Different Types Of Optimization Problems Research Articles

A Metaheuristic Framework with Experience Reuse for Dynamic Multi-Objective Big Data Optimization

Dynamic multi-objective big data optimization problems (DMBDOPs) are challenging because of the difficulty of dealing with large-scale decision variables and continuous problem changes. In contrast to classical multi-objective optimization problems, DMBDOPs are still not intensively explored by researchers in the optimization field. At the same time, there is lacking a software framework to provide algorithmic examples to solve DMBDOPs and categorize benchmarks for relevant studies. This paper presents a metaheuristic software framework for DMBDOPs to remedy these issues. The proposed framework has a lightweight architecture and a decoupled design between modules, ensuring that the framework is easy to use and has enough flexibility to be extended and modified. Specifically, the framework now integrates four basic dynamic metaheuristic algorithms, eight test suites of different types of optimization problems, as well as some performance indicators and data visualization tools. In addition, we have proposed an experience reuse method, speeding up the algorithm’s convergence. Moreover, we have implemented parallel computing with Apache Spark to enhance computing efficiency. In the experiments, algorithms integrated into the framework are tested on the test suites for DMBDOPs on an Apache Hadoop cluster with three nodes. The experience reuse method is compared to two restart strategies for dynamic metaheuristics.

Applications of nature-inspired metaheuristic algorithms for tackling optimization problems across disciplines

Nature-inspired metaheuristic algorithms are important components of artificial intelligence, and are increasingly used across disciplines to tackle various types of challenging optimization problems. This paper demonstrates the usefulness of such algorithms for solving a variety of challenging optimization problems in statistics using a nature-inspired metaheuristic algorithm called competitive swarm optimizer with mutated agents (CSO-MA). This algorithm was proposed by one of the authors and its superior performance relative to many of its competitors had been demonstrated in earlier work and again in this paper. The main goal of this paper is to show a typical nature-inspired metaheuristic algorithmi, like CSO-MA, is efficient for tackling many different types of optimization problems in statistics. Our applications are new and include finding maximum likelihood estimates of parameters in a single cell generalized trend model to study pseudotime in bioinformatics, estimating parameters in the commonly used Rasch model in education research, finding M-estimates for a Cox regression in a Markov renewal model, performing matrix completion tasks to impute missing data for a two compartment model, and selecting variables optimally in an ecology problem in China. To further demonstrate the flexibility of metaheuristics, we also find an optimal design for a car refueling experiment in the auto industry using a logistic model with multiple interacting factors. In addition, we show that metaheuristics can sometimes outperform optimization algorithms commonly used in statistics.

Facial emotion recognition using enhanced multi-verse optimizer method

In recent years, facial emotion recognition has gained significant improvement and attention. This technology utilizes advanced algorithms to analyze facial expressions, enabling computers to detect and interpret human emotions accurately. Its applications span over a wide range of fields, from improving customer service through sentiment analysis, to enhancing mental health support by monitoring emotional states. However, there are several challenges in facial emotion recognition, including variability in individual expressions, cultural differences in emotion display, and privacy concerns related to data collection and usage. Lighting conditions, occlusions, and the need for diverse datasets also impacts accuracy. To solve these issues, an enhanced multi-verse optimizer (EMVO) technique is proposed to improve the efficiency of recognizing emotions. Moreover, EMVO is used to improve the convergence speed, exploration-exploitation balance, solution quality, and the applicability in different types of optimization problems. Two datasets were used to collect the data, namely YouTube and surrey audio-visual expressed emotion (SAVEE) datasets. Then, the classification is done using the convolutional neural networks (CNN) to improve the performance of emotion recognition. When compared to the existing methods shuffled frog leaping algorithm-incremental wrapper-based subset selection (SFLA-IWSS), hierarchical deep neural network (H-DNN) and unique preference learning (UPL), the proposed method achieved better accuracies, measured at 98.65% and 98.76% on the YouTube and SAVEE datasets, respectively.

Multi-robot path planning using learning-based Artificial Bee Colony algorithm

Multi-robot path planning (MRPP) in continuous and known environment is studied in this paper via proposing a novel local path planning approach. To plan optimal collision-free paths for multiple robots simultaneously, a novel implementation method suitable for the meta-heuristic algorithms is devised, and an improved artificial bee colony (ABC) algorithm is developed. Three enhancements to the ABC algorithm are made in this context. Firstly, to better lead the search direction, the global best individual is involved in the search equations of employed bee phase and scout bee phase. Meanwhile, to boost exploitation capability, the learning method of teaching-learning based optimization (TLBO) algorithm is incorporated into the onlooker bee phase. The proposed learning-based ABC (ABCL) algorithm is used to determine the subsequent positions for all the robots based on their current coordinates considering the path length, safety and planning efficiency. The experimental studies on benchmark functions show that ABCL is outstanding in solving different types of optimization problems compared against seven effective meta-heuristic algorithms. More importantly, MRPP simulation results prove that ABCL outperforms its competitors in terms of generating optimal collision-free paths and running time. Compared with the original ABC, ABCL improves these two aspects on average for all tasks by 2.1% and 12.6%, respectively. Therefore, with the proposed implementation method, ABCL can be considered as an effective MRPP solution.

Hybrid genetic algorithm to minimize scheduling cost with unequal and job dependent earliness tardiness cost

This article presents two combinatorial genetic algorithms (GA), unequal earliness tardiness-GA (UET-GA) and job-dependent earliness tardiness-GA (JDET-GA) for the single-machine scheduling problem to minimize earliness tardiness (ET) cost. The sequence of jobs produced in basic UET and JDET as a chromosome is added to the random population of GA. The best sequence from each epoch is also injected as a population member in the subsequent epoch. The proposed improvement seeks to achieve convergence in less time to search for an optimal solution. Although the GA has been implemented very successfully on many different types of optimization problems, it has been learnt that the algorithm has a search ability difficulty that makes computations NP-hard for types of optimization problems, such as permutation-based optimization problems. The use of a plain random population initialization results in this flaw. To reinforce the random population initialization, the proposed enhancement is utilized to obtain convergence and find a promising solution. The cost is further significantly lowered offering the due date as a decision variable with JDET-GA. Multiple tests were run on well-known single-machine benchmark examples to demonstrate the efficacy of the proposed methodology, and the results are displayed by comparing them with the fundamental UET and JDET approaches with a notable improvement in cost reduction.

Dynamic Multi-Swarm Competitive Fireworks Algorithm for Global Optimization and Engineering Constraint Problems

As a novel intelligent algorithm, fireworks algorithm (FWA) is applied to deal with different types of optimization problems. Since FWA’s search processes are relatively simple, it is inefficient. In this paper, a dynamic multi-swarm competitive fireworks algorithm (DMCFWA) is developed to enhance the search capability of FWA. Firstly, based on the scaling coefficient updated by utilizing the fitness value of the optimal firework, the dynamic explosion amplitude strategy is proposed to improve the search capability of the best firework. Secondly, utilizing the location information of the fireworks, an improved search method is designed to enhance the local search capability of firework swarms. Thirdly, a multi-swarm independent selection technique and a restart operation are adopted to boost its abilities of global exploration and local exploitation. Finally, to reduce the computational cost of FWA, a new initialization method is used and a new model for calculating the spark number is embedded in DMCFWA. By adopting these strategies, DMCFWA easily implements and does well in exploitation and exploration. CEC2017 test suite and four engineering constraint problems are used to demonstrate the performance of DMCFWA. Experimental results show that DMCFWA performs more effectively and stably than its competitors.

Cuckoo search algorithm for construction site layout planning

<span lang="EN-US">A novel metaheuristic optimization algorithm based on cuckoo search algorithm (CSA) is presented to solve the construction site layout planning problem (CSLP). CSLP is a complex optimization problem with various applications, such as plant layout, construction site layout, and computer chip layout. Many researchers have investigated the CSLP by applying many algorithms in an exact or heuristic approach. Although both methods yield a promising result, technically, nature-inspired algorithms demonstrate high achievement in successful percentage. In the last two decades, researchers have been developing a new nature-inspired algorithm for solving different types of optimization problems. The CSA has gained popularity in resolving large and complex issues with promising results compared with other nature-inspired algorithms. However, for solving CSLP, the algorithm based on CSA is still minor. Thus, this study proposed CSA with additional modification in the algorithm mechanism, where the algorithm shows a promising result and can solve CSLP cases.</span>

Multi-Group Gorilla Troops Optimizer with Multi-Strategies for 3D Node Localization of Wireless Sensor Networks.

The localization problem of nodes in wireless sensor networks is often the focus of many researches. This paper proposes an opposition-based learning and parallel strategies Artificial Gorilla Troop Optimizer (OPGTO) for reducing the localization error. Opposition-based learning can expand the exploration space of the algorithm and significantly improve the global exploration ability of the algorithm. The parallel strategy divides the population into multiple groups for exploration, which effectively increases the diversity of the population. Based on this parallel strategy, we design communication strategies between groups for different types of optimization problems. To verify the optimized effect of the proposed OPGTO algorithm, it is tested on the CEC2013 benchmark function set and compared with Particle Swarm Optimization (PSO), Sine Cosine Algorithm (SCA), Whale Optimization Algorithm (WOA) and Artificial Gorilla Troops Optimizer (GTO). Experimental studies show that OPGTO has good optimization ability, especially on complex multimodal functions and combinatorial functions. Finally, we apply OPGTO algorithm to 3D localization of wireless sensor networks in the real terrain. Experimental results proved that OPGTO can effectively reduce the localization error based on Time Difference of Arrival (TDOA).

DSGWO: An improved grey wolf optimizer with diversity enhanced strategy based on group-stage competition and balance mechanisms

Grey wolf optimizer (GWO) is a popular algorithm in the field of meta-heuristics with fast convergence speed and strong exploitation ability for solving different types of optimization problems. However, there are two problems presented in the optimization process of GWO. Problem (1): GWO algorithm uses three leading wolves to direct the population for search, resulting in poor population diversity. Problem (2): Individuals selected in the optimization process of GWO have the current optimal fitness value, resulting in poor global search capabilities of the algorithm, and the population may tend to converge prematurely and fall into local optimum. In order to solve the above problems, this paper proposes the Diversity enhanced Strategy based Grey Wolf Optimizer (DSGWO), which combines two mechanisms to improve the performance of the GWO algorithm, including the group-stage competition mechanism and the exploration–exploitation balance mechanism. The experimental results are evaluated by using IEEE CEC 2014 benchmark functions and two engineering problems. The Wilcoxon rank-sum test is also conducted to measure the performance of DSGWO. The results demonstrate that the DSGWO algorithm can efficiently obtain the optimal solution of the dataset used in this paper, preserve more population diversity, and enhance the global search capability. In addition, through the application of two engineering problems, it is verified that DSGWO is suitable for solving engineering design problems.

A twinning bare bones particle swarm optimization algorithm.

A twinning bare bones particle swarm optimization(TBBPSO) algorithm is proposed in this paper. The TBBPSO is combined by two operators, the twins grouping operator (TGO) and the merger operator (MO). The TGO aims at the reorganization of the particle swarm. Two particles will form as a twin and influence each other in subsequent iterations. In a twin, one particle is designed to do the global search while the other one is designed to do the local search. The MO aims at merging the twins and enhancing the search ability of the main group. Two operators work together to enhance the local minimum escaping ability of proposed methods. In addition, no parameter adjustment is needed in TBBPSO, which means TBBPSO can solve different types of optimization problems without previous information or parameter adjustment. In the benchmark functions test, the CEC2014 benchmark functions are used. Experimental results prove that proposed methods can present high precision results for various types of optimization problems.

Development and application of a modularized geometry optimizer for future supercritical CO2 turbomachinery optimization

During the operation of supercritical CO (sCO) turbomachineries, large pressure ratios, supersonic conditions and non-ideal gas fluid dynamic phenomenon may happen, which will decrease the whole cycle efficiencies. Hence non-standard designs for the turbomachineries geometry are needed. Successfully simulations in capturing non-ideal gas fluid dynamics and coupled with optimization algorithm are hard and currently not available in any commercial CFD software. Therefore, the problem of optimizing sCO turbomachinery is difficult to solve, which has become a major obstacle to obtain compact and high-efficiency sCO turbomachineries. In this study, a modularized geometry optimizer is developed to obtain the non-standard geometric designs for sCO turbomachineries. Multiple techniques are applied to this optimizer, include the Nelder–Mead algorithm, Mahalanobis distance and stochastic algorithm. The newly developed optimizer can successfully find the optimum satisfying the objective function under given weighting factors. The computational cost can be reduced through a stochastic algorithm. To validate the optimizer, a convergent–divergent nozzle for air with a target Mach number equal to 2.4 is optimized. Different starting points and combinations of weighting factors are used to create a Pareto front. Adjust the weighting factors for different terms of the objective function leading the optimizer to go to different directions in n-dimensional spaces. Three optimized cases, one is Mach number optimized, one is outlet flow uniformity optimized and the other is compromised case, are picked out and analyzed. The results show that the optimizer can successfully find optimized geometry than the reference case and potentially save computational cost. Due to the modularized characteristics, the components of this optimizer can be replaced with any available techniques, which mean the optimizer can be applied to solve different types of optimization problems.

An innovative deterministic algorithm for optimal placement of micro phasor measurement units in radial electricity distribution systems

PurposeHeuristic algorithms have been widely used in different types of optimization problems. Their unique features in terms of running time and flexibility have made them superior to deterministic algorithms. To accurately compare different heuristic algorithms in solving optimization problems, the final optimal solution needs to be known. Existing deterministic methods such as Exhaustive Search and Integer Linear Programming can provide the final global optimal solution for small-scale optimization problems. However, as the system grows the number of calculations and required memory size incredibly increases, so applying existing deterministic methods is no longer possible for medium and large-scale systems. The purpose of this paper is to introduce a novel deterministic method with short running time and small memory size requirement for optimal placement of Micro Phasor Measurement Units (µPMUs) in radial electricity distribution systems to make the system completely observable.Design/methodology/approachFirst, the principle of the method is explained and the observability of the system is analyzed. Then, the algorithm’s running time and memory usage when applying on some of the modified versions of the Institute of Electrical and Electronics Engineers 123-node test feeder are obtained and compared with those of its deterministic counterparts.FindingsBecause of the innovative method of step-by-step placement of µPMUs, a unique method is developed. Simulation results elucidate that the proposed method has unique features of short running time and small memory size requirements.Originality/valueWhile the mathematical background of the observability study of electricity distribution systems is very well-presented in the referenced papers, the proposed step-by-step placement method of µPMUs, which shrinks unobservable parts of the system in each step, is not discussed yet. The presented paper is directly applicable to typical problems in the field of power systems.

Chaotic neural network algorithm with competitive learning for global optimization

Neural network algorithm (NNA) is one of the newest proposed metaheuristic algorithms. NNA has strong global search ability due to the unique structure of artificial neural networks. Further, NNA is an algorithm without any effort for fine tuning initial parameters. Thus, it is very easy for NNA to solve different types of optimization problems. However, when used for solving complex optimization problems, slow convergence and premature convergence are its drawbacks. To overcome the two drawbacks, this work presents an improved NNA, namely chaotic neural network algorithm with competitive learning (CCLNNA), for global optimization. In CCLNNA, population is first divided into excellent subpopulation and common subpopulation according to the built competitive mechanism. Then, to balance exploration and exploitation of CCLNNA, excellent subpopulation is optimized by the designed transfer operator while common subpopulation is updated by the combination of the designed bias operator and transfer operator. Besides, chaos theory is introduced to increase the chance of CCLNNA to escape from the local optimum. To investigate the effectiveness of the improved strategies, CCLNNA is first used to solve the well-known CEC 2014 test suite with 30 benchmark functions. Then it is employed for solving three constrained real-world engineering design problems. Experimental results reveal that the improved strategies introduced to NNA can significantly improve the optimization performance of NNA and CCLNNA is a very powerful algorithm in solving complex optimization problems with multimodal properties by comparing with the other competitive algorithms.

A modified multi swarm particle swarm optimization algorithm using an adaptive factor selection strategy

In the present study, we suggest a modified version of heterogeneous multi-swarm particle swarm optimization (MSPSO) algorithm, that allows the amelioration of its performance by introducing an adaptive inertia weight approach. In order to bring about a balance between the exploration and exploitation characteristics of MSPSO allowing to promote information exchange amongst the subswarms. However, the classical MSPSO algorithm search behavior has not always been optimal in finding the optimal solution to certain problems, which results in falling into local optimum leading to premature convergence. The most advantages of the MSPSO there are easy to implement and there are few parameters to adjust. The inertia weight (w) is one of the most Particle Swarm Optimization’s (PSO) parameters. Controlling this parameter could facilitate the convergence and prevent an explosion of the swarm. To overcome the above limitations, this paper proposes a heterogeneous multi swarm PSO algorithm based on PSO number selection approach centred on the idea of particle swarm referred to as Multi-Swarm Particle Swarm Optimization algorithm with Factor selection strategy (FMSPSO). In the various process implementations of the particle swarm search, different parameter selection strategies are adopted to ameliorate the global search ability. The proposed FMSPSO is able to improve the population’s diversity and better explore the entire feature space. The statistical test and indicators that are reported in the specialized literature demonstrate that the suggested approach is superior in terms of efficiency to nine other popular PSO algorithms in solving the optimization problem of complex problems. The approach suggests that FMSPSO reaches a very promising performance for solving different types of optimization problems, leading eventually to higher solution accuracy.

Modified Particle Swarm Optimization with Chaotic Initialization Scheme for Unconstrained Optimization Problems

Different variants of particle swarm optimization (PSO) algorithms were introduced in recent years with various improvements to tackle different types of optimization problems more robustly. However, the conventional initialization scheme tends to generate an initial population with relatively inferior solution due to the random guess mechanism. In this paper, a PSO variant known as modified PSO with chaotic initialization scheme is introduced to solve unconstrained global optimization problems more effectively, by generating a more promising initial population. Experimental studies are conducted to assess and compare the optimization performance of the proposed algorithm with four existing well-establised PSO variants using seven test functions. The proposed algorithm is observed to outperform its competitors in solving the selected test problems.

Stability bounds and almost sure convergence of improved particle swarm optimization methods

Particle swarm optimization (PSO) is a member of nature-inspired metaheuristic algorithms. Its formulation is simple and does not need the computation of derivatives. It and its many variants have been applied to many different types of optimization problems across several disciplines. There have been many attempts to study the convergence properties of PSO, but a rigorous and complete proof of its almost sure convergence to the global optimum is still lacking. We propose two modified versions of PSO and prove their convergence to the global optimum. We conduct simulation studies to gain further insights into their properties and evaluate their performance relative to PSO.

A hierarchical optimization approach to robust design of energy supply systems based on a mixed-integer linear model

In designing energy supply systems, designers should heighten the robustness in performance criteria against the uncertainty in energy demands. In this paper, a robust optimal design method using a hierarchical mixed-integer linear programming (MILP) method is proposed to maximize the robustness of energy supply systems under uncertain energy demands based on a mixed-integer linear model. A robust optimal design problem is formulated as a three-level min-max-min MILP one by expressing uncertain energy demands by intervals, evaluating the robustness in a performance criterion based on the minimax regret criterion, and considering relationships among integer design variables, uncertain energy demands, and integer and continuous operation variables. This problem is solved by evaluating upper and lower bounds for the minimum of the maximum regret of the performance criterion repeatedly outside, and evaluating lower and upper bounds for the maximum regret repeatedly inside. Different types of optimization problems are solved by applying a hierarchical MILP method developed for ordinary optimal design problems without and with its modifications. In a case study, the proposed approach is applied to the robust optimal design of a cogeneration system. Through the study, its validity and effectiveness are ascertained, and some features of the obtained robust designs are clarified.

Balancing broad and deep searches in evolutionary computation via a parallel zoning search

Computational time and solution precision are two major concerns in evolutionary computation (EC). Although high-performance computing techniques have been applied to reduce the computational time of meta-heuristic algorithms, it does not mean that they can assist meta-heuristic algorithms in finding a high-quality solution. Moreover, most of meta-heuristic algorithms may belong to the “depth-first” search method, thus achieving a tradeoff between the broad search and the deep search is a crucial objective in the EC. To alleviate the above problems, a parallel zoning search (PZS) strategy is proposed in the current study. In the PZS, the entire search space is divided into many small search spaces for improving the broad search capability of algorithms and reducing the problem complexity. Subsequently, selected meta-heuristic algorithms considered as deep search algorithms are employed to find a satisfactory solution in each search region. The effectiveness of the PZS integrated into six differential evolution (DE) variants is demonstrated on two commonly used test suites, i.e., IEEE CEC2014 and BBOB2012. Results suggest that the PZS is a highly competitive approach to solve different types of optimization problems, especially on complex optimization problems. Finally, the PZS incorporated into six DE variants is used to estimate parameters of a heavy oil thermal cracking model. Results indicate that the PZS is an effective and efficient tool to help selected algorithms solve actual industrial optimization problems.

A new artificial bee colony algorithm employing intelligent forager forwarding strategies

Artificial Bee Colony (ABC) algorithm that mimics the intelligent foraging behaviors of real honey bees has been successfully applied to different types of optimization problems in recent years. Actually, the main reason lying behind the high preference of the ABC algorithm is related with its good performance on solving difficult optimization problems due to the effective search mechanisms existing in a single cycle and easily-implementable bee phases. However, with the purpose of increasing the implementation simplicity and generalizing the principal concept of the algorithm, some significant behaviors of the real foraging bees are not closely simulated and integrated into the workflow of the ABC or tried to be managed by employing simple randomized or conditional operations. In this study, in order to increase the performance of ABC algorithm, the complex behavior of the foraging employed bees related with how they decide to pass through to the dance area and how long they stay on there for informing onlookers is modeled in detail and then a new variant of ABC called intelligent forager forwarding ABC for short iff-ABC is proposed. For analyzing the possible contributions of the intelligent forager forwarding strategy on the performance of the ABC algorithm, thirteen classical benchmark problems and fifteen computationally expensive benchmark problems presented at the CEC 2015 were tested. The results obtained from the experimental studies were compared with the results of the different meta-heuristics in addition to the well-known variants of the standard ABC algorithm. From the experimental studies, it was concluded that the intelligent forager forwarding strategy significantly improves the quality of the final solutions and the convergence speed of the ABC algorithm.

Balancing composite motion optimization

Meta-heuristic algorithms play an important role in the optimization field thanks to their robustness and programming simplicity. Many meta-heuristic methods have been devised in recent years. Inspired by nature, they usually simulate natural or human-specific phenomena in a better way. A large amount of them are based on complicated behaviors requiring several implementation steps and algorithm-specific control parameters, which impedes users and limits solutions to different types of optimization problems. Hence, designing effective simple and parameter-free optimization methods attracts much attention. In this paper, we propose a novel population-based optimization algorithm based on balancing composite motions (BCMO). The core idea is balancing composite motion properties of individuals in solution space. Equalizing global and local searches via a probabilistic selection model creates a movement mechanism of each individual. Four test suites selected in the literature, which vary from numerical benchmarks to practical problems, to demonstrate the performance of BCMO include: (1) 23 classical benchmark functions, (2) CEC 2005 benchmark functions, (3) CEC 2014 benchmark functions, and (4) 3 real engineering design problems. The statistical results reveal the promising performance and application of BCMO in a variety of optimization and practical problems with constrained and unknown search spaces.