Work Package 1

Work package number


Lead beneficiary

1 - NTUA

Work package title

Design Optimization - Algorithms

Start month


End month




In this WP, gradient based and derivative free optimization algorithms for solving the type of problems addressed in this project will be tested. The aim of WP1 is to study the robustness of the algorithms and their computational performance on a wide selection of benchmark engineering optimization problems with different characteristics and draw conclusions on the suitability of the algorithms for each particular type of problem. Following this extensive parametric study, there will be enough evidence for selecting of the appropriate single- and multi-objective optimization algorithm for solving the problems of the accompanying WPs.


Description of work and role of partners

WP1 - Design Optimization - Algorithms [Months: 1-43]
Automatic numerical algorithms have been developed in the past to meet the demands of structural design optimization. These methods can be classified in deterministic and probabilistic approaches. Heuristic and metaheuristic algorithms belong to the second category and are nature-inspired or bio-inspired methods, as they have been developed based on the evolutionary behaviour of natural systems. A number of metaheuristic algorithms for engineering optimization have been proposed, among them: genetic algorithms; evolutionary programming; evolution strategies (ES); genetic programming; simulated annealing; particle swarm optimization; ant colony algorithm; artificial bee colony algorithm; harmony search; cuckoo search algorithm; firefly algorithm; bat algorithm; krill herd algorithm. Several metaheuristic algorithms have been also proposed for treating structural multi-objective optimization problems. The three most wellknown algorithms are the non-domination sort genetic algorithm (NSGA); the strength Pareto evolutionary algorithm (SPEA) and the multi-objective elitist covariance matrix adaptation method. A combination of ES with NSGA and SPEA algorithms has been proposed by the PI and has been proved robust and efficient [1-10]. Task 1.1: Single-objective optimization In this task, a number of metaheuristic optimization algorithms will be improved and integrated into the developed HPC software platform under a unified framework in order to be able to reach objective and reliable conclusions on their performance. Specifically, the following algorithms, which have been applied separately by members of the Network on specific applications, will be assessed for the solution of single objective optimization problems. Task 1.2: Multi-objective optimization Similar to the previous task, multi-objective optimization algorithms that have been elaborated by members of the Network and implemented independently to specific applications, will be improved and incorporated into the proposed software platform for a systematic comparison on the wide range of benchmark problems. Task 1.3: Benchmark tests A number of representative benchmark test examples will be selected from the NASA CometBoards (comparative evaluation test bed of optimization and analysis routines for the design of structures) [11] and from other well-known collections of benchmark structural optimizations problems for testing the optimization algorithms presented in Tasks 1.1 and 1.2. The benchmark tests will be properly selected with different characteristics with respect to the number of design variables, optimization problem, numerical simulation and number and type of stochastic variables. Ten benchmark test cases will be selected for testing the algorithms in structural single-objective sizing optimization among them: the forward-swept wing, the 224-member 3D pyramid, the 120-bar truss dome, the 26-story frame tower, the welded beam, the reinforced concrete beam, the compression spring and the pressure vessel test examples. For testing the algorithms in single-objective structural shape optimization, five benchmark test cases will be considered among which: the 3D connecting rod, the rectangular plate with reinforced hole. For testing the algorithms in single-objective structural topology optimization five benchmark test cases will be considered among which: the cross beam and the MBB beam. In addition to the three classes of optimization considered, combined sizing-shape-topology optimization problems will be studied, among them the stiffened shell problem. Furthermore, five benchmark test cases will be investigated for testing the multi-objective optimization algorithms recently presented by members of the Network.


Participation Per Partner