Applying EGENET to solve continuous constrained optimization problems: a preliminary report

Population-based approaches have given us new search strategies and ideas in order to solve optimization problems. Usually, these methods are based on the performance carried out by a finite number of agents, which by the interaction between them they evolve and work all over the search space. Also, it is well-known that the correct employment of parameter values in this kind of method can positively impact their performance and behavior. In this context, the present work focuses on the design of a hybrid architecture which smartly balances the population size on run-time. In order to smartly balance and control the population size, a modular approach, named Linear Modular Population Balancer (LMPB), is proposed. The main ideas behind the designed architecture include the solving strategy behind a population-based metaheuristic, the influence of learning components based on multiple statistical modeling methods which transform the dynamic data generated into knowledge, and the possibilities to tackle both discrete and continuous optimization problems. In this regard, three modules are proposed for LMPB, which concern tasks such as the management of the population-based algorithm, parameter setting, probabilities, learning methods, and selection mechanism for the population size to employ. In order to test the viability and effectiveness of our proposed approach, we solve a set of well-known benchmark functions and the multidimensional knapsack problem (MKP). Additionally, we illustrate promising solving results, compare them against state-of-the-art methods which have proved to be good options for solving optimization problems, and give solid arguments for future work in the necessity to keep evolving this type of proposed architecture.

Several papers in the scientific literature use metaheuristics to solve continuous global optimization. To perform this task, some metaheuristics originally proposed for solving combinatorial optimization problems, such as Greedy Randomized Adaptive Search Procedure (GRASP), Tabu Search and Simulated Annealing, among others, have been adapted to solve continuous global optimization problems. Proposed by Hirsch et al., the Continuous-GRASP (C-GRASP) is one example of this group of metaheuristics. The C-GRASP is an adaptation of GRASP proposed to solve continuous global optimization problems under box constraints. It is simple to implement, derivative-free and widely applicable method. However, according to Hedar, due to its random construction, C-GRASP may fail to detect promising search directions especially in the vicinity of minima, which may result in a slow convergence. To minimize this problem, in this paper we propose a set of methods to direct the search on C-GRASP, called Directed Continuous-GRASP (DC-GRASP). The proposal is to combine the ability of C-GRASP to diversify the search over the space with some efficient local search strategies to accelerate its convergence. We compare the DC-GRASP with the C-GRASP and other metaheuristics from literature on a set of standard test problems whose global minima are known. Computational results show the effectiveness and efficiency of the proposed methods, as well as their ability to accelerate the convergence of the C-GRASP.

Optimization problems with continuous variables are very often in real-life scenarios. This is why several studies have focused on the use of metaheuristics to solve these problems, known as continuous optimization problems. This chapter focuses on the robust population-based metaheuristic Variable Mesh Optimization (VMO). We review the fundamental aspects of VMO for continuous optimization. Moreover, we analyze the variants of VMO that have been proposed to solve multimodal problems, i.e. those with multiple optima at several search subspaces. The chapter uses a homogeneous algorithmic framework to describe VMO and its variants with niching strategies for multimodal problems.KeywordsMetaheuristicsVariable mesh optimizationContinuous optimization problemsMultimodal optimization problemsNiching

Research into ant colony algorithms for solving continuous optimization problems forms one of the most significant and promising areas in swarm computation. Although traditional ant algorithms are designed for combinatorial optimization, they have shown great potential in solving a wide range of optimization problems, including continuous optimization. Aimed at solving continuous problems effectively, this paper develops a novel ant algorithm termed “continuous orthogonal ant colony” (COAC), whose pheromone deposit mechanisms would enable ants to search for solutions collaboratively and effectively. By using the orthogonal design method, ants in the feasible domain can explore their chosen regions rapidly and efficiently. By implementing an “adaptive regional radius” method, the proposed algorithm can reduce the probability of being trapped in local optima and therefore enhance the global search capability and accuracy. An elitist strategy is also employed to reserve the most valuable points. The performance of the COAC is compared with two other ant algorithms for continuous optimization — API and CACO by testing seventeen functions in the continuous domain. The results demonstrate that the proposed COAC algorithm outperforms the others.

Automatic software generation based on some specification is known as program synthesis. Most existing approaches formulate program synthesis as a search problem with discrete parameters. In this paper, we present a novel formulation of program synthesis as a continuous optimization problem using an evolutionary approach, known as Covariance Matrix Adaptation Evolution Strategy. We then propose several mapping schemes to convert the continuous formulation into actual programs and propose different restart policies for the evolutionary approach. This is the first work that demonstrates the feasibility of continuous approach in synthesizing complex programs, not just simple toy programs. We compare our system, Genesys , to several recent program synthesis techniques (in both discrete and continuous domains). We find that Genesys synthesizes more programs within a fixed time budget than those existing schemes. For example, for programs of length 10, Genesys synthesizes 28% more programs than those existing schemes within the same time budget.

In many recent works, the potential of Exploratory Landscape Analysis (ELA) features to numerically characterize single-objective continuous optimization problems has been demonstrated. These numerical features provide the input for all kinds of machine learning tasks in the domain of continuous optimization problems, ranging, for example, from High-level Property Prediction to Automated Algorithm Selection and Automated Algorithm Configuration. Without ELA features, analyzing and understanding the characteristics of single-objective continuous optimization problems is-to the best of our knowledge-very limited. Yet, despite their usefulness, as demonstrated in several past works, ELA features suffer from several drawbacks. These include, in particular, (1) a strong correlation between multiple features, as well as (2) its very limited applicability to multiobjective continuous optimization problems. As a remedy, recent works proposed deep learning-based approaches as alternatives to ELA. In these works, among others, point-cloud transformers were used to characterize an optimization problem's fitness landscape. However, these approaches require a large amount of labeled training data. Within this work, we propose a hybrid approach, Deep-ELA, which combines (the benefits of) deep learning and ELA features. We pre-trained four transformers on millions of randomly generated optimization problems to learn deep representations of the landscapes of continuous single- and multiobjective optimization problems. Our proposed framework can either be used out of the box for analyzing single- and multiobjective continuous optimization problems, or subsequently fine-tuned to various tasks focusing on algorithm behavior and problem understanding.

In this paper we present two recent metaheuristics, particle swarm optimization and differential evolution algorithms, to solve the single machine total weighted tardiness problem, which is a typical discrete combinatorial optimization problem. Most of the literature on both algorithms is concerned with continuous optimization problems, while a few deal with discrete combinatorial optimization problems. A heuristic rule, the smallest position value (SPV) rule, borrowed from the random key representation in genetic algorithms, is developed to enable the continuous particle swarm optimization and differential evolution algorithms to be applied to all permutation types of discrete combinatorial optimization problems. The performance of these two recent population based algorithms is evaluated on widely used benchmarks from the OR library. The computational results show that both algorithms show promise in solving permutation problems. In addition, a simple but very efficient local search method based on the variable neighbourhood search (VNS) is embedded in both algorithms to improve the solution quality and the computational efficiency. Ultimately, all the best known or optimal solutions of instances are found by the VNS version of both algorithms.

Causal discovery by continuous optimization with weighted superstructure.

Tree-seed algorithm (TSA) is a nature-inspired and population-based algorithm for solving continuous optimization problems. The tree-seed relationship is the main motivation of this algorithm. TSA has only two peculiar parameters which are the total number of trees in the stand (pop) and the controller of the seed production (search tendency). Although many problems have been solved in the literature by TSA which is the successful optimizer for low dimensional unconstrained continuous problems, real-life problems have not been addressed yet. In this study, six continuous unconstrained real-life optimization problems (gas transmission compressor design, optimal capacity of gas production facility, gear train design, frequency modulation sounds parameter identification, the spread spectrum radar polyphase code design with 10 decision variables, the spread spectrum radar polyphase code design with 20 decision variables) have been solved. It is seen that choosing the number of the population as 50 and the value of search tendency as 0.1 is appropriate according to experimental results for these problems.

Model-based methods for continuous and discrete global optimization

This paper presents an adaptive bi-flight cuckoo search algorithm for continuous dynamic optimization problems. Unlike the standard cuckoo search which relies on Levy flight, the proposed method uses two types of flight that are chosen adaptively by a learning automaton to control the global and local search ability of the method during the run. Furthermore, a variable nest scheme and a new cuckoo addition mechanism are introduced. A greedy local search method is also integrated to refine the best found solution. An extensive set of experiments is conducted on a variety of dynamic environments generated by the moving peaks benchmark, to evaluate the performance of the proposed approach. Results are also compared with those of other state-of-the-art algorithms from the literature. The experimental results indicate the effectiveness of the proposed approach.

The cuckoo search (CS) algorithm, which is a new meta-heuristic optimization algorithm, is an efficient approach to solve continuous function optimization problems. Normally, the parameters of the CS are fixed constants. This may result in affecting the algorithm efficiency. To cope with this issue, we properly tune the parameters of the CS and propose an adaptive cuckoo search (ACS) algorithm to enhance the convergence rate and accuracy of the CS. Then, we validate the proposed ACS against test functions and compare its performance with those of particle swarm optimization (PSO), improved cuckoo search algorithm (ICS) and CS by simulation. The simulation results demonstrate that the ACS obtains some solutions better than those obtained by PSO, ICS and CS.

Optimization of formworks shoring location as a continuous optimization problem

We explore a general-purpose heuristic algorithm for finding high-quality solutions to continuous optimization problems. The method, called continuous extremal optimization (CEO), can be considered as an extension of extremal optimization and consists of two components, one which is responsible for global searching and the other which is responsible for local searching. The CEO's performance proves competitive with some more elaborate stochastic optimization procedures such as simulated annealing, genetic algorithms, and so on. We demonstrate it on a well-known continuous optimization problem: the Lennard-Jones cluster optimization problem.

Many real–world problems are modeled as global continuous optimization problems with a nonlinear objective function. Stochastic methods are used to solve these problems approximately, when solving them exactly is impractical. In this class of methods, swarm intelligence (SI) presents metaheuristics that exploit a population of interacting agents able to self–organize, such as ant colony optimization (ACO), particle swarm optimization (PSO), and artificial bee colony (ABC). This paper presents a new SI-based method for solving continuous optimization problems. The new algorithm, called Swarm Random Walk (SwarmRW), is based on a random walk of a swarm of potential solutions. SwarmRW is validated on test functions and compared to PSO and ABC. Results show improved performance on most of the test functions.KeywordsContinuous OptimizationSwarm IntelligenceMeta- heuristic