This paper presents a new and robust framework for real-coded genetic algorithm, called real-code conditional genetic algorithm (rc-CGA). The most important characteristic of the proposed rc-CGA is the implicit self-adaptive feature of the crossover and mutation mechanism. Besides, a new crossover operator with laplace distribution following a few promising descent directions (FPDD-LX) is proposed for the rc-CGA. The proposed genetic algorithm (rc-CGA+FPDD-LX) is tested using 31 benchmark functions and compared with four existing algorithms. The simulation results show excellent performance of the proposed rc-CGA+FPDD-LX for continuous function optimization.

A near-optimum parallel algorithm for bipartite subgraph problem using gradient ascent learning algorithm of the Hopfield neural networks is presented. This parallel algorithm, uses the Hopfield neural network updating to get a near-maximum bipartite subgraph and then performs gradient ascent learning on the Hopfield network to help the network escape from the state of the near-maximum bipartite subgraph until the state of the maximum bipartite subgraph or better one is obtained. A large number of instances have been simulated to verify the proposed algorithm, with the simulation result showing that our algorithm finds the solution quality is superior to that of best existing parallel algorithm. We also test the proposed algorithm on maximum cut problem. The simulation results also show the effectiveness of this algorithm.

In this paper, we present a hill-shift learning method of the Hopfield neural network for bipartite subgraph problem. The method uses the Hopfield neural network to get a near-maximum bipartite subgraph, and shifts the local minimum of energy function by adjusts the balance between two terms in the energy function to help the network escape from the state of the near-maximum bipartite subgraph to the state of the maximum bipartite subgraph or better one. A large number of instances are simulated to verify the proposed method with the simulation results showing that the solution quality is superior to that of best existing parallel algorithm.

The equilibrium optimizer (EO) is a novel physics-based meta-heuristic optimization algorithm that is inspired by estimating dynamics and equilibrium states in controlled volume mass balance models. As a stochastic optimization algorithm, EO inevitably produces duplicated solutions, which is wasteful of valuable evaluation opportunities. In addition, an excessive number of duplicated solutions can increase the risk of the algorithm getting trapped in local optima. In this paper, an improved EO algorithm with a bis-population-based non-revisiting (BNR) mechanism is proposed, namely BEO. It aims to eliminate duplicate solutions generated by the population during iterations, thus avoiding wasted evaluation opportunities. Furthermore, when a revisited solution is detected, the BNR mechanism activates its unique archive population learning mechanism to assist the algorithm in generating a high-quality solution using the excellent genes in the historical information, which not only improves the algorithm's population diversity but also helps the algorithm get out of the local optimum dilemma. Experimental findings with the IEEE CEC2017 benchmark demonstrate that the proposed BEO algorithm outperforms other seven representative meta-heuristic optimization techniques, including the original EO algorithm.

This paper describes a new learning method for Multiple-Value Logic (MVL) networks using the local search method. It is a "non-back-propagation" learning method which constructs a layered MVL network based on canonical realization of MVL functions, defines an error measure between the actual output value and teacher's value and updates a randomly selected parameter of the MVL network if and only if the updating results in a decrease of the error measure. The learning capability of the MVL network is confirmed by simulations on a large number of 2-variable 4-valued problems and 2-variable 16-valued problems. The simulation results show that the method performs satisfactorily and exhibits good properties for those relatively small problems.

This paper represents a feedback artificial immune system (FAIS). Inspired by the feedback mechanisms in the biological immune system, the proposed algorithm effectively manipulates the population size by increasing and decreasing B cells according to the diversity of the current population. Two kinds of assessments are used to evaluate the diversity aiming to capture the characteristics of the problem on hand. Furthermore, the processing of adding and declining the number of population is designed. The validity of the proposed algorithm is tested for several traveling salesman benchmark problems. Simulation results demonstrate the efficiency of the proposed algorithm when compared with the traditional genetic algorithm and an improved clonal selection algorithm.

In 2019, a new selection method, named fitness-distance balance (FDB), was proposed. FDB has been proved to have a significant effect on improving the search capability for evolutionary algorithms. But it still suffers from poor flexibility when encountering various optimization problems. To address this issue, we propose a functional weights-enhanced FDB (FW). These functional weights change the original weights in FDB from fixed values to randomly generated ones by a distribution function, thereby enabling the algorithm to select more suitable individuals during the search. As a case study, FW is incorporated into the spherical search algorithm. Experimental results based on various IEEE CEC2017 benchmark functions demonstrate the effectiveness of FW.

When solving combinatorial optimization problems with a binary Hopfield-type neural network, the updating process in neural network is an important step in achieving a solution. In this letter, we propose a new updating procedure in binary Hopfield-type neural network for efficiently solving combinatorial optimization problems. In the new updating procedure, once the neuron is in excitatory state, then its input potential is in positive saturation where the input potential can only be reduced but cannot be increased, and once the neuron is in inhibitory state, then its input potential is in negative saturation where the input potential can only be increased but cannot be reduced. The new updating procedure is evaluated and compared with the original procedure and other improved methods through simulations based on N-Queens problem. The results show that the new updating procedure improves the searching capability of neural networks with shorter computation time. Particularly, the simulation results show that the performance of proposed method surpasses the exiting methods for N-queens problem in synchronous parallel computation model.

Ant colony optimization (ACO) algorithms are a recently developed, population-based approach which has been successfully applied to optimization problems. However, in the ACO algorithms it is difficult to adjust the balance between intensification and diversification and thus the performance is not always very well. In this work, we propose an improved ACO algorithm in which some of ants can evolve by performing genetic operation, and the balance between intensification and diversification can be adjusted by numbers of ants which perform genetic operation. The proposed algorithm is tested by simulating the Traveling Salesman Problem (TSP). Experimental studies show that the proposed ACO algorithm with genetic operation has superior performance when compared to other existing ACO algorithms.

An improved genetic algorithm for solving the graph planarization problem is presented. The improved genetic algorithm which is designed to embed a graph on a plane, performs crossover and mutation conditionally instead of probability. The improved genetic algorithm is verified by a large number of simulation runs and compared with other algorithms. The experimental results show that the improved genetic algorithm performs remarkably well and outperforms its competitors.

This paper presents a new multi-layered artificial immune system architecture using the ideas generated from the biological immune system for solving combinatorial optimization problems. The proposed methodology is composed of five layers. After expressing the problem as a suitable representation in the first layer, the search space and the features of the problem are estimated and extracted in the second and third layers, respectively. Through taking advantage of the minimized search space from estimation and the heuristic information from extraction, the antibodies (or solutions) are evolved in the fourth layer and finally the fittest antibody is exported. In order to demonstrate the efficiency of the proposed system, the graph planarization problem is tested. Simulation results based on several benchmark instances show that the proposed algorithm performs better than traditional algorithms.

Software watermarking is a digital technique used to protect software by embedding some secret information as identification in order to discourage software piracy and unauthorized modification. Watermarking is still a relatively new field and has good potential in protecting software from privacy threats. However, there appears to be a security vulnerability in the watermark trigger behaviour, and has been frequently attacked. By tracing the watermark trigger behaviour, attackers can easily intrude into the software and locate and expose the watermark for modification. In order to address this problem, we propose an algorithm that obscures the watermark trigger behaviour by utilizing buffer overflow. The code of the watermark trigger behaviour is removed from the software product itself, making it more difficult for attackers to trace the software. Experiments show that the new algorithm has promising performance in terms of the imperceptibility of software watermark.

We present a learning algorithm of the Hopfield neural network for minimizing edge crossings in linear drawings of nonplanar graphs. The proposed algorithm uses the Hopfield neural network to get a local optimal number of edge crossings, and adjusts the balance between terms of the energy function to make the network escape from the local optimal number of edge crossings. The proposed algorithm is tested on a variety of graphs including some "real word" instances of interconnection networks. The proposed learning algorithm is compared with some existing algorithms. The experimental results indicate that the proposed algorithm yields optimal or near-optimal solutions and outperforms the compared algorithms.

In 2019, a completely new algorithm, spherical evolution (SE), was proposed. The brand new search style in SE has been proved to have a strong search capability. In order to take advantage of SE, we propose a novel method called the ladder descent (LD) method to improve the SE' population update strategy and thereafter propose a ladder spherical evolution search (LSE) algorithm. With the number of iterations increasing, the range of parent individuals eligible to produce offspring gradually changes from the entire population to the current optimal individual, thereby enhancing the convergence ability of the algorithm. Experiment results on IEEE CEC2017 benchmark functions indicate the effectiveness of LSE.

The goal of the maximum cut problem is to partition the vertex set of an undirected graph into two parts in order to maximize the cardinality of the set of edges cut by the partition. The maximum cut problem has many important applications including the design of VLSI circuits and communication networks. Moreover, many optimization problems can be formulated in terms of finding the maximum cut in a network or a graph. In this paper, we propose an improved Hopfield neural network algorithm for efficiently solving the maximum cut problem. A large number of instances have been simulated. The simulation results show that the proposed algorithm is much better than previous works for solving the maximum cut problem in terms of the computation time and the solution quality.

The facility layout problem is one of the most fundamental quadratic assignment problems in operations research. In this paper, we present an improved genetic algorithm for solving the facility layout problem. In our computational model, we propose several improvements to the basic genetic procedures including conditional crossover and mutation. The performance of the proposed method is evaluated on some benchmark problems. Computational results showed that the improved genetic algorithm is capable of producing high-quality solutions.

In this paper, we present a modified genetic algorithm for solving combinatorial optimization problems. The modified genetic algorithm in which crossover and mutation are performed conditionally instead of probabilistically has higher global and local search ability and is more easily applied to a problem than the conventional genetic algorithms. Three optimization problems are used to test the performances of the modified genetic algorithm. Experimental studies show that the modified genetic algorithm produces better results over the conventional one and other methods.

Ant Colony Optimization (ACO) is one of the most recent techniques for solving combinatorial optimization problems, and has been unexpectedly successful. Therefore, many improvements have been proposed to improve the performance of the ACO algorithm. In this paper an ant colony optimization with memory is proposed, which is applied to the classical traveling salesman problem (TSP). In the proposed algorithm, each ant searches the solution not only according to the pheromone and heuristic information but also based on the memory which is from the solution of the last iteration. A large number of simulation runs are performed, and simulation results illustrate that the proposed algorithm performs better than the compared algorithms.