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Velocity planning serves as an important issue in motion planning for autonomous vehicles. The presented paper proposes a novel velocity planning method with minimum moving time on the basis of path curvature which is accomplished in three steps. First, the assigned path is divided into some elementary parts based on the path curvature. Second, the velocity planning is transformed into an unconstrained optimization problem by assuming the velocity of vehicle to be a specific cubic polynomial on every elementary part to avoid a sudden acceleration in path switching. Finally, we use a modified projection particle swarm optimization (PPSO) algorithm to obtain the time-optimal velocity profile. The proposed method can generate a smooth time-optimal velocity profile while considering all possible relevant constraints. Three examples are provided on different types of path to demonstrate that the final velocity profile is efficient to avoid the sudden acceleration change. Furthermore, the modified PPSO algorithm in this paper is used to solve the optimization problem with high dimensional variables when its upper bound is known, which can not be achieved by the general PPSO algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a particle swarm optimization with strategy dynamics (SDPSO) to solve single-objective optimization problems. SDPSO consists of four PSO search strategies. Evolutionary game theory is introduced to control the population state. In evolutionary game theory, through the interaction between players, better strategies will eventually dominate among the players. By extending this idea to PSO, a selection mechanism and a mutation mechanism are proposed. By using the selection mechanism, the adoption probability of the high payoff strategies will increase. The mutation mechanism can examine the stability of the incumbent strategy to evolutionary pressures. The performance of SDPSO is compared with 14 algorithms on the CEC 2014 test suite. The results show that SDPSO has the highest rank. SDPSO is applied to solve a real-world problem. SDPSO can find the best mean results comparing with 4 algorithms. The findings show that the proposed evolutionary game theory-based framework can adaptively control the population state. This study proposes a new application of evolutionary game theory to the design of swarm intelligence and contributes to a better understanding of the usefulness of the evolutionary game theory in the optimization method. The source codes of SDPSO are available at https://github.com/zi-ang-liu/SDPSO. [ABSTRACT FROM AUTHOR]

In this paper, optimization of a linear objective function subject to a generalized fuzzy relational inequalities is investigated in which an arbitrary continuous t-norm is considered as fuzzy composition, and fuzzy inequality replaces ordinary inequality in the constraints. Unlike most optimization algorithms, in fuzzy relational inequalities with fuzzy constraints (FRI-FC) we find a near-feasible solution having a better objective value than those resulting from the resolution of the similar problems with crisp (ordinary) inequality constraints. Such solutions are called super-optima in this paper. Subsequently, an algorithm is proposed to find a super-optimum with pre-specified desirable infeasibility. For this purpose, we firstly study some structural properties of the FRI-FC problem and present a new formulization that is independent of t-norms used in the constraints of the problem. This new formulation converts the primary problem into an equivalent problem with simple constraints without considering any penalty parameters. However, it is proved that the transformed equivalent problem enables our algorithm to distinguish unfavorable points and generate a sequence of solutions converging to a super-optimum under a certain sufficient condition. Finally, a modified PSO is presented in which the ability of PSO to solve unconstrained problems with continuous domain, the structure of the transformed problem and some fuzzy structural modifications are combined and form an efficient algorithm to solve the generalized FRI-FC problems. The modified PSO algorithm has been applied to the generalized FRI-FC problem defined with ten well-known continuous t-norms. Additionally, an idea of the FRI-FC problems as outer approximators for FRI problems with ordinary inequalities is also investigated. [ABSTRACT FROM AUTHOR]

Multi-modal optimization is an active research topic that has attracted increasing attention from evolutionary computation community. Particle swarm optimization (PSO) with niching technique is one of the most effective approaches for multi-modal optimization. However, in existing PSO with niching methods, the number of particles around different niches varies distinctly from each other, which makes it difficult for the algorithm to find high-quality solutions in all niches. To address this issue, this paper proposes a new niching PSO with equilibrium factor named E-SPSO. Different from the existing niching PSOs, the numbers of particles in different niches have been kept in balance in E-SPSO. The velocity of each particle is influenced by not only the personal best particle and the global best particle, but also an equilibrium factor (EF). By using the equilibrium factor to update the velocities of particles, the particles can be allocated uniformly among the niches. In this way, the computation resources can be assigned to the niches in a more balanced manner, so that the algorithm can gain more population diversity and find high-quality solutions in all niches. Experimental results on eleven benchmark problems show that the proposed mechanism not only increases the number of optima found, but also improves the search efficiency. [ABSTRACT FROM AUTHOR]

Large-scale optimization, solving real high-dimensional problems, has attracted many research interests. Large-scale optimization problems are far more difficult than traditional optimization problems due to their numerous local optimum. In this paper, a principle of maximizing the fitness difference between learners and exemplars is proposed to improve the performance of the optimization algorithm. Then based on the principle, a improved particle swarm optimization algorithm called the "ranking-based biased learning swarm optimizer for large-scale optimization" (RBLSO) is proposed. The proposed RBLSO contains two types of learning strategies, namely, ranking paired learning (RPL) and biased center learning (BCL). In RPL, the worse particles learn peer to peer from the better particles according to their ranks, so then the convergence speed will be accelerated. In BCL, each particle learns from the biased center that is defined as the fitness weighted center of the whole swarm. This operator is utilized to strengthen the explorative ability of the algorithm. To test the performances of the proposed algorithm, we conduct some experiments on the proposed learning mechanism. RBLSO is compared with several state-of-the-art large-scale optimization algorithms on two widely used benchmark function sets, CEC2010 and CEC2013. These two function sets were proposed for the special session and competition on large-scale global optimization held under the Congress on Evolutionary Computation (CEC) 2010 and 2013. Experimental results show that RBLSO is effective in solving large-scale optimization problems. [ABSTRACT FROM AUTHOR]

Over the last two decades numerous metaheuristics have been proposed and it seems today that nobody is able to understand, evaluate, or compare them all. In principle, optimization methods, including the recently popular Evolutionary Computation or Swarm Intelligence-based ones, should be developed in order to solve real-world problems. Yet the vast majority of metaheuristics are tested in the source papers on artificial benchmarks only, so their usefulness for various practical applications remains unverified. As a result, choosing the proper method for a particular real-world problem is a difficult task. This paper shows that such a choice is even more complicated if one wishes, with good reason, to use metaheuristics twice, once to find the best and then to find the worst solutions for the specific numerical real-world problem. It often occurs that for either case different optimizers are to be recommended. The above finding is based on testing 30 metaheuristics on numerical real-world problems from CEC2011. First we solve 22 minimization problems as defined for CEC2011. Then we reverse the objective function for each problem and search for its maximizing solution. We also observe that algorithms that are highly ranked on average may not perform best for any given specific problem. Rather, the highest average ranking may be achieved by methods that are never among the poorest ones. In other words, occasional winners may get less attention than rare losers. [ABSTRACT FROM AUTHOR]

This paper first identifies a substantial gap in the literature of robust optimisation relating to the simplicity, low-dimensionality, lack of bias, lack of deceptiveness, and lack of multi-modality of test problems. Five obstacles and difficulties such as desired number of variables, bias, deceptiveness, multi-modality, and flatness are then proposed to design challenging robust test problems and resolve the deficiency. A standard test suit of eight robust benchmark problems is proposed along with controlling parameters that allow researchers to adjust and achieve the desired level of difficulty. After the theoretical analysis of each proposed test function, a robust particle swarm optimisation (RPSO) algorithm and a robust genetic algorithm (RGA) are employed to investigate their effectiveness experimentally. The paper also inspects the effects of the proposed controlling parameters on the difficulty of the test problems and the proposal of a novel penalty function to penalize the solutions proportional to their sensitivity to perturbations in parameters. The results demonstrate that the proposed test problems are able to benchmark the performance of robust algorithm effectively and provide different, controllable levels of difficulty. In addition, the comparative results reveal the superior performance and merits of the proposed penalty-based method in finding robust solutions. Note : The source codes of the proposed robust test functions are publicity available at www.alimirjalili.com/RO.html . [ABSTRACT FROM AUTHOR]

Novel Evolutionary Algorithms are usually tested on sets of artificially-constructed benchmark problems. Such problems are often created to make the search of one global extremum (usually minimum) tricky. In this paper it is shown that benchmarking heuristics on either minimization or maximization of the same set of artificially-created functions (with equal bounds and number of allowed function calls) may lead to very different ranking of tested algorithms. As Evolutionary Algorithms and other heuristic optimizers are developed in order to be applicable to real-world problems, such result may raise doubts on the practical meaning of benchmarking them on artificial functions, as there is little reason that searching for the minimum of such functions should be more important than searching for their maximum. Thirty optimization heuristics, including a number of variants of Differential Evolution, as well as other kinds of Evolutionary Algorithms, Particle Swarm Optimization, Direct Search methods and – following the idea borrowed from No Free Lunch – pure random search are tested in the paper. Some discussion regarding the choice of the mean or the median performance for comparison is addressed and a short debate on the overall performance of particular methods is given. [ABSTRACT FROM AUTHOR]

Abstract: Complex optimization problems that cannot be solved using exhaustive search require efficient search metaheuristics to find optimal solutions. In practice, metaheuristics suffer from various types of search bias, the understanding of which is of crucial importance, as it is directly pertinent to the problem of making the best possible selection of solvers. In this paper, two metrics are introduced: one for measuring center-seeking bias (CSB) and one for initialization region bias (IRB). The former is based on “ -center offset”, an alternative to “center offset”, which is a common but inadequate approach to analyzing the center-seeking behavior of algorithms, as will be shown. The latter is proposed on the grounds of “region scaling”. The introduced metrics are used to evaluate the bias of three algorithms while running on a test bed of optimization problems having their optimal solution at, or near, the center of the search space. The most prominent finding of this paper is considerable CSB and IRB in the gravitational search algorithm (GSA). In addition, a partial solution to the center-seeking and initialization region bias of GSA is proposed by introducing a “mass-dispersed” version of GSA, mdGSA. mdGSA promotes the global search capability of GSA. Its performance is verified using the same mathematical optimization problem, next to a gene regulatory network parameter identification problem. The results of these experiments demonstrate the capabilities of mdGSA in solving real-world optimization problems. [Copyright &y& Elsevier]

Meta-heuristic algorithms, which require a large number of fitness evaluations before locating the global optimum, are often prevented from being applied to computationally expensive real-world problems where one fitness evaluation may take from minutes to hours, or even days. Although many surrogate-assisted meta-heuristic optimization algorithms have been proposed, most of them were developed for solving expensive problems up to 30 dimensions. In this paper, we propose a surrogate-assisted hierarchical particle swarm optimizer for high-dimensional problems consisting of a standard particle swarm optimization (PSO) algorithm and a social learning particle swarm optimization algorithm (SL-PSO), where the PSO and SL-PSO work together to explore and exploit the search space, and simultaneously enhance the global and local performance of the surrogate model. Our experimental results on seven benchmark functions of dimensions 30, 50 and 100 demonstrate that the proposed method is competitive compared with the state-of-the-art algorithms under a limited computational budget. [ABSTRACT FROM AUTHOR]

The obnoxious p -median problem can be formulated as a constrained binary linear program. It is NP-hard, and has a lot of real world applications. In this paper, a hybrid binary particle swarm optimization is proposed to solve the obnoxious p -median problem. A new position updating rule is presented to inherit the good structure of previous high quality solutions. Furthermore, two tabu based mutation operators are used to avoid the premature convergence and guide the search to a promising area. A greedy repair procedure is developed to repair infeasible solutions. In addition, an iterated greedy local search procedure is utilized to enhance the exploitation ability. Extensive experiments are done on a set of 72 benchmark instances from the literature. Experimental results and comparisons with some existing algorithms demonstrate the effectiveness of the proposed algorithm. In particular, the proposed algorithm finds new best solutions for 15 instances. Compared with existing algorithms, the proposed algorithm is able to find better average objective function value in a short average computing time. [ABSTRACT FROM AUTHOR]

Robust optimization over time is a new approach to solving dynamic optimization problems. It aims to maximize the time within which a solution remains to be acceptable in a changing environment. Since switching solutions often incurs cost in many real-world applications, it is essential for decision makers to take into account the trade-off between robustness and the switching cost in deciding whether the solution currently in use should be switched to a new solution when an environmental change occurs. This paper proposes a generic multi-objective optimization framework for robust optimization over time that simultaneously maximizes the robustness and minimizes the switching cost. An instantiation of the framework is also implemented, where a multi-objective particle swarm optimization algorithm is adopted as the optimizer and the cost for switching a solution is defined to be the difference in the decision space between the solution used in the previous environment and the one in the current environment. In addition, performance indicators are defined to quantitatively evaluate the performance of the proposed algorithm. Empirical studies are carried out on a number of benchmark problems to analyze the influence of the parameters on the behavior of the algorithm. Our results demonstrate that the proposed algorithm is able to find trade-off solutions between the robustness over time and switching cost in a dynamic environment. Finally, the performance of the algorithm is analyzed in terms of the performance indicators, confirming the effectiveness of the proposed framework in minimizing the switching cost in dynamic environments. [ABSTRACT FROM AUTHOR]

The popularity of metaheuristics, especially Swarm Intelligence and Evolutionary Algorithms, has increased rapidly over the last two decades. Numerous algorithms are proposed each year, and progressively more novel applications are being found. However, different metaheuristics are often compared by their performance on problems with an arbitrarily fixed number of allowed function calls. There are surprisingly few papers that explore the relationship between the relative performance of numerous metaheuristics on versatile numerical real-world problems and the number of allowed function calls. In this study the performance of 33 various metaheuristics proposed between 1960 and 2016 have been tested on 22 numerical real-world problems from different fields of science, with the maximum number of function calls varying between 5000 and 500,000. It is confirmed that the algorithms that succeed in comparisons when the computational budget is low are among the poorest performers when the computational budget is high, and vice versa. Among the tested variants, Particle Swarm Optimization algorithms and some new types of metaheuristics perform relatively better when the number of allowed function calls is low, whereas Differential Evolution and Genetic Algorithms perform better relative to other algorithms when the computational budget is large. It is difficult to find any metaheuristic that would perform adequately over all of the numbers of function calls tested. It was also found that some algorithms may become completely unreliable on specific real-world problems, even though they perform reasonably on others. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic mentoring scheme along with a self-regulation scheme have been incorporated in the standard Particle Swarm Optimization (PSO) algorithm to empower the searching particles with human-like characteristics. The algorithm is referred to as a Dynamic Mentoring and Self-Regulation based Particle Swarm Optimization (DMeSR-PSO) algorithm. Based on their experiences, the particles are divided into three groups, viz., the mentor group, the mentee group and the independent learner group where the number of particles in each group is dynamically changing in every iteration. In human learning psychology, mentoring is regarded as a powerful and effective learning process and independent learners are the ones who do not need mentoring and are capable of performing self-regulation of their own knowledge. Therefore, the particles in each of the above three groups have different learning strategies for their velocity updates where the mentors are equipped with a strong self-belief based search, the mentees are taking guidance from the mentors and the independent learners employ self-perception strategy. The DMeSR-PSO algorithm has been extensively evaluated using the simple unimodal and multimodal benchmark functions from CEC2005, more complex shifted and rotated benchmark functions fromCEC2013 and also based on eight real- world problems from CEC2011. The results have been compared with six state-of-the-art PSO variants and five meta-heuristic algorithms for the CEC2005 problems. Further, a comparative analysis on CEC2013 benchmark functions with different PSO variants has also been presented. Finally, DMeSR-PSO's performance on the real-world problems is compared with the top two algorithms from the CEC2011 competition. The results indicate that the proposed learning strategies help DMeSR-PSO to achieve faster convergence and provide better solutions in most of the problems with a 95% confidence level, yielding an effective optimization algorithm for real-world applications. [ABSTRACT FROM AUTHOR]

This paper proposes an information sharing mechanism (ISM) to improve the performance of particle swarm optimization (PSO). The ISM allows each particle to share its best search information, so that all the other particles can take advantage of the shared information by communicating with it. In this way, the particles could enhance the mutual interaction with the others sufficiently and heighten their search ability greatly by using the search information of the whole swarm. Also, a competitive and cooperative (CC) operator is designed for a particle to utilize the shared information in a proper and efficient way. As the ISM share the search information among all the particles, it is an appropriate way to mix up information of the whole swarm for a better exploration of the landscape. Therefore, the competitive and cooperative PSO with ISM (CCPSO-ISM) is capable to prevent the premature convergence when solving global optimization problems. The satisfactory performance of CCPSO-ISM is evaluated by comparing it with other variants of PSOs on a set of 16 global optimization functions. Moreover, the effectiveness and efficiency of CCPSO-ISM is validated under different test environments such as biased initialization, coordinate rotated and high dimensionality. [ABSTRACT FROM AUTHOR]

Abstract: In recent years, many different variants of the particle swarm optimizer (PSO) for solving optimization problems have been proposed. However, PSO has an inherent drawback in handling constrained problems, mainly because of its complexity and dependency on parameters. Furthermore, one PSO variant may perform well for some test problems but not obtain good results for others. In this paper, our purpose is to develop a new PSO algorithm that can efficiently solve a variety of constrained optimization problems. It considers a mix of different PSO variants each of which evolves with a different number of individuals from the current population. In each generation, the algorithm assigns more individuals to the better-performing variants and fewer to the worse-performing ones. Also, a new PSO variant is developed for use in the proposed algorithm to maintain a better balance between its local and global PSO versions. A new methodology for adapting PSO parameters is presented and the proposed self-adaptive PSO algorithm tested and analyzed on two sets of test problems, namely the CEC2006 and CEC2010 constrained optimization problems. Based on the results, the proposed algorithm shows significantly better performance than the same global and local PSO variants as well as other-state-of-the-art algorithms. Although, based on our analysis, it cannot guarantee an optimal solution for any unknown problem, it is expected to be able to solve a wide variety of practical problems. [Copyright &y& Elsevier]

Abstract: Swarm-based algorithms have acquired an important role in solving real-world optimization problems. In this paper, Kinetic Gas Molecule Optimization (KGMO), an optimization algorithm that is based on the kinetic energy of gas molecules, is introduced. The agents are gas molecules that are moving in the search space; they are subject to the kinetic theory of gases, which defines the rules for gas molecule interactions in the model. The performance of the proposed algorithm, in terms of its ability to find the global minima of 23 nonlinear benchmark functions, is evaluated against the corresponding results of two well-known benchmark algorithms, namely, Particle Swarm Optimization (PSO) and the recently developed high-performance Gravitational Search Algorithm (GSA). The simulations that were undertaken indicate that KGMO achieves better results in decreasing the Mean Square Error (MSE). Significant improvements of up to 107 and 1020 times were achieved by KGMO against PSO and GSA, respectively, in solving unimodal benchmark functions within 150 iterations. Improvements of at least tenfold were achieved in solving the multimodal benchmark functions. The proposed algorithm is more accurate and converges faster than does the benchmark algorithms, which makes this algorithm especially useful in solving complex optimization problems. [Copyright &y& Elsevier]

Abstract: In recent years, particle swarm optimization (PSO) algorithm has been used to solve global optimization problems. This algorithm is widely used as an effective optimization tool in various applications. However, traditional PSO consists of only two searching layers and thus often results in premature convergence into the local minima. Thus, multi-layer particle swarm optimization (MLPSO) is proposed in this paper to improve the performance of traditional PSO by increasing the two layers of swarms to multiple layers. The MLPSO strategy increases the diversity of searching swarms to improve its performance when solving complex problems. The experiment indicates that the novel approach improves the final results and the convergence speed. [Copyright &y& Elsevier]