Self-Adaptive Genetic Algorithm for Constrained Optimization

This study proposes a self-adaptive penalty function algorithm for solving constrained optimization problems using genetic algorithm (GA). Constrained optimization is a practically relevant and challenging field that deals with optimization of real world problems that involve complex constraints that make them difficult to tackle. GA is a stochastic search method based on the evolutionary ideas of natural selection and genetic. In GA candidate solutions to a certain problem, called individuals, will evolve from generation to generation toward finding better solutions. In this research GA based constraint handling algorithm is proposed that combines the merits of previously designed algorithms. In the proposed method a new fitness value, called distance value, and two penalties are applied to infeasible individuals that violate the constraints. The algorithm aims to encourage infeasible individuals with better objective function value and low constraint violation. The number of feasible individuals in the population is used to guide the search process either toward finding the optimum solution or toward finding more feasible solutions.The performance of the algorithm is tested on 22 benchmark functions in the literature. The results show that the approach is able to find very good solutions comparable to other state-of-the-art designs. Furthermore it is able to find feasible solutions in every run for all of the benchmark functions.School of Electrical & Computer Engineerin

Evolutionary Synthesis of HVAC System Configurations: Algorithm Development.

This paper describes the development of an optimization procedure for the synthesis of novel heating, ventilating, and air-conditioning (HVAC) system configurations. Novel HVAC system designs can be synthesized using model-based optimization methods. The optimization problem can be considered as having three sub-optimization problems; the choice of a component set; the design of the topological connections between the components; and the design of a system operating strategy. In an attempt to limit the computational effort required to obtain a design solution, the approach adopted in this research is to solve all three sub-problems simultaneously. Further, the computational effort has been limited by implementing simplified component models and including the system performance evaluation as part of the optimization problem (there being no need in this respect to simulation the system performance). The optimization problem has been solved using a Genetic Algorithm (GA), with data structures and search operators that are specifically developed for the solution of HVAC system optimization problems (in some instances, certain of the novel operators may also be used in other topological optimization problems. The performance of the algorithm, and various search operators has been examined for a two-zone optimization problem (the objective of the optimization being to find a system design that minimizes the system energy use). In particular, the performance of the algorithm in finding feasible system designs has been examined. It was concluded that the search was unreliable when the component set was optimized, but if the component set was fixed as a boundary condition on the search, then the algorithm had an 81% probability of finding a feasible system design. The optimality of the solutions is not examined in this paper, but is described in an associated publication. It was concluded that, given a candidate set of system components, the algorithm described here provides an effective tool for exploring the novel design of HVAC systems. (c) HVAC & R journa

Searching the solution space in constructive geometric constraint solving with genetic algorithms

Geometric problems defined by constraints have an exponential number of solution instances in the number of geometric elements involved. Generally, the user is only interested in one instance such that besides fulfilling the geometric constraints, exhibits some additional properties. Selecting a solution instance amounts to selecting a given root every time the geometric constraint solver needs to compute the zeros of a multi valuated function. The problem of selecting a given root is known as the Root Identification Problem. In this paper we present a new technique to solve the root identification problem. The technique is based on an automatic search in the space of solutions performed by a genetic algorithm. The user specifies the solution of interest by defining a set of additional constraints on the geometric elements which drive the search of the genetic algorithm. The method is extended with a sequential niche technique to compute multiple solutions. A number of case studies illustrate the performance of the method.Postprint (published version

Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control

Constrained optimization of high-dimensional numerical problems plays an important role in many scientific and industrial applications. Function evaluations in many industrial applications are severely limited and no analytical information about objective function and constraint functions is available. For such expensive black-box optimization tasks, the constraint optimization algorithm COBRA was proposed, making use of RBF surrogate modeling for both the objective and the constraint functions. COBRA has shown remarkable success in solving reliably complex benchmark problems in less than 500 function evaluations. Unfortunately, COBRA requires careful adjustment of parameters in order to do so. In this work we present a new self-adjusting algorithm SACOBRA, which is based on COBRA and capable to achieve high-quality results with very few function evaluations and no parameter tuning. It is shown with the help of performance profiles on a set of benchmark problems (G-problems, MOPTA08) that SACOBRA consistently outperforms any COBRA algorithm with fixed parameter setting. We analyze the importance of the several new elements in SACOBRA and find that each element of SACOBRA plays a role to boost up the overall optimization performance. We discuss the reasons behind and get in this way a better understanding of high-quality RBF surrogate modeling