A simplex social spider algorithm for solving integer programming and minimax problems

Integer programming and minimax problems are essential tools in solving various problems that arise in data mining and machine learning such as multi-class data classification and feature selection problems. In this paper, we propose a new hybrid harmony search algorithm by combining the harmony search algorithm with the multidirectional search method in order to solve the integer programming and minimax problems. The proposed algorithm is called multidirectional harmony search algorithm (MDHSA). MDHSA starts the search by applying the standard harmony search for numbers of iteration then the best-obtained solution is passing to the multidirectional search method as an intensification process in order to accelerate the search and overcome the slow convergence of the standard harmony search algorithm. The proposed algorithm is balancing between the global exploration of the harmony search algorithm and the deep exploitation of the multidirectional search method. MDHSA algorithm is tested on seven integer programming problems and 15 minimax problems and compared against 12 algorithms for solving integer programming problems and 11 algorithms for solving minimax problems. The experiments results show the efficiency of the proposed algorithm and its ability to solve integer programming and minimax problems in reasonable time.

The minimization of the molecular potential energy function is one of the most important real-life problems which can help to predict the 3D structure of the protein by knowing the steady (ground) state of the molecules of the protein. In this paper, we propose a new hybrid algorithm between the social spider algorithm and the genetic algorithm in order to minimize a simplified model of the energy function of the molecule. We call the proposed algorithm by hybrid social spider optimization and genetic algorithm (HSSOGA). The HSSOGA comprises of three main steps. In the first step, we apply the social spider optimization algorithm to balance between the exploration and the exploitation processes in the proposed algorithm. In the second step, we use the dimensionality reduction process and the population partitioning process by dividing the population into subpopulations and applying the arithmetical crossover operator for each subpopulation order to increase the diversity of the search in the algorithm. In the last steps, we use the genetic mutation operator in the whole population to avoid the premature convergence and avoid trapping in local minima. The combination of three steps helps the proposed algorithm to solve the molecular potential energy function with different molecules size, especially when the problem dimension $$D>100$$D>100 with powerful performance. We test it on 13 large-scale unconstrained global optimization problems to investigate its performance on these functions. In order to investigate the efficiency of the proposed HSSOGA, we compare HSSOGA against eight benchmark algorithms when we minimize the potential energy function problem. The numerical experiment results show that the proposed algorithm is a promising and efficient algorithm and can obtain the global minimum or near global minimum of the large-scale optimization problems up to 1000 dimension and the molecular potential energy function of the simplified model with up to 200 degrees of freedom faster than the other comparative algorithms.

A Survey of Lagrangean Techniques for Discrete Optimization

A binary social spider algorithm for uncapacitated facility location problem

The Social Spider Algorithm (SSA) was introduced based on the information-sharing foraging strategy of spiders to solve the continuous optimization problems. SSA was shown to have better performance than the other state-of-the-art meta-heuristic algorithms in terms of best-achieved fitness values, scalability, reliability, and convergence speed. By preserving all strengths and outstanding performance of SSA, we propose a novel algorithm named Discrete Social Spider Algorithm (DSSA), for solving discrete optimization problems by making some modifications to the calculation of distance function, construction of follow position, the movement method, and the fitness function of the original SSA. DSSA is employed to solve the symmetric and asymmetric traveling salesman problems. To prove the effectiveness of DSSA, TSPLIB benchmarks are used, and the results have been compared to the results obtained by six different optimization methods: discrete bat algorithm (IBA), genetic algorithm (GA), an island-based distributed genetic algorithm (IDGA), evolutionary simulated annealing (ESA), discrete imperialist competitive algorithm (DICA) and a discrete firefly algorithm (DFA). The simulation results demonstrate that DSSA outperforms the other techniques. The experimental results show that our method is better than other evolutionary algorithms for solving the TSP problems. DSSA can also be used for any other discrete optimization problem, such as routing problems.

For mathematical programming (MP) to have greater impact as a decision tool, MP software systems must offer suitable support in terms of model communication and modelling techniques. In this paper, modelling techniques that allow logical restrictions to be modelled in integer programming terms are described, and their implications discussed. In addition, it is illustrated that many classes of non-linearities which are not variable separable may be, after suitable algebraic manipulation, put in a variable separable form. The methods of reformulating the fuzzy linear programming problem as a max-min problem is also introduced. It is shown that analysis of bounds plays a key role in the following four important contexts: model reduction, reformulation of logical restrictions as 0-1 mixed integer programmes, reformulation of non-linear programmes as variable separable programmes and reformulation of fuzzy linear programmes. It is observed that, as well as incorporating an interface between the modeller and the optimizer, there is a need to make available to the modeller software facilities which support the model reformulation techniques described here.

Social spider algorithm for solving the transmission expansion planning problem

A social spider algorithm for solving the non-convex economic load dispatch problem

PurposeTo design, control and evaluate photovoltaic (PV) systems, an accurate model is required. Accuracy of PV models depends on model parameters. This study aims to use a new algorithm called improved social spider algorithm (ISSA) to detect model parameters.Design/methodology/approachTo improve performance of social spider algorithm (SSA), an elimination period is added. In addition, at the beginning of each period, a certain number of the worst solutions are replaced by new solutions in the search space. This allows the particles to find new paths to get the best solution.FindingsIn this paper, ISSA is used to estimate parameters of single-diode and double-diode models. In addition, effect of irradiation and temperature on I–V curves of PV modules is studied. For this purpose, two different modules called multi-crystalline (KC200GT) module and polycrystalline (SW255) are used. It should be noted that to challenge the performance of the proposed algorithm, it has been used to identify the parameters of a type of widely used module of fuel cell called proton exchange membrane fuel cell. Finally, comparing and analyzing of ISSA results with other similar methods shows the superiority of the presented method.Originality/valueChanges in the spider’s movement process in the SSA toward the desired response have improved the algorithm’s performance. Higher accuracy and convergence rate, skipping local minimums, global search ability and search in a limited space can be mentioned as some advantages of this modified method compared to classic SSA.

Digital micro fluidic biochips have become one of the most promising technologies in many biomedical fields. In a digital micro fluidic biochip, a group of (adjacent) cells in the micro fluidic array can be configured to work as storage, functional operations, as well as for transporting fluid droplets dynamically. There has been proposed a very efficient Integer Linear Programming (ILP)-based method to schedule operations with considering this dynamic reconfigurability. However, the method cannot directly deal with a case having an operation with multiple successors, which is necessary in some bioassays, e.g., Sample preparation applications. Sample preparation is a crucial preprocessing step to produce droplets of the desired target concentrations from input reagents. In every optimized application graphs for sample preparation, there are many operations with more than one successors. Thus, the previous method cannot be used to get an optimal scheduling, and thus we propose a new framework to use another ILP formulation for scheduling operations in a digital micro fluidic biochips. Our formulation can successfully deal with a case where there is a node with multiple successors. Also, our method can find a binding solution at the same time unlike the above-mentioned previous one thanks to our new ILP formulation. Although our ILP formulation seems to be a bit more complex than the previous one, a preliminary experiment demonstrates that the proposed ILP formulation can successfully find the optimal scheduling for practical sample preparation applications within a reasonable time.

In dynamic minimax and stochastic optimization problems frequently one is forced to use a suboptimal controller since the computation and implementation of the optimal controller based on dynamic programming is impractical in many cases. In this paper we study the performance of some suboptimal controllers in relation to the performance of the optimal feedback controller and the optimal open-loop controller. Attention is focused on some classes of, so called, open-loop-feed-back controllers. It is shown under quite general assumptions that these open-loop-feedback controllers perform at least as well as the optimal open-loop controller. The results are developed for general minimax problems with perfect and imperfect state information. In the latter case the open-loop-feedback controller mkes use of an estimator which is required to perform at least as well as a pure predictor in order for the results to hold. Some of the results presented have stochastic counterparts.

The usefulness of group theoretic methods in solving integer programming (IP) problems is extended by procedures for controlling the size of the groups. The main procedure given shows how an optimal linear programming basis can be altered to reduce the magnitude of its determinant thereby reducing the size of the group induced by the basis. An adaption of Benders' mixed IP algorithm is given which uses these methods. Some limited computational experience is given.

Multi objective short term hydro-thermal- CHP scheduling using social spider algorithm

The reactive power control of a power system is discussed under two types of variables: continuous variables (e.g., generator bus voltages) and discrete variables (e.g., transformer taps and the size of switched shunt capacitors). This paper proposes a novel and powerful algorithm, named turbulent flow of water-based optimization (TFWO) as well as a new improved version of this algorithm, called θ-TFWO, for optimal reactive power distribution (ORPD) to reduce losses. The proposed method is applied to two large-scale IEEE 57-bus systems. Furthermore, to demonstrate the competitive performance of the suggested algorithm, its performance was compared to that of several other algorithms, including biogeography-based optimization (BBO), social spider algorithm (SSA), and optics inspired optimization (OIO), in terms of solving the ORPD problem. The results confirmed the robustness and effectiveness of the proposed method as a powerful optimizer applicable to optimal reactive power distribution in power systems.

PurposeCoronavirus disease (Covid-19) has created uncertainty in all countries around the world, resulting in enormous human suffering and global recession. Because the economic impact of this pandemic is still unknown, it would be intriguing to study the incorporation of the Covid-19 period into stock price prediction. The goal of this study is to use an improved extreme learning machine (ELM), whose parameters are optimized by four meta-heuristics: harmony search (HS), social spider algorithm (SSA), artificial bee colony algorithm (ABCA) and particle swarm optimization (PSO) for stock price prediction.Design/methodology/approachIn this study, the activation functions and hidden layer neurons of the ELM were optimized using four different meta-heuristics. The proposed method is tested in five sectors. Analysis of variance (ANOVA) and Duncan's multiple range test were used to compare the prediction methods. First, ANOVA was applied to the test data for verification and validation of the proposed methods. Duncan's multiple range test was used to identify a suitable method based on the ANOVA results.FindingsThe main finding of this study is that the hybrid methodology can improve the prediction accuracy during the pre and post Covid-19 period for stock price prediction. The mean absolute percent error value of each method showed that the prediction errors of the proposed methods were all under 0.13106 in the worst case, which appears to be a remarkable outcome for such a difficult prediction task.Originality/valueThe novelty of this study is the use of four hybrid ELM methods to evaluate the automotive, technology, food, construction and energy sectors during the pre and post Covid-19 period. Additionally, an appropriate method was determined for each sector.