An Artificial Intelligence Approach for Solving Stochastic Transportation Problems

Recent years witness a great deal of interest in artificial intelligence (AI) tools in the area of optimization. AI has developed a large number of tools to solve the most difficult search-and-optimization problems in computer science and operations research. Indeed, metaheuristic-based algorithms are a sub-field of AI. This study presents the use of the metaheuristic algorithm, that is, water cycle algorithm (WCA), in the transportation problem. A stochastic transportation problem is considered in which the parameters supply and demand are considered as random variables that follow the Weibull distribution. Since the parameters are stochastic, the corresponding constraints are probabilistic. They are converted into deterministic constraints using the stochastic programming approach. In this study, we propose evolutionary algorithms to handle the difficulties of the complex high-dimensional optimization problems. WCA is influenced by the water cycle process of how streams and rivers flow toward the sea (optimal solution). WCA is applied to the stochastic transportation problem, and obtained results are compared with that of the new metaheuristic optimization algorithm, namely the neural network algorithm which is inspired by the biological nervous system. It is concluded that WCA presents better results when compared with the neural network algorithm.     

Investigation of static transmission expansion planning using the symbiotic organisms search algorithm

Transmission expansion planning (TEP) has become a complex problem in restructured electricity markets. This article presents the symbiotic organisms search (SOS) algorithm, a novel metaheuristic optimization technique for solving TEP problems in power systems. The SOS algorithm is inspired by the interactions among organisms in an ecosystem. The TEP problem is formulated here as an optimization problem to determine the cost-effective expansion planning of electrical power systems. Several constraints, such as power flow of the lines, right-of-way validity and maximum line addition, are taken into consideration. First, the SOS algorithm is tested with several benchmark functions. Then, it is applied on three standard power system networks (IEEE 24-bus system, Brazilian 46-bus system and Brazilian 87-bus system) in a TEP study to demonstrate the optimization capability of the proposed SOS algorithm. The results are compared with those produced by other state-of-the-art algorithms.     

Dark Forest Algorithm: A Novel Metaheuristic Algorithm for Global Optimization Problems

Metaheuristic algorithms, as effective methods for solving optimization problems, have recently attracted considerable attention in science and engineering fields. They are popular and have broad applications owing to their high efficiency and low complexity. These algorithms are generally based on the behaviors observed in nature, physical sciences, or humans. This study proposes a novel metaheuristic algorithm called dark forest algorithm (DFA), which can yield improved optimization results for global optimization problems. In DFA, the population is divided into four groups: highest civilization, advanced civilization, normal civilization, and low civilization. Each civilization has a unique way of iteration. To verify DFA’s capability, the performance of DFA on 35 well-known benchmark functions is compared with that of six other metaheuristic algorithms, including artificial bee colony algorithm, firefly algorithm, grey wolf optimizer, harmony search algorithm, grasshopper optimization algorithm, and whale optimization algorithm. The results show that DFA provides solutions with improved efficiency for problems with low dimensions and outperforms most other algorithms when solving high dimensional problems. DFA is applied to five engineering projects to demonstrate its applicability. The results show that the performance of DFA is competitive to that of current well-known metaheuristic algorithms. Finally, potential upgrading routes for DFA are proposed as possible future developments.     

A novel metaheuristic for continuous optimization problems: Virus optimization algorithm

A novel metaheuristic for continuous optimization problems, named the virus optimization algorithm (VOA), is introduced and investigated. VOA is an iteratively population-based method that imitates the behaviour of viruses attacking a living cell. The number of viruses grows at each replication and is controlled by an immune system (a so-called ‘antivirus’) to prevent the explosive growth of the virus population. The viruses are divided into two classes (strong and common) to balance the exploitation and exploration effects. The performance of the VOA is validated through a set of eight benchmark functions, which are also subject to rotation and shifting effects to test its robustness. Extensive comparisons were conducted with over 40 well-known metaheuristic algorithms and their variations, such as artificial bee colony, artificial immune system, differential evolution, evolutionary programming, evolutionary strategy, genetic algorithm, harmony search, invasive weed optimization, memetic algorithm, particle swarm optimization and simulated annealing. The results showed that the VOA is a viable solution for continuous optimization.     

A jazz-based approach for optimal setting of pressure reducing valves in water distribution networks

This study presents a model for valve setting in water distribution networks (WDNs), with the aim of reducing the level of leakage. The approach is based on the harmony search (HS) optimization algorithm. The HS mimics a jazz improvisation process able to find the best solutions, in this case corresponding to valve settings in a WDN. The model also interfaces with the improved version of a popular hydraulic simulator, EPANET 2.0, to check the hydraulic constraints and to evaluate the performances of the solutions. Penalties are introduced in the objective function in case of violation of the hydraulic constraints. The model is applied to two case studies, and the obtained results in terms of pressure reductions are comparable with those of competitive metaheuristic algorithms (e.g. genetic algorithms). The results demonstrate the suitability of the HS algorithm for water network management and optimization.     

System Reliability Optimization Using Gray Wolf Optimizer Algorithm

For the past two decades, nature‐inspired optimization algorithms have gained enormous popularity among the researchers. On the other hand, complex system reliability optimization problems, which are nonlinear programming problems in nature, are proved to be non‐deterministic polynomial‐time hard (NP‐hard) from a computational point of view. In this work, few complex reliability optimization problems are solved by using a very recent nature‐inspired metaheuristic called gray wolf optimizer (GWO) algorithm. GWO mimics the chasing, hunting, and the hierarchal behavior of gray wolves. The results obtained by GWO are compared with those of some recent and popular metaheuristic such as the cuckoo search algorithm, particle swarm optimization, ant colony optimization, and simulated annealing. This comparative study shows that the results obtained by GWO are either superior or competitive to the results that have been obtained by these well‐known metaheuristic mentioned earlier. Copyright © 2016 John Wiley & Sons, Ltd.     

Improved mine blast algorithm for optimal cost design of water distribution systems

The design of water distribution systems is a large class of combinatorial, nonlinear optimization problems with complex constraints such as conservation of mass and energy equations. Since feasible solutions are often extremely complex, traditional optimization techniques are insufficient. Recently, metaheuristic algorithms have been applied to this class of problems because they are highly efficient. In this article, a recently developed optimizer called the mine blast algorithm (MBA) is considered. The MBA is improved and coupled with the hydraulic simulator EPANET to find the optimal cost design for water distribution systems. The performance of the improved mine blast algorithm (IMBA) is demonstrated using the well-known Hanoi, New York tunnels and Balerma benchmark networks. Optimization results obtained using IMBA are compared to those using MBA and other optimizers in terms of their minimum construction costs and convergence rates. For the complex Balerma network, IMBA offers the cheapest network design compared to other optimization algorithms.     

Gaining-Sharing Knowledge Based Algorithm for Solving Stochastic Programming Problems

This paper presents a novel application of metaheuristic algorithms for solving stochastic programming problems using a recently developed gaining sharing knowledge based optimization (GSK) algorithm. The algorithm is based on human behavior in which people gain and share their knowledge with others. Different types of stochastic fractional programming problems are considered in this study. The augmented Lagrangian method (ALM) is used to handle these constrained optimization problems by converting them into unconstrained optimization problems. Three examples from the literature are considered and transformed into their deterministic form using the chance-constrained technique. The transformed problems are solved using GSK algorithm and the results are compared with eight other state-of-the-art metaheuristic algorithms. The obtained results are also compared with the optimal global solution and the results quoted in the literature. To investigate the performance of the GSK algorithm on a real-world problem, a solid stochastic fixed charge transportation problem is examined, in which the parameters of the problem are considered as random variables. The obtained results show that the GSK algorithm outperforms other algorithms in terms of convergence, robustness, computational time, and quality of obtained solutions.     

基于演化算法的带频率约束的桁架结构形状和尺寸优化

具有频率约束的桁架结构形状和尺寸优化设计是一个难度大的非线性动力优化问题。形状和尺寸变量的耦合通常导致收敛困难,而频率约束则使得动力灵敏度分析困难,传统的优化准则法和数学规划法难于求解。将单纯形算法、子空间变维技术、均匀变异有机融入郭涛算法,提出一种混合演化算法,避开繁琐的动力灵敏度分析,简单、有效地求解这类桁架形状和尺寸优化问题。典型的桁架算例验证了算法的有效性和可靠性。     

Multi-Objective Grey Wolf Optimization Algorithm for Solving Real-World BLDC Motor Design Problem

The first step in the design phase of the Brushless Direct Current (BLDC) motor is the formulation of the mathematical framework and is often used due to its analytical structure. Therefore, the BLDC motor design problem is considered to be an optimization problem. In this paper, the analytical model of the BLDC motor is presented, and it is considered to be a basis for emphasizing the optimization methods. The analytical model used for the experimentation has 78 non-linear equations, two objective functions, five design variables, and six non-linear constraints, so the BLDC motor design problem is considered as highly non-linear in electromagnetic optimization. Multi-objective optimization becomes the forefront of the current research to obtain the global best solution using metaheuristic techniques. The bio-inspired multi-objective grey wolf optimizer (MOGWO) is presented in this paper, and it is formulated based on Pareto optimality, dominance, and archiving external. The performance of the MOGWO is verified on standard multi-objective unconstraint benchmark functions and applied to the BLDC motor design problem. The results proved that the proposed MOGWO algorithm could handle nonlinear constraints in electromagnetic optimization problems. The performance comparison in terms of Generational Distance, inversion GD, Hypervolume-matrix, scattered-matrix, and coverage metrics proves that the MOGWO algorithm can provide the best solution compared to other selected algorithms. The source code of this paper is backed up with extra online support at and .     

Grey wolf optimizer and hybrid PSO-GWO for reliability optimization and redundancy allocation problem

Analysis and optimization of system reliability have very much importance for developing an optimal design for the system while using the available resources. Several studies are centered towards reliability optimization using metaheuristics. In this study, a recently developed metaheuristic optimization algorithm called hybrid PSO-GWO (HPSGWO) to solve the reliability-redundancy optimization problem has been proposed. The HPSGWO fuses the Particle Swarm Optimization's (PSO) exploitation ability with the grey wolf optimizer's (GWO) exploration ability. The comparison of results with prior best results of PSO and GWO for the four benchmarks of reliability redundancy allocation problem demonstrates the HPSGWO as a productive enhancement strategy since it got promising answers than other metaheuristic algorithms.     

An efficient dynamic load balancing algorithm

In engineering problems, randomness and uncertainties are inherent. Robust design procedures, formulated in the framework of multi-objective optimization, have been proposed in order to take into account sources of randomness and uncertainty. These design procedures require orders of magnitude more computational effort than conventional analysis or optimum design processes since a very large number of finite element analyses is required to be dealt. It is therefore an imperative need to exploit the capabilities of computing resources in order to deal with this kind of problems. In particular, parallel computing can be implemented at the level of metaheuristic optimization, by exploiting the physical parallelization feature of the nondominated sorting evolution strategies method, as well as at the level of repeated structural analyses required for assessing the behavioural constraints and for calculating the objective functions. In this study an efficient dynamic load balancing algorithm for optimum exploitation of available computing resources is proposed and, without loss of generality, is applied for computing the desired Pareto front. In such problems the computation of the complete Pareto front with feasible designs only, constitutes a very challenging task. The proposed algorithm achieves linear speedup factors and almost 100% speedup factor values with reference to the sequential procedure.     

Discrete size optimization of steel trusses using a refined big bang–big crunch algorithm

This article presents a methodology that provides a method for design optimization of steel truss structures based on a refined big bang–big crunch (BB-BC) algorithm. It is shown that a standard formulation of the BB-BC algorithm occasionally falls short of producing acceptable solutions to problems from discrete size optimum design of steel trusses. A reformulation of the algorithm is proposed and implemented for design optimization of various discrete truss structures according to American Institute of Steel Construction Allowable Stress Design (AISC-ASD) specifications. Furthermore, the performance of the proposed BB-BC algorithm is compared to its standard version as well as other well-known metaheuristic techniques. The numerical results confirm the efficiency of the proposed algorithm in practical design optimization of truss structures.     

SoftFEM: The Soft Finite Element Method

While the finite element method (FEM) has now reached full maturity both in academy and industry, its use in optimization pipelines remains either computationally intensive or cumbersome. In particular, currently used optimization schemes leveraging FEM still require the choice of dedicated optimization algorithms for a specific design problem, and a “black box” approach to FEM-based optimization remains elusive. To this end, we propose here an integrated finite element-soft computing method, ie, the soft FEM (SoftFEM), which integrates a finite element solver within a metaheuristic search wrapper. To illustrate this general method, we focus here on solid mechanics problems. For these problems, SoftFEM is able to optimize geometry changes and mechanistic measures based on geometry constraints and material properties inputs. From the optimization perspective, the use of a fitness function based on finite element calculation imposes a series of challenges. To bypass the limitations in search capabilities of the usual optimization techniques (local search and gradient-based methods), we propose, instead a hybrid self adaptive search technique, the multiple offspring sampling (MOS), combining two metaheuristics methods: one population-based differential evolution method and a local search optimizer. The formulation coupling FEM to the optimization wrapper is presented in detail and its flexibility is illustrated with three representative solid mechanics problems. More particularly, we propose here the MOS as the most versatile search algorithm for SoftFEM. A new method for the identification of nonfully determined parameters is also proposed.     

Skill Optimization Algorithm: A New Human-Based Metaheuristic Technique

Metaheuristic algorithms are widely used in solving optimization problems. In this paper, a new metaheuristic algorithm called Skill Optimization Algorithm (SOA) is proposed to solve optimization problems. The fundamental inspiration in designing SOA is human efforts to acquire and improve skills. Various stages of SOA are mathematically modeled in two phases, including: (i) exploration, skill acquisition from experts and (ii) exploitation, skill improvement based on practice and individual effort. The efficiency of SOA in optimization applications is analyzed through testing this algorithm on a set of twenty-three standard benchmark functions of a variety of unimodal, high-dimensional multimodal, and fixed-dimensional multimodal types. The optimization results show that SOA, by balancing exploration and exploitation, is able to provide good performance and appropriate solutions for optimization problems. In addition, the performance of SOA in optimization is compared with ten metaheuristic algorithms to evaluate the quality of the results obtained by the proposed approach. Analysis and comparison of the obtained simulation results show that the proposed SOA has a superior performance over the considered algorithms and achieves much more competitive results.     

Optimal Implementation of Photovoltaic and Battery Energy Storage in Distribution Networks

Recently, implementation of Battery Energy Storage (BES) with photovoltaic (PV) array in distribution networks is becoming very popular in overall the world. Integrating PV alone in distribution networks generates variable output power during 24-hours as it depends on variable natural source. PV can be able to generate constant output power during 24-hours by installing BES with it. Therefore, this paper presents a new application of a recent metaheuristic algorithm, called Slime Mould Algorithm (SMA), to determine the best size, and location of photovoltaic alone or with battery energy storage in the radial distribution system (RDS). This algorithm is modeled from the behavior of SMA in nature. During the optimization process, the total active power loss during 24-hours is used as an objective function considering the equality and inequality constraints. In addition, the presented function is based on the probabilistic for PV output and different types of system load. The candidate buses for integrating PV and BES in the distribution network are determined by the real power loss sensitivity factor (PLSF). IEEE 69-bus RDS with different types of loads is used as a test system. The effectiveness of SMA is validated by comparing its results with those obtained by other well-known optimization algorithms.     

Rock Hyraxes Swarm Optimization: A New Nature-Inspired Metaheuristic Optimization Algorithm

This paper presents a novel metaheuristic algorithm called Rock Hyraxes Swarm Optimization (RHSO) inspired by the behavior of rock hyraxes swarms in nature. The RHSO algorithm mimics the collective behavior of Rock Hyraxes to find their eating and their special way of looking at this food. Rock hyraxes live in colonies or groups where a dominant male watch over the colony carefully to ensure their safety leads the group. Forty-eight (22 unimodal and 26 multimodal) test functions commonly used in the optimization area are used as a testing benchmark for the RHSO algorithm. A comparative efficiency analysis also checks RHSO with Particle Swarm Optimization (PSO), Artificial-Bee-Colony (ABC), Gravitational Search Algorithm (GSA), and Grey Wolf Optimization (GWO). The obtained results showed the superiority of the RHSO algorithm over the selected algorithms; also, the obtained results demonstrated the ability of the RHSO in convergence towards the global optimal through optimization as it performs well in both exploitation and exploration tests. Further, RHSO is very effective in solving real issues with constraints and new search space. It is worth mentioning that the RHSO algorithm has a few variables, and it can achieve better performance than the selected algorithms in many test functions.     

A GRASP algorithm for flexible job-shop scheduling with maintenance constraints

In most realistic situations, machines may be unavailable due to maintenance, pre-schedules and so on. The availability constraints are non-fixed in that the completion time of the maintenance task is not fixed and has to be determined during the scheduling procedure. In this paper a greedy randomised adaptive search procedure (GRASP) algorithm is presented to solve the flexible job-shop scheduling problem with non-fixed availability constraints (FJSSP-nfa). The GRASP algorithm is a metaheuristic algorithm which is characterised by multiple initialisations. Basically, it operates in the following manner: first a feasible solution is obtained, which is then further improved by a local search technique. The main objective is to repeat these two phases in an iterative manner and to preserve the best found solution. Representative FJSSP-nfa benchmark problems are solved in order to test the effectiveness and efficiency of the proposed algorithm.     

An iterative method for finite dimensional structural optimization problems with repeated eigenvalues

A numerical method for solving finite dimensional structural optimization problems with constraints on natural frequency and on buckling is formulated. The method treats nondifferentiable repeated eigenvalues that have been shown to systematically arise in structural optimization. Recent results on differentiability of eigenvalues are used to develop a generalized gradient projection method for structural optimization. The algorithm is shown to overcome technical difficulties associated with nondifferentiability of repeated eigenvalues. The method is used to solve buckling and vibration optimization problems in which repeated eigenvalues occur.     

A Hybrid Model Using Bio-Inspired Metaheuristic Algorithms for Network Intrusion Detection System

Network Intrusion Detection System (IDS) aims to maintain computer network security by detecting several forms of attacks and unauthorized uses of applications which often can not be detected by firewalls. The features selection approach plays an important role in constructing effective network IDS. Various bio-inspired metaheuristic algorithms used to reduce features to classify network traffic as abnormal or normal traffic within a shorter duration and showing more accuracy. Therefore, this paper aims to propose a hybrid model for network IDS based on hybridization bio-inspired metaheuristic algorithms to detect the generic attack. The proposed model has two objectives; The first one is to reduce the number of selected features for Network IDS. This objective was met through the hybridization of bio-inspired metaheuristic algorithms with each other in a hybrid model. The algorithms used in this paper are particle swarm optimization (PSO), multi-verse optimizer (MVO), grey wolf optimizer (GWO), moth-flame optimization (MFO), whale optimization algorithm (WOA), firefly algorithm (FFA), and bat algorithm (BAT). The second objective is to detect the generic attack using machine learning classifiers. This objective was met through employing the support vector machine (SVM), C4.5 (J48) decision tree, and random forest (RF) classifiers. UNSW-NB15 dataset used for assessing the effectiveness of the proposed hybrid model. UNSW-NB15 dataset has nine attacks type. The generic attack is the highest among them. Therefore, the proposed model aims to identify generic attacks. My data showed that J48 is the best classifier compared to SVM and RF for the time needed to build the model. In terms of features reduction for the classification, my data show that the MFO-WOA and FFA-GWO models reduce the features to 15 features with close accuracy, sensitivity and F-measure of all features, whereas MVO-BAT model reduces features to 24 features with the same accuracy, sensitivity and F-measure of all features for all classifiers.