Multimodal Optimization Algorithm Research Articles

Reinforced cuckoo search algorithm-based multimodal optimization

This work proposes a Reinforced Cuckoo Search Algorithm (RCSA) for multimodal optimization, which comprises three different strategies: modified selection strategy, Patron-Prophet concept, and self-adaptive strategy. The modified selection strategy has been proposed for efficient selection of next generation individuals instead of choosing a random set of individuals, which is predominantly followed in a standard Cuckoo Search (CS). The Patron-Prophet concept is based on a donor-acceptor concept where a donor donates information and the acceptor makes use of it. In the RCSA, the deviated information of abandoned solutions from selected solutions will be calculated and subsequently used by the newly generated solutions. A self-adaptive step size has been introduced to achieve multimodality in the RCSA. Experimental results using benchmark problems show that the RCSA performs well in terms of multimodality when compared with other existing algorithms found in the literature. This proposed RCSA is also implemented in three different engineering design problems for performance evaluation.

KGSA: A Gravitational Search Algorithm for Multimodal Optimization based on K-Means Niching Technique and a Novel Elitism Strategy

AbstractGravitational Search Algorithm (GSA) is a metaheuristic for solving unimodal problems. In this paper, a K-means based GSA (KGSA) for multimodal optimization is proposed. This algorithm incorporates K-means and a new elitism strategy called “loop in loop” into the GSA. First in KGSA, the members of the initial population are clustered by K-means. Afterwards, new population is created and divided in different niches (or clusters) to expand the search space. The “loop in loop” technique guides the members of each niche to the optimum direction according to their clusters. This means that lighter members move faster towards the optimum direction of each cluster than the heavier members. For evaluations, KGSA is benchmarked on well-known functions and is compared with some of the state-of-the-art algorithms. Experiments show that KGSA provides better results than the other algorithms in finding local and global optima of constrained and unconstrained multimodal functions.

Multimodal multiobjective optimization with differential evolution

Abstract This paper proposes a multimodal multiobjective Differential Evolution optimization algorithm (MMODE). The technique is conceived for deployment on problems with a Pareto multimodality, where the Pareto set comprises multiple disjoint subsets, all of which map to the same Pareto front. A new contribution is the formulation of a decision-variable preselection scheme that promotes diversity of solutions in both the decision and objective space. A new mutation-bound process is also introduced as a supplement to a classical mutation scheme in Differential Evolution methods, where offspring that lie outside the search bounds are given a second opportunity to mutate, hence reducing the density of individuals on the boundaries of the search space. New multimodal multiobjective test functions are designed, along with analytical expressions for their Pareto sets and fronts. Some test functions introduce more complicated Pareto-front shapes and allow for decision-space dimensions greater than two. The performance of the MMODE algorithm is compared with five other state-of-the-art methods. The results show that MMODE realizes superior performance by finding more and better distributed Pareto solutions.

A clonal selection algorithm for dynamic multimodal function optimization

The objective of dynamic multimodal optimization problems (DMMOPs) is to find all global optima in a dynamic environment. Although dynamic optimization problems (DOPs) have been widely studied in the field of nature-inspired computation, DMMOPs have not yet been paid significant attention yet. It is a challenging task for the classic clonal selection algorithm (CSA) to track all the moving global optima of dynamic multimodal optimization problems. The population of the classic CSA tends to converge to a single optimum, and the shortage of population diversity prevents the classic CSA from adapting to environmental changes. To address these limitations, this paper proposes a so-called dynamic multimodal clonal selection algorithm (DMMCSA). DMMCSA incorporates a niching method called nearest-better clustering, and adapts the scale factor of the hypermutation operator according to the distances among individuals. Experiments on benchmark problems show that DMMCSA significantly outperforms CSA in terms of tracking all the global optima of DMMOPs.

Antlion Optimization Algorithm Based on Quadratic Interpolation

Because of slow convergence speed and low calculation precision of antlion optimization (ALO) algorithm, an improved algorithm named quadratic interpolation antlion optimization (QIALO) is put forward in this paper puts. The new algorithm uses the quadratic interpolation (QI) to obtain the secondary renewal position of ants, which enhances the local search ability of the antlion optimization algorithm and accelerates the global optimization speed of the population. Simulation results on thirteen test functions indicate that the performance of the new algorithm is better than that of the contrast algorithms in the statistical sense, and the performance of QIALO algorithm for multimodal optimization is improved effectively.

A Robust Multimodal Optimization Algorithm Based on a Sub-Division Surrogate Model and an Improved Sampling Method

The characteristics analysis of an electric machine requires the finite-element method. Hence, a large amount of computation occurs in the design process to take into account uncertainties as the manufacturing tolerances. In this paper, an efficient and useful multimodal optimization algorithm using the kriging surrogate model is proposed for the robust optimization of an electric machine. However, the conventional kriging (CK) method has a memory problem in multi-dimensional problem due to the enlarged correlation matrix. Thus, a sub-domain kriging (SDK) strategy and improved Latin hypercube sampling (ILHS) are proposed not only to solve the memory problem of the CK method, but also to increase the convergence speed. In addition, a gradient-free sensitivity index is proposed for robust optimization in order to address the conventional first and second gradient index which causes a numerical error. The outstanding performance of the proposed algorithm is verified by comparing with other optimization methods via several mathematical test functions which includes multi-dimensional problem. Moreover, the proposed algorithm is applied to a cogging torque reduction design case for interior permanent magnet motor.

Multiscale Quantum Harmonic Oscillator Algorithm for Multimodal Optimization.

This paper presents a variant of multiscale quantum harmonic oscillator algorithm for multimodal optimization named MQHOA-MMO. MQHOA-MMO has only two main iterative processes: quantum harmonic oscillator process and multiscale process. In the two iterations, MQHOA-MMO only does one thing: sampling according to the wave function at different scales. A set of benchmark test functions including some challenging functions are used to test the performance of MQHOA-MMO. Experimental results demonstrate good performance of MQHOA-MMO in solving multimodal function optimization problems. For the 12 test functions, all of the global peaks can be found without being trapped in a local optimum, and MQHOA-MMO converges within 10 iterations.

A Multimodal Optimization Algorithm Inspired by the States of Matter

The main objective of multi-modal optimization is to find multiple global and local optima for a problem in only one execution. Detecting multiple solutions to a multi-modal optimization formulation is especially useful in engineering, since the best solution could not represent the best realizable due to various practical restrictions. The States of Matter Search (SMS) is a recently proposed stochastic optimization technique. Although SMS is highly effective in locating single global optimum, it fails in providing multiple solutions within a single execution. To overcome this inconvenience, a new multimodal optimization algorithm called the Multi-modal States of Matter Search (MSMS) in introduced. Under MSMS, the original SMS is enhanced with new multimodal characteristics by means of: (1) the definition of a memory mechanism to efficiently register promising local optima according to their fitness values and the distance to other probable high quality solutions; (2) the modification of the original SMS optimization strategy to accelerate the detection of new local minima; and (3) the inclusion of a depuration procedure at the end of each state to eliminate duplicated memory elements. The performance of the proposed approach is compared to several state-of-the-art multimodal optimization algorithms considering a benchmark suite of fourteen multimodal problems. The results confirm that the proposed method achieves the best balance over its counterparts regarding accuracy and computational cost.

Evolutionary Multiobjective Optimization-Based Multimodal Optimization: Fitness Landscape Approximation and Peak Detection

Recently, by taking advantage of evolutionary multiobjective optimization techniques in diversity preservation, the means of multiobjectivization has attracted increasing interest in the studies of multimodal optimization (MMO). While most existing work of multiobjectivization aims to find all optimal solutions simultaneously, in this paper, we propose to approximate multimodal fitness landscapes via multiobjectivization, thus providing an estimation of potential optimal areas. To begin with, an MMO problem is transformed into a multiobjective optimization problem (MOP) by adding an adaptive diversity indicator as the second optimization objective, and an approximate fitness landscape is obtained via optimization of the transformed MOP using a multiobjective evolutionary algorithm. Then, on the basis of the approximate fitness landscape, an adaptive peak detection method is proposed to find peaks where optimal solutions may exist. Finally, local search is performed inside the detected peaks on the approximate fitness landscape. To assess the performance of the proposed algorithm, extensive experiments are conducted on 20 multimodal test functions, in comparison with three state-of-the-art algorithms for MMO. Experimental results demonstrate that the proposed algorithm not only shows promising performance in benchmark comparisons, but also has good potential in assisting preference-based decision-making in MMO.

A tri-objective differential evolution approach for multimodal optimization

The multimodal optimization problems (MMOPs) need to find multiple optima simultaneously, so the population diversity is a critical issue that should be considered in designing an evolutionary optimization algorithm for MMOPs. Taking advantage of evolutionary multiobjective optimization in maintaining good population diversity, this paper proposes a tri-objective differential evolution (DE) approach to solve MMOPs. Given an MMOP, we first transform it into a tri-objective optimization problem (TOP). The three optimization objectives are constructed based on 1) the objective function of an MMOP, 2) the individual distance information measured by a set of reference points, and 3) the shared fitness based on niching technique. The first two objectives are mutually conflicting so that the advantage of evolutionary multiobjective optimization can be fully used. The population diversity is greatly improved by the third objective constructed by the niching technique which is insensitive to niching parameters. Mathematical proofs are given to demonstrate that the Pareto-optimal front of the TOP contains all global optima of the MMOP. Subsequently, DE-based multiobjective optimization techniques are applied to solve the converted TOP. Moreover, a modified solution comparison criterion and an adaptive ranking strategy for DE are introduced to improve the accuracy of solutions. Experiments have been conducted on 44 benchmark functions to evaluate the performance of the proposed approach. The results show that the proposed approach achieves competitive performance compared with several state-of-the-art multimodal optimization algorithms.

Simulation-based multimodal optimization of decoy system design using an archived noise-tolerant genetic algorithm

The difficulty of warship decoy system design problem is twofold. First, we need to find not just one but as many optimal solutions as possible. Second, it demands a heavy computation to evaluate a candidate solution through a long series of underwater warfare simulations. The previous approach tried to reduce the amount of search by heuristically selecting a set of plausible starting points for the search by a simulated annealing algorithm. However, it shows only limited success and cannot easily scale up to larger problems. This paper proposes an efficient and easy-to-scale-up multimodal optimization algorithm named A-NTGA that is based on a genetic algorithm. A-NTGA quickly evaluates candidate solutions by conducting only a small number of simulations, but instead copes with these inaccurate or noisy fitness values by using a noisy optimization technique. To further enhance the efficiency of search by promoting the population diversity, A-NTGA is provided with an archive to which some good-looking solutions are migrated in order to prevent the population from being too crowded with similar solutions. Usually at the end of the search, many optimal solutions are retrieved from the archive as well as the population. The experimental results show that our method can find multiple optimal solutions more efficiently compared to other methods and can be easily scaled up to larger problems.

Multimodal continuous ant colony optimization for multisensor remote sensing image registration with local search

Abstract Due to the large differences between different imaging sensors, multisensor remote sensing image registration is a challenging work. Multisensor remote sensing image registration can be formulated as a multimodal problem, and general optimization methods may get trapped into a local optimum when solving complex multimodal problems. In this paper, we introduce a multimodal continuous ant colony optimization algorithm for multisensor remote sensing image registration, and an efficient optimization method is designed as local search operation. Multimodal continuous ant colony optimization algorithm can preserve high diversity and has the global search ability for multimodal problems. Meanwhile, efficient local search operation can improve the efficiency and provide the accurate result. The experimental results have demonstrated the effectiveness and robustness of the proposed method.

Globalized and bounded Nelder‐Mead algorithm with deterministic restarts for tuning controller parameters: Method and application

SummaryThis paper develops and examines an optimization algorithm for simulation‐based tuning of controller parameters. The proposed algorithm globalizes the Guin augmented variant of Nelder–Mead's nonlinear downhill simplex by deterministic restarts, linearly growing memory vector, and moving initial simplex. First, the effectiveness of the algorithm is tested using 10 complex and multimodal optimization benchmarks. The algorithm achieves global minima of all benchmarks and compares favorably against the evolutionary, swarm, and other globalized local‐search multimodal optimization algorithms in probability of finding global minimum and numerical cost. Next, the proposed algorithm is applied for tuning sliding mode controller parameters for a servo pneumatic position control application. The experimental results reveal that the system with sliding mode controller parameters tuned using the proposed algorithm targeting smooth position control with maximum possible accuracy, performs as desired and eliminates the need of manual online tuning for desired performance. The results are also compared with the performance of the same servo pneumatic system with parameters tuned using manual online tuning in an earlier published work. The system with controller parameters tuned using the proposed algorithm shows improvement in accuracy by 28.9% in sinusoidal and 42.2% in multiple step polynomials tracking.

Degeneration Recognizing Clonal Selection Algorithm for Multimodal Optimization

In this paper, a computing speed improvement for the clonal selection algorithm (CSA) is proposed based on a degeneration recognizing (DR) method. The degeneration recognizing clonal selection algorithm (DR-CSA) is designed for solving complex engineering multimodal optimization problems. On each iteration of CSA, there is a large amount of eliminated solutions which are usually neglected. But these solutions do contain the knowledge of the nonoptimal area. By storing and utilizing these data, the DR-CSA is aimed to identify part of the new population as degenerated and eliminate them before the evaluation operation, so that a number of evaluation times can be avoided. This pre-elimination operation is able to save computing time because the evaluation is the main reason for the time cost in the complex engineering optimization problem. Experiments on both test function and a real-world engineering optimization problem (wet spinning coagulating process) are conducted. The results show that the proposed DR-CSA is as accurate as regular CSA and is effective in reducing a considerable amount of computing time.

Flower Pollination Algorithm for Multimodal Optimization

This paper proposes a new algorithm called Multimodal Flower Pollination Algorithm (MFPA). Under MFPA, the original Flower Pollination Algorithm (FPA) is enhanced with multimodal capabilities in order to find all possible optima in an optimization problem. The performance of the proposed MFPA is compared to several multimodal approaches considering the evaluation in a set of well-known benchmark functions. Experimental data indicate that the proposed MFPA provides better results over other multimodal competitors in terms of accuracy and robustness.

A niching chaos optimization algorithm for multimodal optimization

Niching is the technique of finding and preserving multiple stable niches, or favorable parts of the solution space possibly around multiple optima, for the purpose of solving multimodal optimization problems. Chaos optimization algorithm (COA) is one of the global optimization techniques, but as far as we know, a niching variant of COA has not been developed . In this paper, a novel niching chaos optimization algorithm (NCOA) is proposed. The circle map with a proper parameter setting is employed considering the fact that the performance of COA is affected by the chaotic map. In order to achieve niching, NCOA utilizes several techniques including simultaneously contracted multiple search scopes, deterministic crowding and clearing. The effects of some components and parameters of NCOA are investigated through numerical experiments. Comparison with other state-of-the-art multimodal optimization algorithms demonstrates the competitiveness of the proposed NCOA.

Balancing global and local search in parallel efficient global optimization algorithms

Most parallel efficient global optimization (EGO) algorithms focus only on the parallel architectures for producing multiple updating points, but give few attention to the balance between the global search (i.e., sampling in different areas of the search space) and local search (i.e., sampling more intensely in one promising area of the search space) of the updating points. In this study, a novel approach is proposed to apply this idea to further accelerate the search of parallel EGO algorithms. In each cycle of the proposed algorithm, all local maxima of expected improvement (EI) function are identified by a multi-modal optimization algorithm. Then the local EI maxima with value greater than a threshold are selected and candidates are sampled around these selected EI maxima. The results of numerical experiments show that, although the proposed parallel EGO algorithm needs more evaluations to find the optimum compared to the standard EGO algorithm, it is able to reduce the optimization cycles. Moreover, the proposed parallel EGO algorithm gains better results in terms of both number of cycles and evaluations compared to a state-of-the-art parallel EGO algorithm over six test problems.

A Novel Multimodal Optimization Algorithm for the Design of Electromagnetic Machines

The design of an electromagnetic machine is a nonlinear, multivariable, and multimodal optimization problem that incurs a great deal of computation time when calculating electromagnetic fields. To overcome these problems effectively, this paper proposes a new evolutionary multimodal optimization algorithm based on the Big Bang-Big Crunch method and aided by a surrogate model using the theory of compressed sensing. Its efficiency is demonstrated by assessing the optimization results for test functions. Moreover, to evaluate the feasibility of its application to an electromagnetic problem, an interior permanent magnet motor is designed using the proposed algorithm. The obtained results confirm that the proposed method has the ability to search for multiple optimal solutions with a good computational efficiency by reducing the number of fitness function evaluations during the optimization process.

Thermodynamic analysis and optimization of a geothermal Kalina cycle system using Artificial Bee Colony algorithm

In this paper, thermodynamic analysis is carried out for a geothermal Kalina cycle employed in Husavic power plant. Afterwards, the optimum operating conditions in which the cycle is at its best performance are calculated. In order to reach the optimum thermal and exergy efficiencies of the cycle, Artificial Bee Colony (ABC) algorithm, a new powerful multi-objective and multi-modal optimization algorithm, is conducted. Regarding the mechanism of ABC algorithm, convergence speed and precision of solutions have been remarkably improved when compared to those of GA, PSO and DE algorithms. Such a relative improvement is indicated by a limit parameter and declining probability of premature convergence. In this research, exergy efficiency including chemical and physical exergies and thermal efficiency are chosen as the objective functions of ABC algorithm where optimum values of the efficiencies for the Kalina cycle are found to be 48.18 and 20.36%, respectively, while the empirical thermal efficiency of the cycle is about 14%. At the optimum thermal and exergy efficiencies, total exergy destruction rates are respectively 4.17 and 3.48 MW. Finally, effects of the separator inlet pressure, temperature, basic ammonia mass fraction and mass flow rate on the first and second law efficiencies are investigated.

Particle swarm optimization for time series motif discovery

Efficiently finding similar segments or motifs in time series data is a fundamental task that, due to the ubiquity of these data, is present in a wide range of domains and situations. Because of this, countless solutions have been devised but, to date, none of them seems to be fully satisfactory and flexible. In this article, we propose an innovative standpoint and present a solution coming from it: an anytime multimodal optimization algorithm for time series motif discovery based on particle swarms. By considering data from a variety of domains, we show that this solution is extremely competitive when compared to the state-of-the-art, obtaining comparable motifs in considerably less time using minimal memory. In addition, we show that it is robust to different implementation choices and see that it offers an unprecedented degree of flexibility with regard to the task. All these qualities make the presented solution stand out as one of the most prominent candidates for motif discovery in long time series streams. Besides, we believe the proposed standpoint can be exploited in further time series analysis and mining tasks, widening the scope of research and potentially yielding novel effective solutions.