Real-world Optimization Problems Research Articles

Revisiting the performance of evolutionary algorithms

The advent of numerical computational approaches permits evolutionary algorithms (EAs) to solve complex, real-world engineering problems. The additional modification or hybridization of such EAs in academic research and application demonstrates improved performance for domain-specific challenges. However, developing a new algorithm or comparison and selection of existing EAs for challenges in the field of optimization is relatively unexplored. The performance of different well-established algorithms is, therefore, investigated in this work. The selection of algorithms using nonparametric tests encompasses different categories to include- Genetic Algorithm, Particle Swarm Optimization, Harmony Search Algorithm, Cuckoo Search Algorithm, Bat Algorithm, Firefly algorithm, Differential Evolution, and Artificial Bee Colony. These algorithms are applied to solve test functions, including unconstrained, constrained, industry specific problems, CEC 2011 real world optimization problems and selected CEC 2013 benchmark test functions. The three distinct performance metrics, namely, efficiency, reliability, and quality of solution derived using the quantitative attributes are provided to evaluate the performance of the employed EAs. The categorical assignment of performance attributes helps to compare different algorithms for a specific optimization problem while the performance metrics are useful to provide the common platform for new or hybrid EA development.

An Enhancing Differential Evolution Algorithm with a Rank-Up Selection: RUSDE

Recently, the differential evolution (DE) algorithm has been widely used to solve many practical problems. However, DE may suffer from stagnation problems in the iteration process. Thus, we propose an enhancing differential evolution with a rank-up selection, named RUSDE. First, the rank-up individuals in the current population are selected and stored into a new archive; second, a debating mutation strategy is adopted in terms of the updating status of the current population to decide the parent’s selection. Both of the two methods can improve the performance of DE. We conducted numerical experiments based on various functions from CEC 2014, where the results demonstrated excellent performance of this algorithm. Furthermore, this algorithm is applied to the real-world optimization problem of the four-bar linkages, where the results show that the performance of RUSDE is better than other algorithms.

A branch-and-Benders-cut algorithm for a bi-objective stochastic facility location problem

In many real-world optimization problems, more than one objective plays a role and input parameters are subject to uncertainty. In this paper, motivated by applications in disaster relief and public facility location, we model and solve a bi-objective stochastic facility location problem. The considered objectives are cost and covered demand, where the demand at the different population centers is uncertain but its probability distribution is known. The latter information is used to produce a set of scenarios. In order to solve the underlying optimization problem, we apply a Benders’ type decomposition approach which is known as the L-shaped method for stochastic programming and we embed it into a recently developed branch-and-bound framework for bi-objective integer optimization. We analyze and compare different cut generation schemes and we show how they affect lower bound set computations, so as to identify the best performing approach. Finally, we compare the branch-and-Benders-cut approach to a straight-forward branch-and-bound implementation based on the deterministic equivalent formulation.

Effect of parametric enhancements on naked mole-rat algorithm for global optimization

Naked mole-rat algorithm (NMRA) is a new swarm intelligence technique based on the mating patterns of NMRs present in nature. The algorithm though is very simple and linear in nature but suffers from poor exploration during the initial stages and poor exploitation towards the end. Thus to overcome these problems and estimate the effect of basic parameters of NMRA, six new inertia weight strategies and five new mutation operators have been employed. After careful investigation, a new Levy mutated NMRA (LNMRA) is proposed. The new algorithm employs combined properties of inertia weights and mutation operators altogether. For performance evaluation, the proposed algorithms are subjected to variable initial population and dimension sizes and testing is done on CEC 2005, CEC 2014 benchmark problems and real world optimization problem of dual band-notched ultra-wideband (UWB) antenna design. Experimental and statistical results show that the proposed LNMRA is better with respect to other algorithms under comparison.

Joint Estimation and Robustness Optimization

Many real-world optimization problems have input parameters estimated from data whose inherent imprecision can lead to fragile solutions that may impede desired objectives and/or render constraints infeasible. We propose a joint estimation and robustness optimization (JERO) framework to mitigate estimation uncertainty in optimization problems by seamlessly incorporating both the parameter estimation procedure and the optimization problem. Toward that end, we construct an uncertainty set that incorporates all of the data, and the size of the uncertainty set is based on how well the parameters are estimated from that data when using a particular estimation procedure: regressions, the least absolute shrinkage and selection operator, and maximum likelihood estimation (among others). The JERO model maximizes the uncertainty set’s size and so obtains solutions that—unlike those derived from models dedicated strictly to robust optimization—are immune to parameter perturbations that would violate constraints or lead to objective function values exceeding their desired levels. We describe several applications and provide explicit formulations of the JERO framework for a variety of estimation procedures. To solve the JERO models with exponential cones, we develop a second-order conic approximation that limits errors beyond an operating range; with this approach, we can use state-of-the-art second-order conic programming solvers to solve even large-scale convex optimization problems. This paper was accepted by J. George Shanthikumar, Management Science Special Section on Data-Driven Prescriptive Analytics.

A gravitational search algorithm with hierarchy and distributed framework

Gravitational search algorithm is an effective population-based algorithm. It simulates the law of gravity to implement the interaction among particles. Although it can effectively optimize many problems, it generally suffers from premature convergence and low search capability. To address these limitations, a gravitational search algorithm with hierarchy and distributed framework is proposed. A distributed framework randomly groups several subpopulations and a three-layered hierarchy manages them. Communication among subpopulations finally enhances the search performance. Experiments discuss parameters and strategies of the proposed algorithm. Comparison between it and sixteen state-of-the-art algorithms demonstrates its superior performance. It also shows the practicality for two real-world optimization problems.

Feasibility-ratio based sequencing for computationally efficient constrained optimization

Real world optimization problems typically involve constraints that must be satisfied for a design to be viable. Such constraints could represent physical limitations on induced behavior such as stress, displacement, temperature etc., or other practical limitations such as cost, geometry, manufacturability, etc. Constraint handling is therefore an active area of research, and a number of approaches have been proposed in the literature to be used with evolutionary algorithms to solve constrained optimization problems. Most approaches assume that the objective and constraints are simultaneously evaluated, and counted together as one evaluation as far as computation budget is concerned. However, in practical applications, there could be situations where the constraints and the objective can be independently evaluated (e.g., using different analyses). Therefore, it is worthwhile exploring if one can forego evaluation of certain constraints or the objective to save computational cost without misleading the search owing to insufficient information. Towards this end, the main focus of this study is to deal with a partial evaluation paradigm. We propose a feasibility-ratio based sequencing for partial evaluation of solutions during the evolutionary search. A lexicographic ranking approach is used for ordering the partially evaluated solutions. To balance the evaluation cost and information gain near constraint boundaries, a dynamic feasibility control technique is incorporated. A number of variants are systematically constructed to demonstrate the efficacy of partial evaluation and proposed sequencing approach. An extensive numerical study is conducted to evaluate the approach on a range of constraint problems, which confirms its competence.

Chaotic Simulator for Bilevel Optimization of Virtual Machine Placements in Cloud Computing

The drastic increase in engineering system complexity has spurred the development of highly efficient optimization techniques. Many real-world optimization problems have been identified as bilevel/multilevel as well as multiobjective. The primary aim of this work is to present a framework to tackle the bilevel virtual machine (VM) placement problem in cloud systems. This is done using the coupled map lattice (CML) approach in conjunction with the Stackelberg game theory and weighted-sum frameworks. The VM placement problem was modified from the original multiobjective (MO) problem to an MO bilevel formulation to make it more realistic albeit more complicated. Additionally comparative analysis on the performance of the CML approach was carried out against the particle swarm optimization method. A new bilevel metric called the cascaded hypervolume indicator is introduced and applied to measure the dominance of the solutions produced by both methods. Detailed analysis on the computational results is presented.

Resource planning in optical OFDM networking with traffic grooming technique

Development of natural computation methods brought a new paradigm in solving real-world optimization problems, namely metaheuristic methods. Metaheuristics based on principles of swarm intelligence are currently widely considered by the research community and engineers in solving a whole range of intractable problems related to network planning and operating problems. Swarm intelligence as the discipline of artificial intelligence investigates individuals’ actions in multi-agent systems. With the intention to show that metaheuristics could be successfully applied in telecommunications, we used Bee Colony Optimization (BCO) metaheuristic in solving the planning and dimensioning problems in optical networking. BCO relies on principles of bee swarm intelligence. 5G generation of optical networking brings the opportunity to a network to be elastic or flexible, i.e. the resources are occupied according to bandwidth on demand. To save network resources, such as spectrum or transmitters, various traffic engineering techniques could be applied. Our focus of interest is the traffic grooming technique applied at the optical layer. Incorporating the grooming technique into the BCO optimization logic, we proposed the model for minimizing the number of transmitters by maximizing its capacity utilization. The results indicate that by applying the grooming technique a significant number of transmitters could be saved and accordingly, power efficiency could be improved.

Harris hawks optimization: a comprehensive review of recent variants and applications

Harris hawks optimizer (HHO) has received widespread attention among researchers in terms of the performance, quality of results, and its acceptable convergence in dealing with different applications in real-world problems. This increased interest led to the emergence of many versions of HHO applied to various optimization problems in different fields. Therefore, this study aims to identify, retrieve, summarize, and analyze the critical studies related to the development of HHO. For this aim, we applied a review methodology. The applied methodology led to identified and selection of 69 related studies from different electronic sources. The review result revealed that although HHO algorithm is still in the infant stage, its superiority over several well-established metaheuristic algorithms in terms of speed and accuracy for addressing various benchmark problems and tackling several real-world optimization problems has been clearly observed. The HHO algorithm was evaluated, and its strengths and weaknesses were discussed. This review not only suggested possible future directions in this domain but also serves as a comprehensive source of information about HHO and HHO variants for future researchers due to the inclusion of charts and tabular comparison across a wide variety of attributes. A public website supports open access to this research and also source codes of the HHO in a different language and its supplementary materials at https://aliasgharheidari.com/HHO.html .

An enhanced opposition-based Salp Swarm Algorithm for global optimization and engineering problems

Real-world optimization problems need methods and techniques to explore search space and avoid local optima in order to find the best solutions. Salp Swarm Algorithm (SSA) is a novel algorithm which mimics the behavior of Salps during foraging and navigation in the ocean. Unfortunately, like other similar algorithms, SSA may fail in avoiding local optima and have a slow convergence curve. In this work, a novel version of SSA named OBSSA is introduced which is depends on Opposition-Based Learning (OBL) Strategy. The proposed algorithm consists of 2 stages: in the first stage where OBL is used to enhance the initialization stage and in the second stage where OBL is used in the updating process of the population in every iteration. To investigate the performance of OBSSA, 30 functions from IEEE Congress on Evolutionary Computation (IEEE CEC2014) and 6 engineering problems are tested and compared with 8 state-of-art algorithms. Moreover, non-parametric test Wilcoxon’s rank-sum is performed at 5% level to test the significant of the obtained results between OBSSA and SSA. The results show that OBSSA can get competitive results with other algorithms.

A Survey of Evolutionary Algorithms for Multi-Objective Optimization Problems With Irregular Pareto Fronts

Evolutionary algorithms have been shown to be very successful in solving multi-objective optimization problems (MOPs). However, their performance often deteriorates when solving MOPs with irregular Pareto fronts. To remedy this issue, a large body of research has been performed in recent years and many new algorithms have been proposed. This paper provides a comprehensive survey of the research on MOPs with irregular Pareto fronts. We start with a brief introduction to the basic concepts, followed by a summary of the benchmark test problems with irregular problems, an analysis of the causes of the irregularity, and real-world optimization problems with irregular Pareto fronts. Then, a taxonomy of the existing methodologies for handling irregular problems is given and representative algorithms are reviewed with a discussion of their strengths and weaknesses. Finally, open challenges are pointed out and a few promising future directions are suggested.

A new metaheuristic algorithm based on water wave optimization for data clustering

Data clustering is an important activity in the field of data analytics. It can be described as unsupervised learning for grouping the similar objects into clusters. The similarity between objects is computed through distance measure. Further, clustering has proven its significance for solving wide range of real-world optimization problems. This work presents water wave optimization (WWO) based metaheuristic algorithm for clustering task. It is seen that WWO algorithm is an effective algorithm for solving constrained and unconstrained optimization problems. But, sometimes WWO cannot obtain promising solution for complex optimization problems due to absence of global best information component and converged on premature solution. To address the absentia of global best information and premature convergence, some improvements are inculcated in WWO algorithm to make it more promising and efficient. These improvements are described in terms of modified search mechanism and decay operator. The absentia of global best information component is handled through updated search mechanism. While, the premature convergence is addressed through a decay operator. The performance of WWO algorithm is evaluated using thirteen benchmark clustering datasets using accuracy and F-score parameters. The simulation results are compared with several state of art existing clustering algorithms and it is observed proposed WWO clustering algorithm achieves a higher accuracy and F-score rates with most of clustering datasets as compared to existing clustering algorithms. It is also showed that the proposed WWO algorithm improves the accuracy and F-score rates an average of 4% and 7% respectively as compared to existing clustering algorithm. Further, statistical test is also conducted to validate the existence of proposed WWO algorithm and statistical results confirm the existence of WWO algorithm in clustering field.

Formula omitted]-polytope decomposition-based algorithm for continuous optimization

This paper presents a new fractal search space decomposition-based algorithm to address the issue of scaling up the divide and conquer approach to deal with large scale problems (up to 50 continuous decision variables). The proposed algorithm, called polyFrac, fractally decomposes the search space using hyper-polytopes. It allows moving throughout different granularity levels by only computing the average of vertices of a hyper-polytope to obtain the coordinates of the centroids. Only the most promising hyper-polytopes are decomposed into child-polytopes. Then, a simple deterministic local search (single solution-based metaheuristic) is used to perform the intensification process to find the best solution within the selected lowest hyper-polytope. The proposed algorithm performance is evaluated on the well-known SOCO 2011, CEC 2013, and CEC 2017 benchmarks and compared with 26 states of the art algorithms. A real-world optimization problem is also used to calibrate its performance. The obtained results show that polyFrac outperforms all the algorithms. Moreover, experimental results and analysis suggest that polyFrac is a highly competitive optimization algorithm for solving large-scale and complex optimization problems.

A comparative study of many-objective optimizers on large-scale many-objective software clustering problems

Over the past 2 decades, several multi-objective optimizers (MOOs) have been proposed to address the different aspects of multi-objective optimization problems (MOPs). Unfortunately, it has been observed that many of MOOs experiences performance degradation when applied over MOPs having a large number of decision variables and objective functions. Specially, the performance of MOOs rapidly decreases when the number of decision variables and objective functions increases by more than a hundred and three, respectively. To address the challenges caused by such special case of MOPs, some large-scale multi-objective optimization optimizers (L-MuOOs) and large-scale many-objective optimization optimizers (L-MaOOs) have been developed in the literature. Even after vast development in the direction of L-MuOOs and L-MaOOs, the supremacy of these optimizers has not been tested on real-world optimization problems containing a large number of decision variables and objectives such as large-scale many-objective software clustering problems (L-MaSCPs). In this study, the performance of nine L-MuOOs and L-MaOOs (i.e., S3-CMA-ES, LMOSCO, LSMOF, LMEA, IDMOPSO, ADC-MaOO, NSGA-III, H-RVEA, and DREA) is evaluated and compared over five L-MaSCPs in terms of IGD, Hypervolume, and MQ metrics. The experimentation results show that the S3-CMA-ES and LMOSCO perform better compared to the LSMOF, LMEA, IDMOPSO, ADC-MaOO, NSGA-III, H-RVEA, and DREA in most of the cases. The LSMOF, LMEA, IDMOPSO, ADC-MaOO, NSGA-III, and DREA, are the average performer, and H-RVEA is the worst performer.

Modified salp swarm algorithm for global optimisation

Salp swarm algorithm (SSA) is a newly swarm-based metaheuristic algorithm that simulate the swimming and foraging behaviour of salps in oceans so to search for global optimum solution. Similarly to other metaheuristic algorithms, SSA suffers from poor convergence rate and stagnation in local optima. In this paper, three different improvements to the original population update process are proposed in order to enhance its exploitation and exploration capabilities. The first modification (MSSA1) introduces the concept of local best information to the followers salps update process allowing a better exploration of local search neighbourhood. The second improvement (MSSA2) provide two followers update process. The first is based on a differential evolution combined with a randomly selected local best position, and the second uses a local search in the global best neighbourhood which is triggered by a non-improvement in the corresponding local best. A third modification to the SSA algorithm (MSSA3) penalises a non-improvement of the local best solution by computing a new corresponding follower’s position based on a local jump in the local best neighbourhood for better exploitation. The performances of the proposed algorithms are tested on 27 CEC’15 test suite, and two real-world optimisation problems. A comparative study using nonparametric statistical tests of the obtained results is conducted against those of eight well-known metaheuristics, including the original SSA. The results indicate an overall distinctive performance of all three modification compared to the remaining algorithms, while MSSA1 scored generally better than MSSA2 and MSSA3.

Optimal Stochastic Process Optimizer: A New Metaheuristic Algorithm With Adaptive Exploration-Exploitation Property

Metaheuristic algorithms are constructed to solve optimization problems, but they cannot solve all the problems with best solutions. This work proposes a novel self-adaptive metaheuristic optimization algorithm, named Optimal Stochastic Process Optimizer (OSPO), which can solve different kinds of optimization problems with promising performance. Specifically, OSPO regards the procedure of optimization as a realization of stochastic process, and with the help of Subjective Probability Distribution Function (SPDF) and Receding Sampling Strategy proposed in this paper, OSPO can control the exploration-exploitation property online by the adaptive modification of the parameters in SPDF. This adaptive exploration-exploitation property of OSPO contributes to dealing with different kinds of problems; thus, it makes OSPO have the potential to solve at least a vast majority of optimization problems. The proposed algorithm is first benchmarked on uni-modal, multi-modal and composite test functions both in low and high dimensions. The results are verified by comparative studies with seven well-performed metaheuristic algorithms. Then, 21 real-world optimization problems are used to further investigate the effectiveness of OSPO. The winners of CEC2020 Competition on Real-World Single Objective Constrained Optimization, SASS algorithm, sCMAgES algorithm, EnMODE algorithm and COLSHADE algorithm are used as four comparative algorithms in real-world optimization problems. The analysis of simulations demonstrates that OSPO is able to provide very competitive performance compared to the comparative meta-heuristics both in benchmark functions and in real-world optimization problems; thus, the potential of OSPO to solve at least a vast majority of optimization problems is verified. A corresponding MATLAB APP demo is available on https://github.com/JiahongXu123/OSPO-algorithm.git.

A Modified Jellyfish Search Optimizer With Orthogonal Learning Strategy

The jellyfish search optimizer (JSO) is one of the newest swarm intelligence algorithms which has been widely used to solve different real-world optimization problems. However, its most challenging task is to regulate the exploration and exploitation search to avoid problems in harmonic convergence or be trapped into local optima. In this paper, we propose a new variant of JSO named OJSO, based on orthogonal learning with the aim to improve the capability of global searching of the original algorithm. The orthogonal learning is a strategy for discovering more useful information from two recent solution vectors by predicting the best combination using limited trials instead of exhaustive trials via an orthogonal experimental design.To evaluate the effectiveness of our approach, 23 benchmark functions are used. The evaluation process leads us to conclude that the proposed algorithm strongly outperforms the original algorithm in all aspects except the execution time.

Assamese Word Sense Disambiguation using Cuckoo Search Algorithm

Natural language processing is associated with human-computer interaction, where several challenges require natural language understanding. The Word sense disambiguation problem comprises the computational assignment of meaning to a word according to a specific context in which it occurs. There are numerous natural language processing applications, such as machine translation, information retrieval, and information extraction, which require this task which takes place at the semantic level. To solve this problem unsupervised computation proposals can be effective since they have been successfully used for many real-world optimization problems. In this paper, we propose to solve the word sense disambiguation problem using the cuckoo search algorithm in the Assamese language. We illustrate the performance of our algorithm by carrying out experiments on an Assamese corpus. And comparing them against an unsupervised genetic algorithm that is implemented in the Assamese language. Results of the experiment show that the cuckoo algorithm can achieve more precision, recall and F-measure, attaining 87.5, 84, and 85.71 percentages respectively.

A Modified Slime Mould Algorithm for Global Optimization.

Slime mould algorithm (SMA) is a population-based metaheuristic algorithm inspired by the phenomenon of slime mould oscillation. The SMA is competitive compared to other algorithms but still suffers from the disadvantages of unbalanced exploitation and exploration and is easy to fall into local optima. To address these shortcomings, an improved variant of SMA named MSMA is proposed in this paper. Firstly, a chaotic opposition-based learning strategy is used to enhance population diversity. Secondly, two adaptive parameter control strategies are proposed to balance exploitation and exploration. Finally, a spiral search strategy is used to help SMA get rid of local optimum. The superiority of MSMA is verified in 13 multidimensional test functions and 10 fixed-dimensional test functions. In addition, two engineering optimization problems are used to verify the potential of MSMA to solve real-world optimization problems. The simulation results show that the proposed MSMA outperforms other comparative algorithms in terms of convergence accuracy, convergence speed, and stability.