Optimization Problems In Continuous Domain Research Articles

Algorithms for Constrained Best-fit Alignment

Manufacturing complex structures as planes requires the assembly of several pieces. The first step in the process is to align the pieces. This article is concerned with some mathematical and computational aspects of new algorithms devoted to the alignment of the pieces. We describe the properties of suitable algorithms to handle a non standard constrained optimization problem that occurs in the assembly process of a manufactured product. Then we present two kinds of algorithms: the first based on a fractional step algorithm and the second on a local search algorithm. We assess them on real cases and compare their results with an evolutionary algorithm for difficult non-linear or non-convex optimization problems in continuous domain.

A New Metaheuristic Inspired by the Vapour-Liquid Equilibrium for Continuous Optimization

In this article, a novel optimization metaheuristic based on the vapour-liquid equilibrium is described to solve highly nonlinear optimization problems in continuous domains. During the search for the optimum, the procedure truly simulates the vapour-liquid equilibrium state of multiple binary chemical systems. Each decision variable of the optimization problem behaves as the molar fraction of the lightest component of a binary chemical system. The equilibrium state of each system is modified several times, independently and gradually, in two opposite directions and at different rates. The best thermodynamic conditions of equilibrium for each system are searched and evaluated to identify the following step towards the solution of the optimization problem. While the search is carried out, the algorithm randomly accepts inadequate solutions. This process is done in a controlled way by setting a minimum acceptance probability to restart the exploration in other areas to prevent becoming trapped in local optimal solutions. Moreover, the range of each decision variable is reduced autonomously during the search. The algorithm reaches competitive results with those obtained by other stochastic algorithms when testing several benchmark functions, which allows us to conclude that our metaheuristic is a promising alternative in the optimization field.

Particle state change algorithm

The matter state change, which is a common phenomenon in nature, shows the process that the matter how to reach the optimal state in the environment. This paper presents a novel particle state change model (PSCM) inspired by mimicking the process of the matter state change. Based on PSCM, a novel particle state change (PSC) algorithm is proposed for solving continuous optimization problems. As a new algorithm, PSC has many differences from other similar nature-inspired algorithms in terms of the basic principle models, mathematical formalization and properties. This paper considers three states of the matter, namely gas state, liquid state and solid state. In a certain circumstance, the matter always converts from an unstable state into a stable state. It is similar to find the optimal solution of an optimization problem. The proposed algorithm also has the advantages in the respects of higher intelligence, effectiveness and lower computation complexity. And the convergence property of PSC is discussed in detail. In order to illustrate the ability of solving optimization problems in continuous domain, the new proposed algorithm is tested on basic function optimization, CEC2016 single-objective real-parameter numerical optimization and CEC2016 learning-base real-parameter single-objective optimization, and compared with eleven existing algorithms. The numerous simulations have shown the effectiveness and suitability of the proposed approach.

Multiwinner Voting in Genetic Algorithms

Genetic algorithms are a group of powerful tools for solving ill-posed global optimization problems in continuous domains. When insensitivity in the fitness function is an obstacle, the most desired feature of a genetic algorithm is its ability to explore plateaus of the fitness function surrounding its minimizers. The authors suggest a way of maintaining diversity of the population in the plateau regions based on a new approach for selection according to the theory of multiwinner elections among autonomous agents. The article delivers a detailed description of the new selection algorithm, computational experiments that put the choice of the proper multiwinner rule to use, and a preliminary experiment showing the proposed algorithm's effectiveness in exploring a fitness function's plateau.

An Efficient Adaptive Strategy for Melody Search Algorithm

An efficient adaptive version of Melody Search algorithm (EAMS) is introduced in this study, which is a powerful tool to solve optimization problems in continuous domains. Melody search (MS) algorithm is a recent newly improved version of harmony search (HS), while the algorithm performance strongly depends on fine-tuning of its parameters. Although MS is more efficient for solving continuous optimization problems than most of other HS-based algorithms, the large number of algorithm parameters makes it difficult to use. Hence, the main objective in this study is to reduce the number of algorithm parameters and improving its efficiency. To achieve this, a novel improvisation scheme is introduced to generate new solutions, a useful procedure is developed to determine the possible variable ranges in different iterations and an adaptive strategy is employed to calculate proper parameters' values and choose suitable memory consideration rules during the evolution process. Extensive computational comparisons are carried out by employing a set of eighteen well-known benchmark optimization problems with various characteristics from the literature. The obtained results reveal that EAMS algorithm can achieve better solutions compared to some other HS variants, basic MS algorithms and certain cases of well-known robust optimization algorithms.

Opposition versus randomness in binary spaces

Evolutionary algorithms start with an initial population vector, which is randomly generated when no preliminary knowledge about the solution is available. Recently, it has been claimed that in solving continuous domain optimization problems, the simultaneous consideration of randomness and opposition is more effective than pure randomness. In this paper it is mathematically proven that this scheme, called opposition-based learning, also does well in binary spaces. The proposed binary opposition-based scheme can be embedded inside many binary population-based algorithms. We applied it to accelerate the convergence rate of binary gravitational search algorithm (BGSA) as an application. The experimental results and mathematical proofs confirm each other.