-to-quantities. An iterative coordination mechanism is proposed for changing the review periods and order up-to-quantities for each retailer and the warehouse in such a way that all parties within the DSC are satisfied with respect to total incurred costs per unit time interval. Coordination is performed by introducing fuzzy constraints on review periods and fuzzy tolerances on retailers and warehouse costs in local optimisation subproblems.