Real-world Optimization Problems Research Articles

Slime Mould Algorithm Based on a Gaussian Mutation for Solving Constrained Optimization Problems

The slime mould algorithm may not be enough and tends to trap into local optima, low population diversity, and suffers insufficient exploitation when real-world optimization problems become more complex. To overcome the limitations of SMA, the Gaussian mutation (GM) with a novel strategy is proposed to enhance SMA and it is named as SMA-GM. The GM is used to increase population diversity, which helps SMA come out of local optima and retain a robust local search capability. Additionally, the oscillatory parameter is updated and incorporated with GM to set the balance between exploration and exploitation. By using a greedy selection technique, this study retains an optimal slime mould position while ensuring the algorithm’s rapid convergence. The SMA-GM performance was evaluated by using unconstrained, constrained, and CEC2022 benchmark functions. The results show that the proposed SMA-GM has a more robust capacity for global search, improved stability, a faster rate of convergence, and the ability to solve constrained optimization problems. Additionally, the Wilcoxon rank sum test illustrates that there is a significant difference between the optimization outcomes of SMA-GM and each compared algorithm. Furthermore, the engineering problem such as industrial refrigeration system (IRS), optimal operation of the alkylation unit problem, welded beam and tension/compression spring design problem are solved, and results prove that the proposed algorithm has a better optimization efficiency to reach the optimum value.

Improved Driving Training-Based Optimization Algorithm Using Levy Flight and Crowding Distance Techniques

This study presents an improved version of the Driving Training-Based Optimization (DTBO) algorithm, the Improved Driving Training-Based Optimization (IDTBO). The work addresses fundamental issues in selecting drivers and learners for the conventional DTBO, which substantially impact the algorithm's accuracy and convergence speed. Two significant improvements are proposed: including the crowding distance technique for more diverse driver and learner selection and incorporating the Levy Flight distribution for better exploration and local optima avoidance. The IDTBO's performance is evaluated using twelve benchmark functions, including unimodal and high-dimensional multimodal optimization functions. The results indicate that IDTBO performs exceptionally well, with more extraordinary exploitation ability on unimodal functions and consistent achievement of the global optima. The proposed IDTBO demonstrated exceptional exploration capabilities on high-dimensional multimodal functions and performed competitively with other algorithms in the literature. From six functions, the IDTBO obtained zero optimal values. Again, the rate of convergence analysis demonstrates that IDTBO finds optimal solutions in fewer iterations, demonstrating its capacity to balance exploration and exploitation. To assess the strength of the IDTBO in solving real-world problems, the improved DTBO is further tested on two practical benchmark engineering problems. The IDTBO again produced a competitive performance against other algorithms in the literature. The study shows that IDTBO is a valuable metaheuristic algorithm that can tackle various real-world optimization problems.

Secretary bird optimization algorithm: a new metaheuristic for solving global optimization problems

This study introduces a novel population-based metaheuristic algorithm called secretary bird optimization algorithm (SBOA), inspired by the survival behavior of secretary birds in their natural environment. Survival for secretary birds involves continuous hunting for prey and evading pursuit from predators. This information is crucial for proposing a new metaheuristic algorithm that utilizes the survival abilities of secretary birds to address real-world optimization problems. The algorithm's exploration phase simulates secretary birds hunting snakes, while the exploitation phase models their escape from predators. During this phase, secretary birds observe the environment and choose the most suitable way to reach a secure refuge. These two phases are iteratively repeated, subject to termination criteria, to find the optimal solution to the optimization problem. To validate the performance of SBOA, experiments were conducted to assess convergence speed, convergence behavior, and other relevant aspects. Furthermore, we compared SBOA with 15 advanced algorithms using the CEC-2017 and CEC-2022 benchmark suites. All test results consistently demonstrated the outstanding performance of SBOA in terms of solution quality, convergence speed, and stability. Lastly, SBOA was employed to tackle 12 constrained engineering design problems and perform three-dimensional path planning for Unmanned Aerial Vehicles. The results demonstrate that, compared to contrasted optimizers, the proposed SBOA can find better solutions at a faster pace, showcasing its significant potential in addressing real-world optimization problems.

Fractional-Order Water Flow Optimizer

The water flow optimizer (WFO) is the latest swarm intelligence algorithm inspired by the shape of water flow. Its advantages of simplicity, efficiency, and robust performance have motivated us to further enhance it. In this paper, we introduce fractional-order (FO) technology with memory properties into the WFO, called fractional-order water flow optimizer (FOWFO). To verify the superior performance and practicality of FOWFO, we conducted comparisons with nine state-of-the-art algorithms on benchmark functions from the IEEE Congress on Evolutionary Computation 2017 (CEC2017) and four real-world optimization problems with large dimensions. Additionally, tuning adjustments were made for two crucial parameters within the fractional-order framework. Finally, an analysis was performed on the balance between exploration and exploitation within FOWFO and its algorithm complexity.

A study on the solution of interval linear fractional programming problem

Interval linear fractional programming problem (ILFPP) approaches uncertain-ties in real-world systems such as business, manufacturing, finance, and eco-nomics. In this study, we propose solving the interval linear fractional pro-gramming (ILFP) problem using interval arithmetic. Further, to construct the problem, a suitable variable transformation is used to form an equivalent ILP problem, and a new algorithm is depicted to obtain the optimal solution with-out converting the problem into its conventional form. This paper compares the range, solutions, and approaches of ILFP with fuzzy linear fractional pro-gramming (FLFP) in solving real-world optimization problems. The illustrated numerical examples show a better range of interval solutions on practical appli-cations of ILFPs and uncertain parameters.

WOA: Wombat Optimization Algorithm for Solving Supply Chain Optimization Problems

Supply Chain (SC) Optimization is a key activity in today’s industry with the goal of increasing operational efficiency, reducing costs, and improving customer satisfaction. Traditional optimization methods often struggle to effectively use resources while handling complex and dynamic Supply chain networks. This paper introduces a novel biomimetic metaheuristic algorithm called the Wombat Optimization Algorithm (WOA) for supply chain optimization. This algorithm replicates the natural behaviors observed in wombats living in the wild, particularly focusing on their foraging tactics and evasive maneuvers towards predators. The theory of WOA is described and then mathematically modeled in two phases: (i) exploration based on the simulation of wombat movements during foraging and trying to find food and (ii) exploitation based on simulating wombat movements when diving towards nearby tunnels to defend against its predators. The effectiveness of WOA in addressing optimization challenges is assessed by handling the CEC 2017 test suite across various problem dimensions, including 10, 30, 50, and 100. The findings of the optimization indicate that WOA demonstrates a strong ability to effectively manage exploration and exploitation, and maintains a balance between them throughout the search phase to deliver optimal solutions for optimization problems. A total of twelve well-known metaheuristic algorithms are called upon to test their performance against WOA in the optimization process. The outcomes of the simulations reveal that WOA outperforms the other algorithms, achieving superior results across most benchmark functions and securing the top ranking as the most efficient optimizer. Using a Wilcoxon rank sum test statistical analysis, it has been proven that WOA outperforms other algorithms significantly. WOA is put to the test with twenty-two constrained optimization problems from the CEC 2011 test suite and four engineering design problems to showcase its ability to solve real-world optimization problems. The results of the simulations demonstrate that WOA excels in real-world applications by delivering superior solutions and outperforming its competitors.

Actively learning costly reward functions for reinforcement learning

Transfer of recent advances in deep reinforcement learning to real-world applications is hindered by high data demands and thus low efficiency and scalability. Through independent improvements of components such as replay buffers or more stable learning algorithms, and through massively distributed systems, training time could be reduced from several days to several hours for standard benchmark tasks. However, while rewards in simulated environments are well-defined and easy to compute, reward evaluation becomes the bottleneck in many real-world environments, e.g. in molecular optimization tasks, where computationally demanding simulations or even experiments are required to evaluate states and to quantify rewards. When ground-truth evaluations become orders of magnitude more expensive than in research scenarios, direct transfer of recent advances would require massive amounts of scale, just for evaluating rewards rather than training the models. We propose to alleviate this problem by replacing costly ground-truth rewards with rewards modeled by neural networks, counteracting non-stationarity of state and reward distributions during training with an active learning component. We demonstrate that using our proposed method, it is possible to train agents in complex real-world environments orders of magnitudes faster than would be possible when using ground-truth rewards. By enabling the application of RL methods to new domains, we show that we can find interesting and non-trivial solutions to real-world optimization problems in chemistry, materials science and engineering. We demonstrate speed-up factors of 50–3000 when applying our approach to challenges of molecular design and airfoil optimization.

Efficient implicit constraint handling approaches for constrained optimization problems

Many real-world optimization problems, particularly engineering ones, involve constraints that make finding a feasible solution challenging. Numerous researchers have investigated this challenge for constrained single- and multi-objective optimization problems. In particular, this work extends the boundary update (BU) method proposed by Gandomi and Deb (Comput. Methods Appl. Mech. Eng. 363:112917, 2020) for the constrained optimization problem. BU is an implicit constraint handling technique that aims to cut the infeasible search space over iterations to find the feasible region faster. In doing so, the search space is twisted, which can make the optimization problem more challenging. In response, two switching mechanisms are implemented that transform the landscape along with the variables to the original problem when the feasible region is found. To achieve this objective, two thresholds, representing distinct switching methods, are taken into account. In the first approach, the optimization process transitions to a state without utilizing the BU approach when constraint violations reach zero. In the second method, the optimization process shifts to a BU method-free optimization phase when there is no further change observed in the objective space. To validate, benchmarks and engineering problems are considered to be solved with well-known evolutionary single- and multi-objective optimization algorithms. Herein, the proposed method is benchmarked using with and without BU approaches over the whole search process. The results show that the proposed method can significantly boost the solutions in both convergence speed and finding better solutions for constrained optimization problems.

Reinforcement learning-assisted evolutionary algorithm: A survey and research opportunities

Evolutionary algorithms (EA), a class of stochastic search methods based on the principles of natural evolution, have received widespread acclaim for their exceptional performance in various real-world optimization problems. While researchers worldwide have proposed a wide variety of EAs, certain limitations remain, such as slow convergence speed and poor generalization capabilities. Consequently, numerous scholars actively explore improvements to algorithmic structures, operators, search patterns, etc., to enhance their optimization performance. Reinforcement learning (RL) integrated as a component in the EA framework has demonstrated superior performance in recent years. This paper presents a comprehensive survey on integrating reinforcement learning into the evolutionary algorithm, referred to as reinforcement learning-assisted evolutionary algorithm (RL-EA). We begin with the conceptual outlines of reinforcement learning and the evolutionary algorithm. We then provide a taxonomy of RL-EA. Subsequently, we discuss the RL-EA integration method, the RL-assisted strategy adopted by RL-EA, and its applications according to the existing literature. The RL-assisted procedure is divided according to the implemented functions including solution generation, learnable objective function, algorithm/operator/sub-population selection, parameter adaptation, and other strategies. Additionally, different attribute settings of RL in RL-EA are discussed. In the applications of RL-EA section, we also demonstrate the excellent performance of RL-EA on several benchmarks and a range of public datasets to facilitate a quick comparative study. Finally, we analyze potential directions for future research. This survey serves as a rich resource for researchers interested in RL-EA as it overviews the current state-of-the-art and highlights the associated challenges. By leveraging this survey, readers can swiftly gain insights into RL-EA to develop efficient algorithms, thereby fostering further advancements in this emerging field.

Optimizing grid-connected PV systems with novel super-twisting sliding mode controllers for real-time power management

Over the past years, the use of renewable energy sources (RESs) has grown significantly as a means of providing clean energy to counteract the devastating effects of climate change. Reducing energy costs and pollution have been the primary causes of the rise in solar photovoltaic (PV) system integrations with the grid in recent years. A load that is locally connected to a GCPV requires both active and reactive power control. In order to control both active and reactive power, MAs and advanced controllers are essential. Researchers have used one of the recently developed MAs, known as the CAOA, which is based on mathematical arithmetic operators to tackle a few real-world optimization problems. Some disadvantages of CAOA include its natural tendency to converge to a local optimum and its limited capacity for exploration. By merging the PSO and CAOA methodologies, this article suggests the IAOA. To show how applicable IAOA is, its performance has been evaluated using four benchmark functions. The implementation of an IAOA-based ST-SMC for active and reactive power control is addressed in this article, which offers an innovative approach of research. In comparison to PSO-based ST-SMC and CAOA-based ST-SMC, the proposed IAOA-based ST-SMC appears to be superior, with settling time for active and reactive power control at a minimum of 0.01012 s and 0.5075 s. A real-time OPAL-RT 4510 simulator is used to validate the performance results of a 40 kW GCPV system after it has been investigated in the MATLAB environment.

A comparison of alternative models for solving a non-linear single plant Hydro Unit Commitment problem

A wide range of real world optimization problems involves continuous decisions and non-linearities. Each non-linear component of such problems can be modeled either linearly or non-linearly, considering or not additional integer variables. This results into different modeling choices that can drastically impact the solution time and quality. In this paper, we evaluate representative modeling alternatives, including common models from the literature as well as new models featuring less common functions. The single plant Hydro Unit Commitment problem (1-HUC) is the considered non-linear use case. Among the non-linearities of the 1-HUC, we focus on those involved in the power production, more precisely the head effect and the turbines efficiency. The power is defined as a two-dimensional non-convex and non-concave function of the water flow and head decision variables, the latter being itself a one-dimensional concave function of the turbined volume. We consider both the general problem and a common special case, assuming that the water head is fixed. Several available solvers are used for each non-linear model and the best virtual solver is retained to focus on the model capabilities rather than on the solver performance. Based on the numerical experiments, three models stand out as the most efficient in terms of computational time, solution quality and feasibility, sometimes in a counter-intuitive manner. For each of these models, a solver is highlighted as the most adequate.

Modified genetic algorithm to solve worker assignment problem with time windows

In recent years, the demand for electronic products has been increasing rapidly. T mounting technology (SMT) line is one of the production areas for electronic products, directly affecting this situation. In an SMT line, multiple machines mount electronic parts to the board. The worker must complete work when the parts used in these machines are within the remaining parts available for replacement. When a worker fails to replace parts at the right time, the production line stops, and delays occur. Besides, there may be a designated worker who should be assigned to each task. In the current situation, workers’ work procedures are not optimized, so they should schedule work procedures for each worker. This problem is called Worker Assignment Problem with Time Window (WAPTW). This paper proposes a method to solve WAPTW called Genetic Algorithm with Local Restriction (GALR). GALR combines a genetic algorithm (GA) and local search with local restriction. This paper’s main contribution is introducing WAPTW as a novel real-world optimization problem in an electricity company, its mathematical formulation, and a proposed GALR to solve WAPTW. The experiment shows that the proposed method could yield the best result in real-world WAPTW compared with other methods.

Dendritic Growth Optimization: A Novel Nature-Inspired Algorithm for Real-World Optimization Problems.

In numerous scientific disciplines and practical applications, addressing optimization challenges is a common imperative. Nature-inspired optimization algorithms represent a highly valuable and pragmatic approach to tackling these complexities. This paper introduces Dendritic Growth Optimization (DGO), a novel algorithm inspired by natural branching patterns. DGO offers a novel solution for intricate optimization problems and demonstrates its efficiency in exploring diverse solution spaces. The algorithm has been extensively tested with a suite of machine learning algorithms, deep learning algorithms, and metaheuristic algorithms, and the results, both before and after optimization, unequivocally support the proposed algorithm's feasibility, effectiveness, and generalizability. Through empirical validation using established datasets like diabetes and breast cancer, the algorithm consistently enhances model performance across various domains. Beyond its working and experimental analysis, DGO's wide-ranging applications in machine learning, logistics, and engineering for solving real-world problems have been highlighted. The study also considers the challenges and practical implications of implementing DGO in multiple scenarios. As optimization remains crucial in research and industry, DGO emerges as a promising avenue for innovation and problem solving.

An Interactive Knowledge-Based Multiobjective Evolutionary Algorithm Framework for Practical Optimization Problems

Experienced users often have useful knowledge and intuition in solving real-world optimization problems. User knowledge can be formulated as inter-variable relationships to assist an optimization algorithm in finding good solutions faster. Such inter-variable interactions can also be automatically learned from high-performing solutions discovered at intermediate iterations in an optimization run – a process called innovization. These relations, if vetted by the users, can be enforced among newly generated solutions to steer the optimization algorithm towards practically promising regions in the search space. Challenges arise for large-scale problems where the number of such variable relationships may be high. This paper proposes an interactive knowledge-based evolutionary multi-objective optimization () framework that extracts hidden variable-wise relationships as knowledge from evolving high-performing solutions, shares them with users to receive feedback, and applies them back to the optimization process to improve its effectiveness. The knowledge extraction process uses a systematic and elegant graph analysis method which scales well with number of variables. The working of the proposed is demonstrated on three large-scale real-world engineering design problems. The simplicity and elegance of the proposed knowledge extraction process and achievement of high-performing solutions quickly indicate the power of the proposed framework. The results presented should motivate further such interaction-based optimization studies for their routine use in practice.

Bayesian Optimisation for Constrained Problems

Many real-world optimisation problems such as hyperparameter tuning in machine learning or simulation-based optimisation can be formulated as expensive-to-evaluate black-box functions. A popular approach to tackle such problems is Bayesian optimisation, which builds a response surface model based on the data collected so far, and uses the mean and uncertainty predicted by the model to decide what information to collect next. In this paper, we propose a generalisation of the well-known Knowledge Gradient acquisition function that allows it to handle constraints. We empirically compare the new algorithm with four other state-of-the-art constrained Bayesian optimisation algorithms and demonstrate its superior performance. We also prove theoretical convergence in the infinite budget limit.

Differential evolution with evolutionary scale adaptation

The performance of differential evolution (DE) algorithm heavily depends on the evolutionary scale, which is controlled by the generation operations including mutation, crossover and the control parameters including mutation factor and crossover rate. Adjusting the evolutionary scale to suit different types of problems is a critical yet challenging open question in DE research. To efficiently address this issue, this paper proposes a novel DE based on evolutionary scale adaptation, termed as ESADE. First, a successful scale estimation mechanism is proposed to measure the appropriate evolutionary scale by utilizing the successful evolutionary feedback from the solution space provided by the trial vectors and the target vectors. With the appropriate evolutionary scale, an evolutionary scale adaptation mechanism pre-selects the closest or the farthest trial vector from each target vector, which corresponds to a small or large evolutionary scale respectively to match the search requirements of different evolutionary stages. The effectiveness of the ESA method is demonstrated by performance comparisons with each single baseline strategy, state-of-the-art DEs and state-of-the-art multi-strategy methods on 29 benchmark functions with three dimensionalities. Further applications on several real-world optimization problems also reveal the competitive performance of ESADE.

Boosting aquila optimizer by marine predators algorithm for combinatorial optimization

Abstract In this study, an improved version of aquila optimizer (AO) known as EHAOMPA has been developed by using the marine predators algorithm (MPA). MPA is a recent and well-behaved optimizer with a unique memory saving and fish aggregating devices mechanism. At the same time, it suffers from various defects such as inadequate global search, sluggish convergence, and stagnation of local optima. However, AO has contented robust global exploration capability, fast convergence speed, and high search efficiency. Thus, the proposed EHAOMPA aims to complement the shortcomings of AO and MPA while bringing new features. Specifically, the representative-based hunting technique is incorporated into the exploration stage to enhance population diversity. At the same time, random opposition-based learning is introduced into the exploitation stage to prevent the optimizer from sticking to local optima. This study tests the performance of EHAOMPA’s on 23 standard mathematical benchmark functions, 29 complex test functions from the CEC2017 test suite, six constrained industrial engineering design problems, and a convolutional neural network hyperparameter (CNN-hyperparameter) optimization for Corona Virus Disease 19 (COVID-19) computed tomography-image detection problem. EHAOMPA is compared with four existing optimization algorithm types, achieving the best performance on both numerical and practical issues. Compared with other methods, the test function results demonstrate that EHAOMPA exhibits a more potent global search capability, a higher convergence rate, increased accuracy, and an improved ability to avoid local optima. The excellent experimental results in practical problems indicate that the developed EHAOMPA has great potential in solving real-world optimization problems. The combination of multiple strategies can effectively improve the performance of the algorithm. The source code of the EHAOMPA is publicly available at https://github.com/WangShuang92/EHAOMPA.

Multi-objective non-linear programming problem with rough interval parameters: an application in municipal solid waste management

In dealing with the real-world optimization problems, a decision-maker has to frequently face the ambiguity and hesitancy due to various uncontrollable circumstances. Rough set theory has emerged as an indispensable tool for representing this ambiguity because of its characteristic of incorporating agreement and understanding of all the involved specialists and producing more realistic conclusions. This paper studies an application of the rough set theory for a multi-objective non-linear programming problem that originates for the management of solid wastes. Municipal solid waste management is a global problem that affects every country. Because of the poor waste management system in many nations, the bulk of municipal solid waste is disposed of in open landfills with no recovery mechanism. Hence, an effective and long term waste management strategy is the demand of the day. This research offers an incinerating, composting, recycling, and disposing system for the long-term management of the municipal solid waste. A model for the municipal solid waste management with the goal of minimizing the cost of waste transportation, cost of waste treatment and maximizing the revenue generated from various treatment facilities is developed under rough interval environment. To tackle the conflicting nature of different objectives, an approach is proposed that gives the optimistic and pessimistic views of the decision-maker for optimizing the proposed model. Also, the biasness/preference of the decision-maker for a specific objective is handled by establishing the respective non-linear membership and non-membership functions instead of the linear ones. Finally, to demonstrates the practicality of the proposed methodology, a case study is solved and the obtained Pareto-optimal solution has been compared to those obtained by the existing approaches.

An evolutionary algorithm based on fully connected weight networks for mixed-variable multi-objective optimization

Multi-objective optimization research has mostly focused on continuous-variable problems. However, real-world optimization problems often involve multiple types of variables (continuous, integer, and discrete) and multiple conflicting optimization objectives, called mixed-variable multi-objective optimization problems (MVMOPs). Discrete variables make the decision space of the problem discrete. In contrast, while different types of variables need different treatments by the evolutionary algorithm, which poses a challenge to the efficient search of the evolutionary algorithm. Therefore, we propose an evolutionary algorithm based on a fully connected weight network (FCWNEA). The fully connected network structure characterizes the entire decision space, the node access count records the frequency of visits to the node, and the weights of connections and the activity of variables estimate the distribution of the decision space. This information assists in generating offspring solutions. To evaluate the performance of the proposed algorithm, we conduct empirical experiments on different types of problems. The results show that the proposed algorithm has a significant advantage in mixed-variable multi-objective problems. Moreover, the proposed algorithm is also quite competitive in continuous problems and can better handle the correlation between variables in optimization problems.

High-Dimensional Multi-Objective Bayesian Optimization With Block Coordinate Updates: Case Studies in Intelligent Transportation System

Many transportation system problems can be formulated as high-dimensional expensive multi-objective problems. They are challenging for Gaussian process-based Bayesian optimization methods to find the Pareto fronts due to the curse of dimensionality and the boundary issue in the acquisition function optimization. This paper presents a multi-objective Bayesian optimization method with block coordinate updates, Block-MOBO, to solve high-dimensional expensive multi-objective problems. Block-MOBO first partitions the decision variable space into different blocks, each of which includes a low-dimensional multi-objective problem. At each iteration, one block is considered and the decision variables not in this block are approximated by context-vector generation embedded with the Pareto prior knowledge thus promoting convergence. To tackle the boundary issue, we present <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> -greedy acquisition function in a Bayesian and multi-objective fashion, which recommends candidates either from the exploitation-exploration trade-off perspective or with probability <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> from the Pareto dominance relationship perspective. We verify the effectiveness of Block-MOBO by comparing it with other multi-objective Bayesian methods on two real-world optimization problems in transportation system and three multi-objective synthetic test suites. The experimental results show that Block-MOBO can find more evenly distributed and non-dominated solutions in the whole search space with lower complexity compared with other state-of-the-art approaches. Our analyses illustrate that block coordinate updates and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula> -greedy acquisition function contribute to computational complexity reduction and convergence-diversity trade-offs, respectively.