Ali Wagdy Mohamed

An improved scheduling the disinfection process of the new coronavirus (COVID-19) is introduced. The scheduling aims at achieving the best utilization of the available day time, which is calculated as the total disinfection time minus the total loss travelling time. In this regard, a new application problem is presented, which is called a travelling disinfection-man problem (TDP). The new problem (TDP) in network optimization resemble somehow the famous travelling salesman problems (TSP) but with basic distinct variations where a disinfection group is likely to select a route to reach a subset of predetermined places to be disinfected with the most utilization of the available day working hours. A nonlinear binary model is introduced with a detailed real application case study involving the improving the scheduling of coronavirus disinfection process for five contaminated faculties in Ain Shams University in Cairo, and the case study is solved using a novel discrete binary gaining-sharing knowledge-based optimization algorithm (DBGSK).

This article proposes a new problem which is called the Stochastic Travelling Advisor Problem (STAP) in network optimization, and it is defined for an advisory group who wants to choose a subset of candidate workplaces comprising the most profitable route within the time limit of day working hours. A nonlinear binary mathematical model is formulated and a real application case study in the occupational health and safety field is presented. The problem has a stochastic nature in travelling and advising times since the deterministic models are not appropriate for such real-life problems. The STAP is handled by proposing suitable probability distributions for the time parameters and simulating the problem under such conditions. Many application problems like this one are formulated as nonlinear binary programming models which are hard to be solved using exact algorithms especially in large dimensions. A novel binary version of the recently developed gaining-sharing knowledge-based optimization algorithm (GSK) to solve binary optimization problems is given. GSK algorithm is based on the concept of how humans acquire and share knowledge during their life span. The binary version of GSK (BGSK) depends mainly on two stages that enable BGSK for exploring and exploitation of the search space efficiently and effectively to solve problems in binary space. The generated simulation runs of the example are solved using the BGSK, and the output histograms and the best-fitted distributions for the total profit and for the route length are obtained.

This paper presents a new approach to Differential Evolution algorithm for solving stochastic programming problems, named DESP. The proposed algorithm introduces a new triangular mutation rule based on the convex combination vector of the triangle and the difference vector between the best and the worst individuals among the three randomly selected vectors. The proposed novel approach to mutation operator is shown to enhance the global and local search capabilities and to increase the convergence speed of the new algorithm compared with conventional DE. DESP uses Deb’s constraint handling technique based on feasibility and the sum of constraint violations without any additional parameters. Besides, a new dynamic tolerance technique to handle equality constraints is also adopted. Two models of stochastic programming (SP) problems are considered: Linear Stochastic Fractional Programming Problems and Multi-objective Stochastic Linear Programming Problems. The comparison results between the DESP and basic DE, basic particle swarm optimization (PSO), Genetic Algorithm (GA) and the available results from where it is indicated that the proposed DESP algorithm is competitive with, and in some cases superior to, other algorithms in terms of final solution quality, efficiency and robustness of the considered problems in comparison with the quoted results in the literature.

This paper presents enhanced adaptive differential evolution (EADE) algorithm for solving high-dimensional optimization problems over continuous space. To utilize the information of good and bad vectors in the DE population, the proposed algorithm introduces a new mutation rule. It uses two random chosen vectors of the top and bottom 100p% individuals in the current population of size NP, while the third vector is selected randomly from the middle [NP-2(100p%)] individuals. The mutation rule is combined with the basic mutation strategy DE/rand/1/bin, where the only one of the two mutation rules is applied with the probability of 0.5. This new mutation scheme helps to maintain effectively the balance between the global exploration and local exploitation abilities for searching process of the DE. Furthermore, we propose a novel self-adaptive scheme for gradual change of the values of the crossover rate that can excellently benefit from the past experience of the individuals in the search space during evolution process which, in turn, can considerably balance the common trade-off between the population diversity and convergence speed. The proposed algorithm has been evaluated on the 7 and 20 standard high-dimensional benchmark numerical optimization problems for both the IEEE CEC-2008 and the IEEE CEC-2010 Special Session and Competition on Large-Scale Global Optimization. The comparison results between EADE and its version and the other state-of-art algorithms that were all tested on these test suites indicate that the proposed algorithm and its version are highly competitive algorithms for solving large-scale global optimization problems.

This article proposes a novel binary version of recently developed Gaining Sharing knowledge-based optimization algorithm (GSK) to solve binary optimization problems. GSK algorithm is based on the concept of how humans acquire and share knowledge during their life span. A binary version of GSK named novel binary Gaining Sharing knowledge-based optimization algorithm (NBGSK) depends on mainly two binary stages: binary junior gaining sharing stage and binary senior gaining sharing stage with knowledge factor 1. These two stages enable NBGSK for exploring and exploitation of the search space efficiently and effectively to solve problems in binary space. Moreover, to enhance the performance of NBGSK and prevent the solutions from trapping into local optima, NBGSK with population size reduction (PR-NBGSK) is introduced. It decreases the population size gradually with a linear function. The proposed NBGSK and PR-NBGSK applied to set of knapsack instances with small and large dimensions, which shows that NBGSK and PR-NBGSK are more efficient and effective in terms of convergence, robustness, and accuracy.

This paper proposes an enhanced modified Differential Evolution algorithm (MI-EDDE) to solve global constrained optimization problems that consist of mixed/non-linear integer variables. The MI-EDDE algorithm, which is based on the constraints violation, introduces a new mutation rule that sort all individuals ascendingly due to their constraint violations (cv) value and then the population is divided into three clusters (best, better and worst) with sizes 100p%, (NP-2) * 100p% and 100p% respectively. Where p is the proportion of the partition with respect to the total number of individuals in the population (NP). MI-EDDE selects three random individuals, one of each partition to implement the mutation process. This new mutation scheme shown to enhance the global and local search capabilities and increases the convergence speed. Eighteen test problems with different features are tested to evaluate the performance of MI-EDDE, and a comparison is made with four state-of-the-art evolutionary algorithms. The results show superiority of MI-EDDE to the four algorithms in terms of the quality, efficiency and robustness of the final solutions. Moreover, MI-EDDE shows a superior performance in solving two high dimensional problems and finding better solutions than the known optimal solution.

This paper proposes an enhanced modified Differential Evolution algorithm (MI-EDDE) to solve global constrained optimization problems that consist of mixed/non-linear integer variables. The MI-EDDE algorithm, which is based on the constraints violation, introduces a new mutation rule that sort all individuals ascendingly due to their constraint violations (cv) value and then the population is divided into three clusters (best, better and worst) with sizes 100p%, (NP-2) * 100p% and 100p% respectively. Where p is the proportion of the partition with respect to the total number of individuals in the population (NP). MI-EDDE selects three random individuals, one of each partition to implement the mutation process. This new mutation scheme shown to enhance the global and local search capabilities and increases the convergence speed. Eighteen test problems with different features are tested to evaluate the performance of MI-EDDE, and a comparison is made with four state-of-the-art evolutionary algorithms. The results show superiority of MI-EDDE to the four algorithms in terms of the quality, efficiency and robustness of the final solutions. Moreover, MI-EDDE shows a superior performance in solving two high dimensional problems and finding better solutions than the known optimal solution.

Hadi, Anas A.Mohamed, Ali W.Jambi, Kamal M.Real parameter optimization is one of the active research fields during the last decade. The performance of LSHADE-SPACMALSHADE was competitive in IEEE CEC’2017 competition on Single Objective Bound Constrained Real-Parameter Single Objective Optimization. Besides, it was ranked fourth among twelve papers were presented on and compared to this new benchmark problems. In this work, an improved version named ELSHADE-SPACMASPACMA is introduced. In LSHADE-SPACMA, p value that controls the greediness of the mutation strategy is constant. While in ELSHADE-SPACMAESHADE, p value is dynamic. Larger value of p will enhance the exploration, while smaller values will enhance the exploitation. We further enhanced the performance of ELSHADE-SPACMA by integrating another directed mutation strategy within the hybridization framework. The proposed algorithm has been evaluated using IEEE CEC’2017 benchmark. According to the comparison results, the proposed ELSHADE-SPACMA algorithm is better than LSHADE and LSHADE-SPACMA. Besides, The comparison results between ELSHADE-SPACMA and the best three algorithms from the IEEE CEC’2017 Competition indicate that ELSHADE-SPACMA algorithm shows overall better performance and it is highly competitive algorithm for solving global optimization problems.

The purpose of this paper is to present a proposal for scheduling shuttle ambulance vehicles assigned to COVID-19 patients using one of the discrete optimization techniques, namely, the multi-objective multiple 0–1 knapsack problem. The scheduling aims at achieving the best utilization of the predetermined planning time slot; the best utilization is evaluated by maximizing the number of evacuated people who might be infected with the virus to the isolation hospital and maximizing the effectiveness of prioritizing the patients relative to their health status. The complete mathematical model for the problem is formulated including the representation of the decision variables, the problem constraints, and the multi-objective functions. The proposed multi-objective multiple knapsack model is applied to an illustrated case study in Cairo, Egypt, the case study aims at improving the scheduling of ambulance vehicles in the back and forth shuttle movements between patient’ locations and the isolation hospital. The case study is solved using a novel Discrete Binary Gaining-Sharing knowledge-based optimization algorithm (DBGSK). The detail procedure of the novel DBGSK is presented along with the complete steps for solving the case study.

In machine learning, searching for the optimal feature subset from the original datasets is a very challenging and prominent task. The metaheuristic algorithms are used in finding out the relevant, important features, that enhance the classification accuracy and save the resource time. Most of the algorithms have shown excellent performance in solving feature selection problems. A recently developed metaheuristic algorithm, gaining-sharing knowledge-based optimization algorithm (GSK), is considered for finding out the optimal feature subset. GSK algorithm was proposed over continuous search space; therefore, a total of eight S-shaped and V-shaped transfer functions are employed to solve the problems into binary search space. Additionally, a population reduction scheme is also employed with the transfer functions to enhance the performance of proposed approaches. It explores the search space efficiently and deletes the worst solutions from the search space, due to the updation of population size in every iteration. The proposed approaches are tested over twenty-one benchmark datasets from UCI repository. The obtained results are compared with state-of-the-art metaheuristic algorithms including binary differential evolution algorithm, binary particle swarm optimization, binary bat algorithm, binary grey wolf optimizer, binary ant lion optimizer, binary dragonfly algorithm, binary salp swarm algorithm. Among eight transfer functions, V4 transfer function with population reduction on binary GSK algorithm outperforms other optimizers in terms of accuracy, fitness values and the minimal number of features. To investigate the results statistically, two non-parametric statistical tests are conducted that concludes the superiority of the proposed approach.

This paper presents enhanced fitness-adaptive differential evolution algorithm with novel mutation (EFADE) for solving global numerical optimization problems over continuous space. A new triangular mutation operator is introduced. It is based on the convex combination vector of the triplet defined by the three randomly chosen vectors and the difference vectors between the best, better and the worst individuals among the three randomly selected vectors. Triangular mutation operator helps the search for better balance between the global exploration ability and the local exploitation tendency as well as enhancing the convergence rate of the algorithm through the optimization process. Besides, two novel, effective adaptation schemes are used to update the control parameters to appropriate values without either extra parameters or prior knowledge of the characteristics of the optimization problem. In order to verify and analyze the performance of EFADE, numerical experiments on a set of 28 test problems from the CEC2013 benchmark for 10, 30 and 50 dimensions, including a comparison with 12 recent DE-based algorithms and six recent evolutionary algorithms, are executed. Experimental results indicate that in terms of robustness, stability and quality of the solution obtained, EFADE is significantly better than, or at least comparable to state-of-the-art approaches with outstanding performance.

Adaptive guided differential evolution algorithm (AGDE) is a differential evolution (DE) algorithm that utilizes the information of good and bad vectors in the population, it introduced a novel mutation rule in order to balance effectively the exploration and exploitation tradeoffs. It divided the population into three clusters (best, better and worst) with sizes 100p%, NP − 2 * 100% and 100% respectively. where p is the proportion of the partition with respect to the total number of individuals in the population (NP). AGDE selects three random individuals, one of each partition to implement the mutation process. Besides, a novel adaptation scheme was proposed in order to update the value of crossover rate without previous knowledge about the characteristics of the problems. This paper introduces enhanced AGDE (EAGDE) with non-linear population size reduction, which gradually decreases the population size according to a non-linear function. Moreover, a newly developed rule developed to determine the initial population size, that is related to the dimensionality of the problems. The performance of the proposed algorithm is evaluated using CEC2013 benchmarks and the results are compared with the state-of-art DE and non-DE algorithms, the results showed a great competitiveness for the proposed algorithm over the other algorithms, and the original AGDE.

Performance of real-parameter global optimization algorithms is typically evaluated using sets of test problems. We propose a new methodology of extending these benchmarks to obtain a more balanced experimental design. This can be done by selectively removing some of the transformations originally used in the definitions of the test problems such as rotation, scaling, or translation. In this way, we obtain several variants of each problem parametrized by interpretable, high-level characteristics. These binary parameters are used as predictors in a multiple regression model explaining the algorithmic performance. Linear models allow for the attribution of strength and direction of performance changes to particular characteristics of the optimization problems and thus provide insight into the underlying mechanics of the investigated algorithms. The proposed ideas are illustrated with an application example showing the feasibility of the new benchmark. Parametrized benchmarking is a step towards obtaining multi-faceted insight into algorithmic performance and the optimization problems. The overall goal is to systematize a method of matching problems to algorithms and in this way constructively address the limitations imposed by the no free lunch theorem.

This work is dedicated to the economic scheduling of the required electric stations in the upcoming 10-year long-term plan. The calculation of the required electric stations is carried out by estimating the yearly consumption of electricity over a long-time plan and then determining the required number of stations. The aim is to minimize the total establishing and operating costs of the stations based on a mathematical programming model with nonlinear objective function and integer decision variables. The introduced model is applied for a real practical case study to conclude the number of yearly constructed stations over a long-term plan in the electricity sector in Jeddah City, Saudi Arabia. The current planning method is based only on intuition by constructing the same number of required stations in each year without searching for better solutions. To solve the introduced mathematical model, a novel recent gaining sharing knowledge-based algorithm, named GSK, has been used. The Augmented Lagrangian Method (ALM) is applied to transform the constrained formulation to become unconstrained with penalization to the objective function. According to the obtained results of the real case study, the proposed GSK with ALM approved an ability to solve this case with respect to convergence, efficiency, quality, and robustness.

Determining the optimum location of facilities is critical in many fields, particularly in healthcare. This study proposes the application of a suitable location model for field hospitals during the novel coronavirus 2019 (COVID-19) pandemic. The used model is the most appropriate among the three most common location models utilized to solve healthcare problems (the set covering model, the maximal covering model, and the P-median model). The proposed nonlinear binary constrained model is a slight modification of the maximal covering model with a set of nonlinear constraints. The model is used to determine the optimum location of field hospitals for COVID-19 risk reduction. The designed mathematical model and the solution method are used to deploy field hospitals in eight governorates in Upper Egypt. In this case study, a discrete binary gaining–sharing knowledge-based optimization (DBGSK) algorithm is proposed. The DBGSK algorithm is based on how humans acquire and share knowledge throughout their life. The DBGSK algorithm mainly depends on two junior and senior binary stages. These two stages enable DBGSK to explore and exploit the search space efficiently and effectively, and thus it can solve problems in binary space.

Many application problems are formulated as nonlinear binary programming models which are hard to be solved using exact algorithms especially in large dimensions. One of these practical applications is to optimally distribute protective materials for the newly emerged COVID-19. It is defined for a decision-maker who wants to choose a subset of candidate hospitals comprising the maximization of the distributed quantities of protective materials to a set of chosen hospitals within a specific time shift. A nonlinear binary mathematical programming model for the problem is introduced with a real application case study; the case study is solved using a novel discrete binary gaining-sharing knowledge-based optimization algorithm (DBGSK). The solution algorithm proposes a novel binary adaptation of a recently developed gaining-sharing knowledge-based optimization algorithm (GSK) to solve binary optimization problems. GSK algorithm is based on the concept of how humans acquire and share knowledge through their life span. Discrete binary version of GSK named novel binary gaining-sharing knowledge-based optimization algorithm (DBGSK) depends mainly on two binary stages: binary junior gaining-sharing stage and binary senior gaining-sharing stage with knowledge factor 1. These two stages enable DBGSK for exploring and exploitation of the search space efficiently and effectively to solve problems in binary space.

Proposing new mutation strategies to improve the optimization performance of differential evolution (DE) is an important research study. Therefore, the main contribution of this paper goes in three directions: The first direction is introducing a less greedy mutation strategy with enhanced exploration capability, named DE/current-to-ord_best/1 (ord stands for ordered) or ord_best for short. In the second direction, we introduce a more greedy mutation strategy with enhanced exploitation capability, named DE/current-to-ord_pbest/1 (ord_pbest for short). Both of the proposed mutation strategies are based on ordering three selected vectors from the current generation to perturb the target vector, where the directed differences are used to mimic the gradient decent behavior to direct the search toward better solutions. In ord_best, the three vectors are selected randomly to enhance the exploration capability of the algorithm. On the other hand, ord_pbest is designed to enhance the exploitation capability where two vectors are selected randomly and the third is selected from the global p best vectors. Based on the proposed mutation strategies, ord_best and ord_pbest, two DE variants are introduced as EDE and EBDE, respectively. The third direction of our work is a hybridization framework. The proposed mutations can be combined with DE family algorithms to enhance their search capabilities on difficult and complicated optimization problems. Thus, the proposed mutations are incorporated into SHADE and LSHADE to enhance their performance. Finally, in order to verify and analyze the performance of the proposed mutation strategies, numerical experiments were conducted using CEC2013 and CEC2017 benchmarks. The performance was also evaluated using CEC2010 designed for Large-Scale Global Optimization. Experimental results indicate that in terms of robustness, stability, and quality of the solution obtained, both mutation strategies are highly competitive, especially as the dimension increases.