Real-world Optimization Problems Research Articles

Optimal Design of Large-scale Dome Truss Structures with Multiple Frequency Constraints Using Success-history Based Adaptive Differential Evolution Algorithm

The success-history based adaptive differential evolution (SHADE) algorithm is an efficient modified version of the differential evolution (DE) algorithm, and it has been successfully applied to solve some real-world optimization problems. However, to the best of our knowledge, it has been rarely applied in the field of structural optimization. The optimal design of structures with frequency constraints is well known as a highly nonlinear and non-convex optimization problem with many local optima. In this paper, the SHADE algorithm is examined in the context of size optimization of large-scale truss structures with multiple frequency constraints. In SHADE, a historical memory of successful control parameter settings is used to guide the generation of new control parameters. In order to demonstrate the effectiveness and efficiency of SHADE, three truss optimization problems with multiple frequency constraints are presented. The three examples considered in this paper include a 600-bar single-layer dome-shaped truss, a 1180-bar single-layer dome-shaped truss, and a 1410-bar double-layer dome-shaped truss. The results obtained by the SHADE algorithm are presented and compared with the best-known results reported in the literature. Numerical results indicate the effectiveness and superior performance of SHADE over other algorithms in terms of solution accuracy and robustness. It is worth mentioning that in all the three cases considered, the optimal designs obtained by SHADE are the best ones reported in the literature so far. However, SHADE often requires fewer structural analyses than those required by the other algorithms.

Vibrating Particles System Algorithm: Overview, Modifications and Applications

Real-world problems are difficult enough to encourages academics to develop innovative, effective problem-solving methods. Generally, metaheuristics algorithms that are inspired by nature, biology, and physics have a flexibility and capacity to adapt to different situations, metaheuristics based on evolutionary computation algorithms have been widely employed to solve complicated, constrained/unconstrained, single/multiple objective, and Non-deterministic polynomial hard (NP-Hard) optimization problems.
 This paper describes Vibrating Particles System (VPS) as a Physics Based metaheuristic algorithm inspired by the free vibration of an under-damping objects for solving complex and real-world optimization problems. Since the appearance of VPS many modifications for improving the performance of the algorithm and has been applied to various Applications in several fields. At the end of this paper, the improvements are listed.

Marine predator inspired naked mole-rat algorithm for global optimization

This paper proposes a hybrid version of marine predator algorithm (MPA) and naked mole-rat algorithm (NMRA) to aggregate the strengths of both algorithms. The new proposed algorithm is named as MpNMRA and designed to overcome the inherent drawbacks of MPA (slow exploitation) and NMRA (limited exploration). The algorithm adds the basic structure of MPA to the worker phase of NMRA, while keeping all the major parameters of both the algorithm. The major parameters of both the algorithms are subjected to four different mutation strategies namely, exponential, linear, simulated annealing and logarithmic mutation strategies. The concept of simulated annealing-based mutation is found to be best for most of the parameters, whereas in some cases exponentially decreasing weights provide better results. Leveraging on the best mutation strategies for all the parameters, the proposed MpNMRA is tested on CEC2005, CEC2014 and CEC 2019 benchmark problems. The experimental results demonstrate that MpNMRA provides best results when compared to other algorithms in the literature on higher-dimensional problems. This work also considers solving three real-world optimization problems and training of a multi-layer perceptron using the proposed algorithm. Statistical results obtained from Wilcoxon’s rank-sum test, Freidman’s test and computational complexity further proves that the proposed algorithm is highly efficient and provide superior results.11The link of source-code will be added after publishing.

Ladybug Beetle Optimization algorithm: application for real-world problems.

In this paper, a novel optimization algorithm is proposed, called the Ladybug Beetle Optimization (LBO) algorithm, which is inspired by the behavior of ladybugs in nature when they search for a warm place in winter. The new proposed algorithm consists of three main parts: (1) determine the heat value in the position of each ladybug, (2) update the position of ladybugs, and (3) ignore the annihilated ladybug(s). The main innovations of LBO are related to both updating the position of the population, which is done in two separate ways, and ignoring the worst members, which leads to an increase in the search speed. Also, LBO algorithm is performed to optimize 78 well-known benchmark functions. The proposed algorithm has reached the optimal values of 73.3% of the benchmark functions and is the only algorithm that achieved the best solution of 20.5% of them. These results prove that LBO is substantially the best algorithm among other well-known optimization methods. In addition, two fundamentally different real-world optimization problems include the Economic-Environmental Dispatch Problem (EEDP) as an engineering problem and the Covid-19 pandemic modeling problem as an estimation and forecasting problem. The EEDP results illustrate that the proposed algorithm has obtained the best values in either the cost of production or the emission or even both, and the use of LBO for Covid-19 pandemic modeling problem leads to the least error compared to others.

Efficient evolutionary optimization using predictive auto-scaling in containerized environment

Solving complex real-world optimization problems is a computationally demanding task. To solve it efficiently and effectively, one must possess expert knowledge in various fields (problem domain knowledge, optimization, parallel and distributed computing) and appropriate expensive software and hardware resources. In this regard, we present a cloud-native, container-based distributed optimization framework that enables efficient and cost-effective optimization over platforms such as Amazon ECS/EKS, Azure AKS, and on-premise Kubernetes. The solution consists of dozens of microservices scaled out using a specially developed PETAS Auto-scaler based on predictive analytics. Existing schedulers, whether Kubernetes or commercial, do not take into account the specifics of optimization based on evolutionary algorithms. Therefore, their performance is not optimal in terms of results’ delivery time and cloud infrastructure costs. The proposed PETAS Auto-scaler elastically maintains an adequate number of worker pods following the exact pace dictated by the demands of the optimization process. We evaluate the proposed framework’s performance using two real-world computationally demanding optimizations. The first use case belongs to the manufacturing domain and involves optimization of the transportation pallets for train parts. The second use case belongs to the field of automated machine learning and includes neural architecture search and hyperparameter optimization. The results indicate an IaaS cost savings of up to 49% can be achieved, with almost unchanged result delivery time.

Search graph structure and its implications for multi-graph constrained routing and scheduling problems

Multi-graphs where several edges connect a pair of nodes are an important modelling approach for many real-world optimisation problems. The multi-graph structure is often based on infrastructure and available connections between nodes. In this study, we conduct case studies for a special type of constrained routing and scheduling problems. Using the airport ground movement problem as an example, we analyse how the number of parallel edges and their costs in multi-graph structure influence the quality of obtained solutions found by the routing algorithm. The results show that the number of parallel edges not only affects the computational complexity but also the number of trade-off solutions and the quality of the found solutions. An indicator is further proposed which can estimate when the multi-graph would benefit from a higher number of parallel edges. Furthermore, we show that including edges with dominated costs in the multi-graph can also improve the results in the presence of time window constraints. The findings pave the way to an informed approach to multi-graph creation for similar problems based on multi-graphs.

An Overview of Self-Adaptive Differential Evolution Algorithms with Mutation Strategy

Differential Evolution (DE) is a widely used global searching algorithm that solves real-world optimization problems. It is categorized as a stochastic parameter optimization method that has a broad spectrum of applications, notably neural networks, logistics, scheduling, and modeling. In practice, different optimization issues need different parameter settings. Due to DE simplicity, ease of implementation, and dependability, many scientists were interested in examining this algorithm. Nonetheless, the quality of DE and its variations are directly influenced by different mutation techniques and control parameter settings. In this paper, an overview and analogy of some algorithms that employ different mutation techniques will be illustrated. Additionally, a novel strategy that uses different mutation methods is proposed and compared with some existing strategies.

Moth Flame Optimization: Theory, Modifications, Hybridizations, and Applications.

The Moth flame optimization (MFO) algorithm belongs to the swarm intelligence family and is applied to solve complex real-world optimization problems in numerous domains. MFO and its variants are easy to understand and simple to operate. However, these algorithms have successfully solved optimization problems in different areas such as power and energy systems, engineering design, economic dispatch, image processing, and medical applications. A comprehensive review of MFO variants is presented in this context, including the classic version, binary types, modified versions, hybrid versions, multi-objective versions, and application part of the MFO algorithm in various sectors. Finally, the evaluation of the MFO algorithm is presented to measure its performance compared to other algorithms. The main focus of this literature is to present a survey and review the MFO and its applications. Also, the concluding remark section discusses some possible future research directions of the MFO algorithm and its variants.

Cε-LDE: A lightweight variant of differential evolution algorithm with combined ε constrained method and Lévy flight for constrained optimization problems

Differential evolution (DE) algorithm is popular to tackle real-world optimization problems. The standard DE, however, is not able to solve constrained optimization problems (COPs) for their complicated linear or nonlinear constraints. The transformation of constraints, which is realized via constraint handling technique, has a great impact on dealing with constrained algorithms. In this paper, a lightweight and efficient variant of DE named Cε-LDE is proposed to solve constrained single-objective optimization problems. This study firstly introduces a combined constraint handling method, which is designed based on the difference and relationship between two different ε constrained methods and balances infeasible solution and feasible solution with rules from the perspective of probability allocation. In addition, an extra control parameter is redefined in terms of different initial ε level in consideration of the complexity and diversity of COPs. On the other hand, DE evolves by opposition-based learning initialization and modifications on mutation operator and crossover rate selection, respectively. Mutation strategies frequently named rand/1 and best/1 are adopted and Lévy flight is added to the mutation strategy as a multiplier with scale factor F for a long jump. The crossover rate CR tends to be a larger or smaller stochastic value according to the pros and cons of the selected vector. A set of 28 problems under different dimension settings (D = 10, 30, 50 and 100) used for the CEC 2017 Competition is employed to evaluate the performance of the proposed Cε-LDE. The computational results demonstrate the effectiveness and superiority of the proposed combined ε constrained method. A comparative study of Cε-LDE with state-of-art algorithms is conducted on the obtained experimental results under the rules of CEC 2017 Competition. The ranking outcomes reveal that Cε-LDE is equipped with high competitiveness. Furthermore, the applications in several standard real-life engineering problems verify the effectiveness and practicability of the proposed scheme.

Artificial bee colony algorithm based on adaptive neighborhood topologies

During the past few years, many neighborhood-based ABC variants have been developed to utilize the valuable information of neighbors for guiding searches instead of using the best individual or elite individuals. However, neighbor selection is determined by the neighborhood topology, and different neighborhood topologies are suitable for different problems. Unfortunately, previous neighborhood-based ABC variants have often used a single type of neighborhood topology, which significantly affects algorithm performance. Hence, to take advantage of different neighborhood topologies, we propose a new neighborhood-based ABC variant using adaptive neighborhood topologies, called ABC-ANT. In ABC-ANT, to determine which type of neighborhood topology should be selected, the fitness distance correlation technique is first used to identify the feature of the fitness landscape for a given problem. Then, according to the identified feature, the most suitable neighborhood topology is adaptively selected, which is beneficial to adapt the search to the fitness landscape. Moreover, in ABC-ANT, the scout bee phase is modified by developing a dual-elite search strategy to save the search experience. Extensive experiments are conducted on two test suites, i.e., CEC2013 and CEC2017, and one real-world optimization problem, i.e., the dynamic economic dispatch problem. Seven ABC variants and six non-ABC variants are included in the performance comparison. The results verify that ABC-ANT has very competitive performance.

A comprehensive investigation on novel center-based sampling for large-scale global optimization

During the last decade, metaheuristic algorithms have been well-established approaches which are utilized for solving complex real-world optimization problems. The most metaheuristic algorithms uses stochastic strategies in their initialization phase as well as during their new candidate generation steps when there is no a-priori knowledge about the solution, which is a common valid assumption for any black-box optimization algorithm. In recent years, researchers have introduced a new concept called center-based sampling which can be utilized in any search component of the optimization process, but so far it mainly has been used just for population initialization. This novel concept clarifies that in a search space, the center point has a higher chance to be closer to an unknown solution compared to a random point, especially when the dimension of the search space increases. Thus, this concept helps the optimizer to find a better solution in a shorter time. In this paper, a comprehensive study has been conducted on the effect of center-based sampling to solve an optimization problem using three different levels of detailed investigation. These levels are as the follows: 1) considering no specific algorithm and no specific landscape (i.e., Monte-Carlo simulation); 2) considering a specific landscape but no specific algorithm (i.e., random search vs. center-based random search), and finally, 3) considering a specific algorithm and specific landscape which includes the proposing three different schemes for using center-based sampling scheme for solving Large-scale Global Optimization (LSGO) problems effectively. Furthermore, in this study, we seek to investigate the properties and capabilities of center-based sampling during optimization, which can be extended to utilize it in machine learning too, because optimization is a key role player in search and learning models. The proposed methods in this paper are evaluated on CEC 2013 LSGO benchmark functions and a real-world optimization problem, i.e., evolving ANN on two medical data sets. The experimental results confirm that center-based sampling has a crucial impact in improving the convergence rate of optimization/search algorithms when solving high-dimensional optimization problems.

A comprehensive performance analysis of meta-heuristic optimization techniques for effective organic rankine cycle design

Optimizing the operating parameters is of great importance to improve Organic Rankine Cycle (ORC) system efficiency. Nowadays, meta-heuristic algorithms are widely used to obtain fast and effective solutions. However, it is a difficult task to determine the most effective algorithm among dozens of available algorithms to solve the ORC design problem like many other real-world optimization problems. Moreover, defining a feasible solution and determining a method that can find this solution quickly and decisively is a major challenge. To overcome these challenges, a well-planned and comprehensive research is essential. In this article, a research consisting of two stages was conducted to determine the most effective meta-heuristic optimization methods that can find the optimum and feasible solutions of the ORC design problem in a stable and fast way. 31 algorithms selected among the most up-to-date and powerful meta-heuristic search algorithms in the literature were used in simulation studies. The data obtained were analyzed by using the non-parametric statistical test methods. The results show that TLABC, DE, and PSO algorithms are very successful in finding a feasible solution. In addition, the TLABC algorithm can find a feasible solution in a shorter time than its alternatives. The maximum net power output and the total cost of the system were calculated as 74.593 kW and 692,452 $, respectively for optimum design. Thus, the total cost per net power output of the ORC system was determined as 9283.066 $/kW.

A hybrid granular-evolutionary computing method for cooperative scheduling optimization on integrated energy system in steel industry

Integrated Energy System (IES) in steel industry, typically involving gas, heat and electricity, exhibits distributed nature and complex coupling relationship, which demands effective scheduling optimization to cooperatively utilize the multiple energy media. For this purpose, a Granular-Evolutionary Hybrid Computing (GEHC) framework is proposed in this study to solve the scheduling of IES as a Constrained Multi-Objective Problem (CMOP). More specifically, a Collaborative Fuzzy C-Means (CFCM) clustering model is firstly established, where the horizontal and vertical structures are well constructed to obtain information granules regarding the cooperative relationship among the units in different energy subsystems. Then, a Probability-based Granular Computing (PGrC) approach is proposed for the initial optimization of the IES scheduling, which is guided by the expert knowledge compacted in the information granules. To determine the collaborative parameters in CFCM that essentially controls the cooperation among the multiple energy media, as well as satisfying the complex practical constraints, a Multi-Objective Differential Evolution (MODE)-based method is proposed for further scheduling optimization. To evaluate the performance on cooperativity, convergency and diversity, the proposed GEHC and the compared methods that either has partial collaborations or use other optimization frameworks are applied to a real-world optimization problem. The experimental results demonstrate that the proposed GEHC performs superior to the other methods considering both the objective functions and performance indicators, which can be potentially helpful to achieve well-performed unmanned IES scheduling in steel industry.

An Improved Aquila Optimizer Based on Search Control Factor and Mutations

The Aquila Optimizer (AO) algorithm is a meta-heuristic algorithm with excellent performance, although it may be insufficient or tend to fall into local optima as as the complexity of real-world optimization problems increases. To overcome the shortcomings of AO, we propose an improved Aquila Optimizer algorithm (IAO) which improves the original AO algorithm via three strategies. First, in order to improve the optimization process, we introduce a search control factor (SCF) in which the absolute value decreasing as the iteration progresses, improving the hunting strategies of AO. Second, the random opposition-based learning (ROBL) strategy is added to enhance the algorithm’s exploitation ability. Finally, the Gaussian mutation (GM) strategy is applied to improve the exploration phase. To evaluate the optimization performance, the IAO was estimated on 23 benchmark and CEC2019 test functions. Finally, four real-world engineering problems were used. From the experimental results in comparison with AO and well-known algorithms, the superiority of our proposed IAO is validated.

Chaotic Wind Driven Optimization with Fitness Distance Balance Strategy

Wind driven optimization (WDO) is a meta-heuristic algorithm based on swarm intelligence. The original selection method makes it easy to converge prematurely and trap in local optima. Maintaining population diversity can solve this problem well. Therefore, we introduce a new fitness-distance balance-based selection strategy to replace the original selection method, and add chaotic local search with selecting chaotic map based on memory to further improve the search performance of the algorithm. A chaotic wind driven optimization with fitness-distance balance strategy is proposed, called CFDBWDO. In the experimental section, we find the optimal parameter settings for the proposed algorithm. To verify the effect of the algorithm, we conduct comparative experiments on the CEC 2017 benchmark functions. The experimental results denote that the proposed algorithm has superior performance. Compared with WDO, CFDBWDO can gradually converge in function optimization. We further verify the practicality of the proposed algorithm with six real-world optimization problems, and the obtained results are all better than other algorithms.

Boosting branch-and-bound MaxSAT solvers with clause learning

The Maximum Satisfiability Problem, or MaxSAT, offers a suitable problem solving formalism for combinatorial optimization problems. Nevertheless, MaxSAT solvers implementing the Branch-and-Bound (BnB) scheme have not succeeded in solving challenging real-world optimization problems. It is widely believed that BnB MaxSAT solvers are only superior on random and some specific crafted instances. At the same time, SAT-based MaxSAT solvers perform particularly well on real-world instances. To overcome this shortcoming of BnB MaxSAT solvers, this paper proposes a new BnB MaxSAT solver called MaxCDCL. The main feature of MaxCDCL is the combination of clause learning of soft conflicts and an efficient bounding procedure. Moreover, the paper reports on an experimental investigation showing that MaxCDCL is competitive when compared with the best performing solvers of the 2020 MaxSAT Evaluation. MaxCDCL performs very well on real-world instances, and solves a number of instances that other solvers cannot solve. Furthermore, MaxCDCL, when combined with the best performing MaxSAT solvers, solves the highest number of instances of a collection from all the MaxSAT evaluations held so far.

Dandelion Optimizer: A nature-inspired metaheuristic algorithm for engineering applications

This paper proposes a novel swarm intelligence bioinspired optimization algorithm, called the Dandelion Optimizer (DO), for solving continuous optimization problems. DO simulates the process of dandelion seed long-distance flight relying on wind, which is divided into three stages. In the rising stage, seeds raise in a spiral manner due to the eddies from above or drift locally in communities according to different weather conditions. In the descending stage, flying seeds steadily descend by constantly adjusting their direction in global space. In the landing stage, seeds land in randomly selected positions so that they grow. The moving trajectory of a seed in the descending stage and landing stage are described by Brownian motion and a Levy random walk. CEC2017 benchmark functions are utilized to evaluate the performance of DO, including the optimization accuracy, stability, convergence, and scalability, through a comparison with 9 well-known nature-inspired metaheuristic algorithms. Finally, the applicability of DO is verified by solving 4 real-world optimization problems. The experimental results indicate that the proposed DO method is a higher performing optimizer with outstanding iterative optimization and strong robustness compared with well-established algorithms. Source codes of DO are publicly available at https://ww2.mathworks.cn/matlabcentral/fileexchange/114680-dandelion-optimizer.

Performance analysis of distance metrics on the exploitation properties and convergence behaviour of the conventional firefly algorithm

The nature of the distance metric used to compare the span between two fireflies in conventional firefly algorithm can significantly enhance the exploitation properties of the algorithm and improve its convergence towards the optimum solution. Therefore, this research proposes several variants of the firefly algorithm based on different distance relations like Minkowski distance, Canberra distance, and Angular Cosine distance. To compare the performance of these variants, benchmark non-linear and non-convex objective functions are solved under the varying nature of the medium absorption coefficient and attractiveness constant. It is observed from detail analysis of results that Canberra distance provides optimal results for almost all of the benchmark functions. Furthermore, the importance of the distance metric for real-world optimization problems with very large or small magnitude of decision variables is also presented by solving a practical hydro thermal scheduling problem. It is also presented that the optimal set of parameters for a particular distance criterion may not always be optimal and better convergence results can be achieved by varying the distance metric to measure the length between the fireflies.

Estimation of distribution algorithms using Gaussian Bayesian networks to solve industrial optimization problems constrained by environment variables

Many real-world optimization problems involve two different subsets of variables: decision variables, and those variables which are not present in the cost function but constrain the solutions, and thus, must be considered during optimization. Thus, dependencies between and within both subsets of variables must be considered. In this paper, an estimation of distribution algorithm (EDA) is implemented to solve this type of complex optimization problems. A Gaussian Bayesian network is used to build an abstraction model of the search space in each iteration to identify patterns among the variables. As the algorithm is initialized from data, we introduce a new hyper-parameter to control the influence of the initial data in the decisions made during the EDA execution. The results show that our algorithm improves the cost function more than the expert knowledge does.

The Perils of Learning Before Optimizing

Formulating real-world optimization problems often begins with making predictions from historical data (e.g., an optimizer that aims to recommend fast routes relies upon travel-time predictions). Typically, learning the prediction model used to generate the optimization problem and solving that problem are performed in two separate stages. Recent work has showed how such prediction models can be learned end-to-end by differentiating through the optimization task. Such methods often yield empirical improvements, which are typically attributed to end-to-end making better error tradeoffs than the standard loss function used in a two-stage solution. We refine this explanation and more precisely characterize when end-to-end can improve performance. When prediction targets are stochastic, a two-stage solution must make an a priori choice about which statistics of the target distribution to model---we consider expectations over prediction targets---while an end-to-end solution can make this choice adaptively. We show that the performance gap between a two-stage and end-to-end approach is closely related to the \emph{price of correlation} concept in stochastic optimization and show the implications of some existing POC results for the predict-then-optimize problem. We then consider a novel and particularly practical setting, where multiple prediction targets are combined to obtain each of the objective function’s coefficients. We give explicit constructions where (1) two-stage performs unboundedly worse than end-to-end; and (2) two-stage is optimal. We use simulations to experimentally quantify performance gaps and identify a wide range of real-world applications from the literature whose objective functions rely on multiple prediction targets, suggesting that end-to-end learning could yield significant improvements.