Galactic Swarm Optimization: A new global optimization metaheuristic inspired by galactic motion

This paper proposes a new global optimization metaheuristic called Galactic Swarm Optimization (GSO) inspired by the motion of stars, galaxies and superclusters of galaxies under the influence of gravity. GSO employs multiple cycles of exploration and exploitation phases to strike an optimal trade-off between exploration of new solutions and exploitation of existing solutions. In the explorative phase different subpopulations independently explore the search space and in the exploitative phase the best solutions of different subpopulations are considered as a superswarm and moved towards the best solutions found by the superswarm. In this paper subpopulations as well as the superswarm are updated using the PSO algorithm. However, the GSO approach is quite general and any population based optimization algorithm can be used instead of the PSO algorithm. Statistical test results indicate that the GSO algorithm proposed in this paper significantly outperforms 4 state-of-the-art PSO algorithms and 4 multiswarm PSO algorithms on an overwhelming majority of 15 benchmark optimization problems over 50 independent trials and up to 50 dimensions. Extensive simulation results show that the GSO algorithm proposed in this paper converges faster to a significantly more accurate solution on a wide variety of high dimensional and multimodal benchmark optimization problems.     

Emergent nature inspired algorithms for multi-objective optimization

Many real-world decision-making situations possess both a discrete and combinatorial structure and involve the simultaneous consideration of conflicting objectives. Problems of this kind are in general of large size and contains several objectives to be “optimized”. Although Multiple Objective Optimization is a well-established field of research, one branch, namely nature inspired metaheuristics is currently experienced a tremendous growth. Over the last few years, developments of new methodologies, methods, and techniques to deal with multi-objective large size problems in particular those with a combinatorial structure and the strong improvement on computing technologies (during and after the 80s) made possible to solve very hard problems with the help of inspired nature based metaheuristics.     

Global Simplex Optimization—A simple and efficient metaheuristic for continuous optimization

A new hybrid optimization algorithm is proposed for minimization of continuous multi-modal functions. The algorithm called Global Simplex Optimization (GSO) is a population set based Evolutionary Algorithm (EA) incorporating a special multi-stage, stochastic and weighted version of the reflection operator of the classical simplex method. An optional mutation operator has also been tested and then removed from the structure of the final algorithm in favor of simplicity and because of insignificant effect on performance. The promising performance achieved by GSO is demonstrated by comparisons made to some other state-of-the-art global optimization algorithms over a set of conventional benchmark problems.     

Water wave optimization: A new nature-inspired metaheuristic

Nature-inspired computing has been a hot topic in scientific and engineering fields in recent years. Inspired by the shallow water wave theory, the paper presents a novel metaheuristic method, named water wave optimization (WWO), for global optimization problems. We show how the beautiful phenomena of water waves, such as propagation, refraction, and breaking, can be used to derive effective mechanisms for searching in a high-dimensional solution space. In general, the algorithmic framework of WWO is simple, and easy to implement with a small-size population and only a few control parameters. We have tested WWO on a diverse set of benchmark problems, and applied WWO to a real-world high-speed train scheduling problem in China. The computational results demonstrate that WWO is very competitive with state-of-the-art evolutionary algorithms including invasive weed optimization (IWO), biogeography-based optimization (BBO), bat algorithm (BA), etc. The new metaheuristic is expected to have wide applications in real-world engineering optimization problems.     

改进光学优化算法及其在函数优化中的应用

光学优化算法是一种新型优化算法,源自物理学中的光学原理。针对基本光学优化算法中适应度函数随进化过程恒定不变导致算法搜索能力差、精度低等不足之处,结合遗传算法中自适应度的改进方法,提出一种可随进化代数动态调整的非线性适应度函数,改进了光学优化算法的适应度函数。通过一系列典型的基准函数测试了改进算法的性能,实验结果验证了改进算法的可行性与有效性。     

PSOGSA-Explore: A new hybrid metaheuristic approach for beampattern optimization in collaborative beamforming

A conventional collaborative beamforming (CB) system suffers from high sidelobes due to the random positioning of the nodes. This paper introduces a hybrid metaheuristic optimization algorithm called the Particle Swarm Optimization and Gravitational Search Algorithm-Explore (PSOGSA-E) to suppress the peak sidelobe level (PSL) in CB, by the means of finding the best weight for each node. The proposed algorithm combines the local search ability of the gravitational search algorithm (GSA) with the social thinking skills of the legacy particle swarm optimization (PSO) and allows exploration to avoid premature convergence. The proposed algorithm also simplifies the cost of variable parameter tuning compared to the legacy optimization algorithms. Simulations show that the proposed PSOGSA-E outperforms the conventional, the legacy PSO, GSA and PSOGSA optimized collaborative beamformer by obtaining better results faster, producing up to 100% improvement in PSL reduction when the disk size is small.     

A T-cell algorithm for solving dynamic optimization problems

In this paper, a metaheuristic inspired on the T-Cell model of the immune system (i.e., an artificial immune system) is introduced. The proposed approach (called DTC, for Dynamic T-Cell) is used to solve dynamic optimization problems, and is validated using test problems taken from the specialized literature on dynamic optimization. Results are compared with respect to artificial immune approaches representative of the state-of-the-art in the area. Some statistical analyses are also performed, in order to determine the sensitivity of the proposed approach to its parameters.     

A new algorithm inspired in the behavior of the social-spider for constrained optimization

During the past decade, solving constrained optimization problems with swarm algorithms has received considerable attention among researchers and practitioners. In this paper, a novel swarm algorithm called the Social Spider Optimization (SSO-C) is proposed for solving constrained optimization tasks. The SSO-C algorithm is based on the simulation of cooperative behavior of social-spiders. In the proposed algorithm, individuals emulate a group of spiders which interact to each other based on the biological laws of the cooperative colony. The algorithm considers two different search agents (spiders): males and females. Depending on gender, each individual is conducted by a set of different evolutionary operators which mimic different cooperative behaviors that are typically found in the colony. For constraint handling, the proposed algorithm incorporates the combination of two different paradigms in order to direct the search towards feasible regions of the search space. In particular, it has been added: (1) a penalty function which introduces a tendency term into the original objective function to penalize constraint violations in order to solve a constrained problem as an unconstrained one; (2) a feasibility criterion to bias the generation of new individuals toward feasible regions increasing also their probability of getting better solutions. In order to illustrate the proficiency and robustness of the proposed approach, it is compared to other well-known evolutionary methods. Simulation and comparisons based on several well-studied benchmarks functions and real-world engineering problems demonstrate the effectiveness, efficiency and stability of the proposed method.     

The runner-root algorithm: A metaheuristic for solving unimodal and multimodal optimization problems inspired by runners and roots of plants in nature

This paper proposes a new metaheuristic, the runner-root algorithm (RRA), inspired by the function of runners and roots of some plants in nature. The plants which are propagated through runners look for water resources and minerals by developing runners and roots (as well as root hairs). The first tool helps the plant for search around with random big steps while the second one is appropriate for search around with small steps. Moreover, the plant which is placed at a very good location by chance spreads in a larger area through its longer runners and roots. Similarly, the proposed algorithm is equipped with two tools for exploration: random jumps with big steps, which model the function of runners in nature, and a re-initialization strategy in case of trapping in local optima, which redistributes the computational agents randomly in the domain of problem and models the propagation of plant in a larger area in case of being located in a good position. Exploitation in RRA is performed by the so-called roots and root hairs which respectively apply random large and small changes to the variables of the best computational agent separately (in case of stagnation). Performance of the proposed algorithm is examined by applying it to the standard CEC’ 2005 benchmark problems and then comparing the results with 9 state-of-the-art algorithms using nonparametric methods.     

jMetal: A Java framework for multi-objective optimization

This paper describes jMetal, an object-oriented Java-based framework aimed at the development, experimentation, and study of metaheuristics for solving multi-objective optimization problems. jMetal includes a number of classic and modern state-of-the-art optimizers, a wide set of benchmark problems, and a set of well-known quality indicators to assess the performance of the algorithms. The framework also provides support to carry out full experimental studies, which can be configured and executed by using jMetal’s graphical interface. Other features include the automatic generation of statistical information of the obtained results, and taking advantage of the current availability of multi-core processors to speed-up the running time of the experiments. In this work, we include two case studies to illustrate the use of jMetal in both solving a problem with a metaheuristic and designing and performing an experimental study.     

C-PSA: Constrained Pareto simulated annealing for constrained multi-objective optimization

In recent years, evolutionary algorithms (EAs) have been extensively developed and utilized to solve multi-objective optimization problems. However, some previous studies have shown that for certain problems, an approach which allows for non-greedy or uphill moves (unlike EAs), can be more beneficial. One such approach is simulated annealing (SA). SA is a proven heuristic for solving numerical optimization problems. But owing to its point-to-point nature of search, limited efforts has been made to explore its potential for solving multi-objective problems. The focus of the presented work is to develop a simulated annealing algorithm for constrained multi-objective problems. The performance of the proposed algorithm is reported on a number of difficult constrained benchmark problems. A comparison with other established multi-objective optimization algorithms, such as infeasibility driven evolutionary algorithm (IDEA), Non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective Scatter search II (MOSS-II) has been included to highlight the benefits of the proposed approach.     

A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming

The conventional unconstrained binary quadratic programming (UBQP) problem is known to be a unified modeling and solution framework for many combinatorial optimization problems. This paper extends the single-objective UBQP to the multiobjective case (mUBQP) where multiple objectives are to be optimized simultaneously. We propose a hybrid metaheuristic which combines an elitist evolutionary multiobjective optimization algorithm and a state-of-the-art single-objective tabu search procedure by using an achievement scalarizing function. Finally, we define a formal model to generate mUBQP instances and validate the performance of the proposed approach in obtaining competitive results on large-size mUBQP instances with two and three objectives.     

A new filled function method for unconstrained global optimization

Many real world problems can be modelled as optimization problems. However, the traditional algorithms for these problems often encounter the problem of being trapped in local minima. The filled function method is an effective approach to tackle this kind of problems. However the existing filled functions have the disadvantages of discontinuity, non-differentiability or sensitivity to parameters which limit their efficiency. In this paper, we proposed a new filled function which is continuous and differentiable without any parameter to tune. Compared to discontinuous or non-differentiable filled functions, the continuous and differentiable filled function mainly has three advantages: firstly, it is not easier to produce extra local minima, secondly, more efficient local search algorithms using gradient information can be applied and thirdly, a continuous and differentiable filled function can be optimized more easily. Based on the new proposed filled function, a new algorithm was designed for unconstrained global optimization problems. Numerical experiments were conducted and the results show the proposed algorithm was more efficient.     

Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization

This paper shows that Lyapunov-based state feedback controller synthesis for piecewise-affine (PWA) slab systems can be cast as an optimization problem subject to a set of linear matrix inequalities (LMIs) analytically parameterized by a vector. Furthermore, it is shown that continuity of the control inputs at the switchings can be guaranteed by adding equality constraints to the problem without affecting its parameterization structure. Finally, it is shown that piecewise-affine state feedback controller synthesis for piecewise-affine slab systems to maximize the decay rate of a quadratic control Lyapunov function can be cast as a set of quasi-concave optimization problems analytically parameterized by a vector. Before casting the synthesis in the format presented in this paper, Lyapunov-based piecewise-affine state feedback controller synthesis could only be formulated as a bi-convex optimization program, which is very expensive to solve globally. Thus, the fundamental importance of the contributions of the paper relies on the fact that, for the first time, the piecewise-affine state feedback synthesis problem has been formulated as a convex problem with a parameterized set of LMIs that can be relaxed to a finite set of LMIs and solved efficiently to a point near the global optimum using available software. Furthermore, it is shown for the first time that, in some situations, the global can be exactly found by solving only one concave problem.     

A hybrid steepest descent method for constrained convex optimization

This paper describes a hybrid steepest descent method to decrease over time any given convex cost function while keeping the optimization variables in any given convex set. The method takes advantage of the properties of hybrid systems to avoid the computation of projections or of a dual optimum. The convergence to a global optimum is analyzed using Lyapunov stability arguments. A discretized implementation and simulation results are presented and analyzed. This method is of practical interest to integrate real-time convex optimization into embedded controllers thanks to its implementation as a dynamical system, its simplicity, and its low computation cost.     

A new heuristic approach for non-convex optimization problems

In this work a new optimization method, called the heuristic Kalman algorithm (HKA), is presented. This new algorithm is proposed as an alternative approach for solving continuous, non-convex optimization problems. The principle of HKA is to explicitly consider the optimization problem as a measurement process designed to give an estimate of the optimum. A specific procedure, based on the Kalman estimator, was developed to improve the quality of the estimate obtained through the measurement process. The main advantage of HKA, compared to other metaheuristics, lies in the small number of parameters that need to be set by the user. Further, it is shown that HKA converges almost surely to a near-optimal solution. The efficiency of HKA was evaluated in detail using several non-convex test problems, both in the unconstrained and constrained cases. The results were then compared to those obtained via other metaheuristics. The numerical experiments show that HKA is a promising approach for solving non-convex optimization problems, particularly in terms of computation time and success ratio.     

New Hermite-Hadamard-type inequalities for convex functions (II)

In this paper, we establish some Hermite-Hadamard-type inequalities for convex functions and give several applications for special means. They complete the results from the previous recent paper Tseng et al. (submitted for publication) [11].     

A perturbed particle swarm algorithm for numerical optimization

The canonical particle swarm optimization (PSO) has its own disadvantages, such as the high speed of convergence which often implies a rapid loss of diversity during the optimization process, which inevitably leads to undesirable premature convergence. In order to overcome the disadvantage of PSO, a perturbed particle swarm algorithm (pPSA) is presented based on the new particle updating strategy which is based upon the concept of perturbed global best to deal with the problem of premature convergence and diversity maintenance within the swarm. A linear model and a random model together with the initial max–min model are provided to understand and analyze the uncertainty of perturbed particle updating strategy. pPSA is validated using 12 standard test functions. The preliminary results indicate that pPSO performs much better than PSO both in quality of solutions and robustness and comparable with GCPSO. The experiments confirm us that the perturbed particle updating strategy is an encouraging strategy for stochastic heuristic algorithms and the max–min model is a promising model on the concept of possibility measure.     

A restarted and modified simplex search for unconstrained optimization

In this paper we propose a simple but efficient modification of the well-known Nelder–Mead (NM) simplex search method for unconstrained optimization. Instead of moving all n simplex vertices at once in the direction of the best vertex, our “shrink” step moves them in the same direction but one by one until an improvement is obtained. In addition, for solving non-convex problems, we simply restart the so-modified NM (MNM) method by constructing an initial simplex around the solution obtained in the previous phase. We repeat restarts until there is no improvement in the objective function value. Thus, our restarted modified NM (RMNM) is a descent and deterministic method and may be seen as an extended local search for continuous optimization. In order to improve computational complexity and efficiency, we use the heap data structure for storing and updating simplex vertices. Extensive empirical analysis shows that: our modified method outperforms in average the original version as well as some other recent successful modifications; in solving global optimization problems, it is comparable with the state-of-the-art heuristics.