Do not be afraid of local minima: affine shaker and particle swarm

Stochastic local search techniques are powerful and flexible methods to optimize difficult functions. While each method is characterized by search trajectories produced through a randomized selection of the next step, a notable difference is caused by the interaction of different searchers, as exemplified by the Particle Swarm methods. In this paper we evaluate two extreme approaches, Particle Swarm Optimization, with interaction between the individual "cognitive" component and the "social" knowledge, and Repeated Affine Shaker, without any interaction between searchers but with an aggressive capability of scouting out local minima. The results, unexpected to the authors, show that Affine Shaker provides remarkably efficient and effective results when compared with PSO, while the advantage of Particle Swarm is visible only for functions with a very regular structure of the local minima leading to the global optimum and only for specific experimental conditions

Global Optimization by Differential Evolution and Particle Swarm Methods: Evaluation on Some Benchmark Functions

In this paper we compare the performance of the Differential Evolution (DE) and the Repulsive Particle Swarm (RPS) methods of global optimization. To this end, seventy test functions have been chosen. Among these test functions, some are new while others are well known in the literature; some are unimodal, the others multi-modal; some are small in dimension (no. of variables, x in f(x)), while the others are large in dimension; some are algebraic polynomial equations, while the other are transcendental, etc. FORTRAN programs of DE and RPS have been appended. Among 70 functions, a few have been run for small as well as large dimensions. In total, 73 optimization exercises have been done. DE has succeeded in 63 cases while RPS has succeeded in 55 cases. In almost all cases, DE has converged faster and given much more accurate results. The convergence of RPS is much slower even for lesser stringency on accuracy. Some test functions have been hard for both the methods. These are: Zero-Sum (30D), Perm#1, Perm#2, Power and Bukin functions, Weierstrass, and Michalewicz functions. From what we find, one cannot reach at the definite conclusion that the DE performs better or worse than the RPS. None could assure a supremacy over the other. Each one faltered in some cases; each one succeeded in some others. However, DE is unquestionably faster, more accurate and more frequently successful than the RPS. It may be argued, nevertheless, that alternative choice of adjustable parameters could have yielded better results in either method’s case. The protagonists of either method could suggest that. Our purpose is not to join with the one or the other. We simply want to highlight that in certain cases they both succeed, in certain other case they both fail and each one has some selective preference over some particular type of surfaces. What is needed is to identify such structures and surfaces that suit a particular method most. It is needed that we find out some criteria to classify the problems that suit (or does not suit) a particular method. This classification will highlight the comparative advantages of using a particular method for dealing with a particular class of problems.: Global optimization; Stochastic search; Repulsive particle swarm; Differential Evolution; Clustering algorithm; Simulated annealing; Genetic algorithm; Tabu search; Ant Colony algorithm; Monte Carlo method; Box algorithm; Nelder-Mead; Nonlinear programming; FORTRAN computer program; local optima; Benchmark; test functions

Facility layout problem: Bibliometric and benchmarking analysis

Facility layout problem is related to the location of departments in a facility area, with the aim of determining the most effective configuration. Researches based on different approaches have been published in the last six decades and, to prove the effectiveness of the results obtained, several instances have been developed. This paper presents a general overview on the extant literature on facility layout problems in order to identify the main research trends and propose future research questions. Firstly, in order to give the reader an overview of the literature, a bibliometric analysis is presented. Then, a clusterization of the papers referred to the main instances reported in literature was carried out in order to create a database that can be a useful tool in the benchmarking procedure for researchers that would approach this kind of problems

A hybrid GA–PS–SQP method to solve power system valve-point economic dispatch problems

This study presents a new approach based on a hybrid algorithm consisting of Genetic Algorithm (GA), Pattern Search (PS) and Sequential Quadratic Programming (SQP) techniques to solve the well-known power system Economic dispatch problem (ED). GA is the main optimizer of the algorithm, whereas PS and SQP are used to fine tune the results of GA to increase confidence in the solution. For illustrative purposes, the algorithm has been applied to various test systems to assess its effectiveness. Furthermore, convergence characteristics and robustness of the proposed method have been explored through comparison with results reported in literature. The outcome is very encouraging and suggests that the hybrid GA–PS–SQP algorithm is very efficient in solving power system economic dispatch problem

Tabu Search for the Single Row Facility Layout Problem in FMS using a 3-opt Neighborhood

Since material handling agents in a FMS are most efficient when moving in straight lines, a common layout of machines in a FMS is a single row layout. This allows a floor designer to model the problem of generating an optimal machine layout in a FMS as a single row facility layout problem (SRFLP). Due to the computational complexity involved in solving the SRFLP, researchers have developed several heuristics to solve large instances of the problem. In this paper, we present a tabu search implementation based on a 3-opt neighborhood search scheme. We also present a technique to speed up the exhaustive 3-opt neighborhood search process significantly. Our computational experiments show that speed up of the 3-opt search is effective, and our tabu search implementation is competitive. The results we present here are better than the currently known best layouts for several large sized benchmark SRFLP instances, and competitive for other benchmark instances.

Using nodal coordinates as variables for the dimensional synthesis of mechanisms

The method of the lower deformation energy has been successfully used for the synthesis of mechanisms for quite a while. It has shown to be a versatile, yet powerful method for assisting in the design of mechanisms. Until now, most of the implementations of this method used the dimensions of the mechanism as the synthesis variables, which has some advantages and some drawbacks. For example, the assembly configuration is not taken into account in the optimization process, and this means that the same initial configuration is used when computing the deformed positions in each synthesis point. This translates into a reduction of the total search space. A possible solution to this problem is the use of a set of initial coordinates as variables for the synthesis, which has been successfully applied to other methods. This also has some additional advantages, such as the fact that any generated mechanism can be assembled. Another advantage is that the fixed joint locations are also included in the optimization at no additional cost. But the change from dimensions to initial coordinates means a reformulation of the optimization problem when using derivatives if one wants them to be analytically derived. This paper tackles this reformulation, along with a proper comparison of the use of both alternatives using sequential quadratic programming methods. In order to do so, some examples are developed and studied.The authors wish to thank the Spanish Ministry of Economy and Competitiveness for its support through Grant DPI2013-46329-P and DPI2016-80372-R. Additionally the authors wish to thank the Education Department of the Basque Government for ist support through grant IT947-16