Multi-Guide Particle Swarm Optimization for Large-Scale Multi-Objective Optimization Problems

Multi-guide particle swarm optimization (MGPSO) is a novel metaheuristic for multi-objective optimization based on particle swarm optimization (PSO). MGPSO has been shown to be competitive when compared with other state-of-the-art multi-objective optimization algorithms for low-dimensional problems. However, to the best of the author’s knowledge, the suitability of MGPSO for high-dimensional multi-objective optimization problems has not been studied. One goal of this thesis is to provide a scalability study of MGPSO in order to evaluate its efficacy for high-dimensional multi-objective optimization problems. It is observed that while MGPSO has comparable performance to state-of-the-art multi-objective optimization algorithms, it experiences a performance drop with the increase in the problem dimensionality. Therefore, a main contribution of this work is a new scalable MGPSO-based algorithm, termed cooperative co-evolutionary multi-guide particle swarm optimization (CCMGPSO), that incorporates ideas from cooperative PSOs. A detailed empirical study on well-known benchmark problems comparing the proposed improved approach with various state-of-the-art multi-objective optimization algorithms is done. Results show that the proposed CCMGPSO is highly competitive for high-dimensional problems

A Black-Box Discrete Optimization Benchmarking (BB-DOB) Pipeline Survey: Taxonomy, Evaluation, and Ranking

This paper provides a taxonomical identification survey of classes in discrete optimization challenges that can be found in the literature including a proposed pipeline for benchmarking, inspired by previous computational optimization competitions. Thereby, a Black-Box Discrete Optimization Benchmarking (BB-DOB) perspective is presented for the BB-DOB@GECCO Workshop. It is motivated why certain classes together with their properties (like deception and separability or toy problem label) should be included in the perspective. Moreover, guidelines on how to select significant instances within these classes, the design of experiments setup, performance measures, and presentation methods and formats are discussed.authorsversio

Balancing the trade-off between cost and reliability for wireless sensor networks: a multi-objective optimized deployment method

The deployment of the sensor nodes (SNs) always plays a decisive role in the system performance of wireless sensor networks (WSNs). In this work, we propose an optimal deployment method for practical heterogeneous WSNs which gives a deep insight into the trade-off between the reliability and deployment cost. Specifically, this work aims to provide the optimal deployment of SNs to maximize the coverage degree and connection degree, and meanwhile minimize the overall deployment cost. In addition, this work fully considers the heterogeneity of SNs (i.e. differentiated sensing range and deployment cost) and three-dimensional (3-D) deployment scenarios. This is a multi-objective optimization problem, non-convex, multimodal and NP-hard. To solve it, we develop a novel swarm-based multi-objective optimization algorithm, known as the competitive multi-objective marine predators algorithm (CMOMPA) whose performance is verified by comprehensive comparative experiments with ten other stateof-the-art multi-objective optimization algorithms. The computational results demonstrate that CMOMPA is superior to others in terms of convergence and accuracy and shows excellent performance on multimodal multiobjective optimization problems. Sufficient simulations are also conducted to evaluate the effectiveness of the CMOMPA based optimal SNs deployment method. The results show that the optimized deployment can balance the trade-off among deployment cost, sensing reliability and network reliability. The source code is available on https://github.com/iNet-WZU/CMOMPA.Comment: 25 page

A population-based optimization method using Newton fractal

Department of Mathematical SciencesMetaheuristic is a general procedure to draw an agreement in a group based on the decision making of each individual beyond heuristic. For last decade, there have been many attempts to develop metaheuristic methods based on swarm intelligence to solve global optimization such as particle swarm optimizer, ant colony optimizer, firefly optimizer. These methods are mostly stochastic and independent on specific problems. Since metaheuristic methods based on swarm intelligence require no central coordination (or minimal, if any), they are especially well-applicable to those problems which have distributed or parallel structures. Each individual follows few simple rules, keeping the searching cost at a decent level. Despite its simplicity, the methods often yield a fast approximation in good precision, compared to conventional methods. Exploration and exploitation are two important features that we need to consider to find a global optimum in a high dimensional domain, especially when prior information is not given. Exploration is to investigate the unknown space without using the information from history to find undiscovered optimum. Exploitation is to trace the neighborhood of the current best to improve it using the information from history. Because these two concepts are at opposite ends of spectrum, the tradeoff significantly affects the performance at the limited cost of search. In this work, we develop a chaos-based metaheuristic method, ???Newton Particle Optimization(NPO)???, to solve global optimization problems. The method is based on the Newton method which is a well-established mathematical root-finding procedure. It actively utilizes the chaotic nature of the Newton method to place a proper balance between exploration and exploitation. While most current population-based methods adopt stochastic effects to maximize exploration, they often suffer from weak exploitation. In addition, stochastic methods generally show poor reproducing ability and premature convergence. It has been argued that an alternative approach using chaos may mitigate such disadvantages. The unpredictability of chaos is correspondent with the randomness of stochastic methods. Chaos-based methods are deterministic and therefore easy to reproduce the results with less memory. It has been shown that chaos avoids local optimum better than stochastic methods and buffers the premature convergence issue. Newton method is deterministic but shows chaotic movements near the roots. It is such complexity that enables the particles to search the space for global optimization. We initialize the particle???s position randomly at first and choose the ???leading particles??? to attract other particles near them. We can make a polynomial function whose roots are those leading particles, called ???a guiding function???. Then we update the positions of particles using the guiding function by Newton method. Since the roots are not updated by Newton method, the leading particles survive after update. For diverse movements of particles, we use modified newton method, which has a coefficient $m$ in the variation of movements for each particle. Efficiency in local search is closely related to the value of m which determines the convergence rate of the Newton method. We can control the balance between exploration and exploitation by choice of leading particles. It is interesting that selection of excellent particles as leading particles not always results in the best result. Including mediocre particles in the roots of guiding function maintains the diversity of particles in position. Though diversity seems to be inefficient at first, those particles contribute to the exploration for global search finally. We study the conditions for the convergence of NPO. NPO enjoys the well-established analysis of the Newton method. This contrasts with other ???nature-inspired??? algorithms which have often been criticized for lack of rigorous mathematical ground. We compare the results of NPO with those of two popular metaheuristic methods, particle swarm optimizer(PSO) and firefly optimizer(FO). Though it has been shown that there are no such algorithms superior to all problems by no free lunch theorem, that is why the researchers are concerned about adaptable global optimizer for specific problems. NPO shows good performance to CEC 2013 competition test problems comparing to PSO and FO.ope

Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control

Constrained optimization of high-dimensional numerical problems plays an important role in many scientific and industrial applications. Function evaluations in many industrial applications are severely limited and no analytical information about objective function and constraint functions is available. For such expensive black-box optimization tasks, the constraint optimization algorithm COBRA was proposed, making use of RBF surrogate modeling for both the objective and the constraint functions. COBRA has shown remarkable success in solving reliably complex benchmark problems in less than 500 function evaluations. Unfortunately, COBRA requires careful adjustment of parameters in order to do so. In this work we present a new self-adjusting algorithm SACOBRA, which is based on COBRA and capable to achieve high-quality results with very few function evaluations and no parameter tuning. It is shown with the help of performance profiles on a set of benchmark problems (G-problems, MOPTA08) that SACOBRA consistently outperforms any COBRA algorithm with fixed parameter setting. We analyze the importance of the several new elements in SACOBRA and find that each element of SACOBRA plays a role to boost up the overall optimization performance. We discuss the reasons behind and get in this way a better understanding of high-quality RBF surrogate modeling

Metaheuristic Optimization of Power and Energy Systems: Underlying Principles and Main Issues of the `Rush to Heuristics'

In the power and energy systems area, a progressive increase of literature contributions that contain applications of metaheuristic algorithms is occurring. In many cases, these applications are merely aimed at proposing the testing of an existing metaheuristic algorithm on a specific problem, claiming that the proposed method is better than other methods that are based on weak comparisons. This ‘rush to heuristics’ does not happen in the evolutionary computation domain, where the rules for setting up rigorous comparisons are stricter but are typical of the domains of application of the metaheuristics. This paper considers the applications to power and energy systems and aims at providing a comprehensive view of the main issues that concern the use of metaheuristics for global optimization problems. A set of underlying principles that characterize the metaheuristic algorithms is presented. The customization of metaheuristic algorithms to fit the constraints of specific problems is discussed. Some weaknesses and pitfalls that are found in literature contributions are identified, and specific guidelines are provided regarding how to prepare sound contributions on the application of metaheuristic algorithms to specific problems

Ranking and significance of variable-length similarity-based time series motifs

The detection of very similar patterns in a time series, commonly called motifs, has received continuous and increasing attention from diverse scientific communities. In particular, recent approaches for discovering similar motifs of different lengths have been proposed. In this work, we show that such variable-length similarity-based motifs cannot be directly compared, and hence ranked, by their normalized dissimilarities. Specifically, we find that length-normalized motif dissimilarities still have intrinsic dependencies on the motif length, and that lowest dissimilarities are particularly affected by this dependency. Moreover, we find that such dependencies are generally non-linear and change with the considered data set and dissimilarity measure. Based on these findings, we propose a solution to rank those motifs and measure their significance. This solution relies on a compact but accurate model of the dissimilarity space, using a beta distribution with three parameters that depend on the motif length in a non-linear way. We believe the incomparability of variable-length dissimilarities could go beyond the field of time series, and that similar modeling strategies as the one used here could be of help in a more broad context.Comment: 20 pages, 10 figure

Niching grey wolf optimizer for multimodal optimization problems

Metaheuristic algorithms are widely used for optimization in both research and the industrial community for simplicity, flexibility, and robustness. However, multi-modal optimization is a difficult task, even for metaheuristic algorithms. Two important issues that need to be handled for solving multi-modal problems are (a) to categorize multiple local/global optima and (b) to uphold these optima till the ending. Besides, a robust local search ability is also a prerequisite to reach the exact global optima. Grey Wolf Optimizer (GWO) is a recently developed nature-inspired metaheuristic algorithm that requires less parameter tuning. However, the GWO suffers from premature convergence and fails to maintain the balance between exploration and exploitation for solving multi-modal problems. This study proposes a niching GWO (NGWO) that incorporates personal best features of PSO and a local search technique to address these issues. The proposed algorithm has been tested for 23 benchmark functions and three engineering cases. The NGWO outperformed all other considered algorithms in most of the test functions compared to state-of-the-art metaheuristics such as PSO, GSA, GWO, Jaya and two improved variants of GWO, and niching CSA. Statistical analysis and Friedman tests have been conducted to compare the performance of these algorithms thoroughly