The role of crossover operator in the genetic optimization of magnetic models

The Ising model, introduced almost 100 years ago by Wilhelm Lenz and Ernst Ising, is the formalism still popular as a tool to describe magnetic properties of a wide class of materials. Among many issues which arise when using this model there exist problems related to the process of finding minimum energy of the system. Since these problems are NP-hard, optimizations can either be performed for some approximated cases or be the subject of global optimization techniques. In this paper we present an analysis of the effect of different crossover operators on the efficiency of genetic algorithm used to minimize energy in the Ising model. Although it is not a benchmark tool, we hope it may be interesting as a testing tool.     

Quantum-inspired space search algorithm (QSSA) for global numerical optimization

This work presents the evolutionary quantum-inspired space search algorithm (QSSA) for solving numerical optimization problems. In the proposed algorithm, the feasible solution space is decomposed into regions in terms of quantum representation. As the search progresses from one generation to the next, the quantum bits evolve gradually to increase the probability of selecting the regions that render good fitness values. Through the inherent probabilistic mechanism, the QSSA initially behaves as a global search algorithm and gradually evolves into a local search algorithm, yielding a good balance between exploration and exploitation. To prevent a premature convergence and to speed up the overall search speed, an overlapping strategy is also proposed. The QSSA is applied to a series of numerical optimization problems. The experiments show that the results obtained by the QSSA are quite competitive compared to those obtained using state-of-the-art IPOP-CMA-ES and QEA.     

A new hybrid method for solving global optimization problem

In this paper we present a new hybrid method, called the SASP method. The purpose of this method is the hybridization of the simulated annealing (SA) with the descent method, where we estimate the gradient using simultaneous perturbation. Firstly, the new hybrid method finds a local minimum using the descent method, then SA is executed in order to escape from the currently discovered local minimum to a better one, from which the descent method restarts a new local search, and so on until convergence.The new hybrid method can be widely applied to a class of global optimization problems for continuous functions with constraints. Experiments on 30 benchmark functions, including high dimensional functions, show that the new method is able to find near optimal solutions efficiently. In addition, its performance as a viable optimization method is demonstrated by comparing it with other existing algorithms. Numerical results improve the robustness and efficiency of the method presented.     

Complexity analysis of an assignment problem with controllable assignment costs and its applications in scheduling

We extend the classical linear assignment problem to the case where the cost of assigning agent j to task i is a multiplication of task i’s cost parameter by a cost function of agent j. The cost function of agent j is a linear function of the amount of resource allocated to the agent. A solution for our assignment problem is defined by the assignment of agents to tasks and by a resource allocation to each agent. The quality of a solution is measured by two criteria. The first criterion is the total assignment cost and the second is the total weighted resource consumption. We address these criteria via four different problem variations. We prove that our assignment problem is NP-hard for three of the four variations, even if all the resource consumption weights are equal. However, and somewhat surprisingly, we find that the fourth variation is solvable in polynomial time. In addition, we find that our assignment problem is equivalent to a large set of important scheduling problems whose complexity has been an open question until now, for three of the four variations.     

MB-GNG: Addressing drawbacks in multi-objective optimization estimation of distribution algorithms

We examine the model-building issue related to multi-objective estimation of distribution algorithms (MOEDAs) and show that some of their, as yet overlooked, characteristics render most current MOEDAs unviable when addressing optimization problems with many objectives. We propose a novel model-building growing neural gas (MB-GNG) network that is specially devised for properly dealing with that issue and therefore yields a better performance. Experiments are conducted in order to show from an empirical point of view the advantages of the new algorithm.     

Shape and topology optimization for elliptic boundary value problems using a piecewise constant level set method

The aim of this paper is to propose a variational piecewise constant level set method for solving elliptic shape and topology optimization problems. The original model is approximated by a two-phase optimal shape design problem by the ersatz material approach. Under the piecewise constant level set framework, we first reformulate the two-phase design problem to be a new constrained optimization problem with respect to the piecewise constant level set function. Then we solve it by the projection Lagrangian method. A gradient-type iterative algorithm is presented. Comparisons between our numerical results and those obtained by level set approaches show the effectiveness, accuracy and efficiency of our algorithm.     

A hybrid trust region algorithm for unconstrained optimization

This paper presents a hybrid trust region algorithm for unconstrained optimization problems. It can be regarded as a combination of ODE-based methods, line search and trust region techniques. A feature of the proposed method is that at each iteration, a system of linear equations is solved only once to obtain a trial step. Further, when the trial step is not accepted, the method performs an inexact line search along it instead of resolving a new linear system. Under reasonable assumptions, the algorithm is proven to be globally and superlinearly convergent. Numerical results are also reported that show the efficiency of this proposed method.     

关于良定问题

本文应用有限理性模型M,对非线性问题的良定性进行了统一的研究,对最优化、多目标最优化、非合作博弈和广义博弈得到了一些新的良定性结果.     

The rotational dimension of a graph

Given a connected graph G = (N, E) with node weights s∈? and nonnegative edge lengths, we study the following embedding problem related to an eigenvalue optimization problem over the second smallest eigenvalue of the (scaled) Laplacian of G: Find v_i∈?^|N|, i∈N so that distances between adjacent nodes do not exceed prescribed edge lengths, the weighted barycenter of all points is at the origin, and is maximized. In the case of a two‐dimensional optimal solution this corresponds to the equilibrium position of a quickly rotating net consisting of weighted mass points that are linked by massless cables of given lengths. We define the rotational dimension of G to be the minimal dimension k so that for all choices of lengths and weights an optimal solution can be found in ?^k and show that this is a minor monotone graph parameter. We give forbidden minor characterizations up to rotational dimension 2 and prove that the rotational dimension is always bounded above by the tree‐width of G plus one. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:283‐302, 2011