# Weight Reduction of a Ship Crane Truss Structure Made of Composites
## 4 Constraints and Relationships of the Optimization Problem Parameters
### The Proposed Technique  
The robotic winding technology used makes it possible to provide 465 different diameters of rovings using various paths and directions of continuous winding. The purpose of the optimal design procedure is the calculated selection of diameters that ensures the minimum use of material while ensuring the strength and reliability of the CM. It must also be carried out in accordance with the current regulatory rules for the design of ship cranes. After calculating the constraints, the optimization of the design was carried out in three stages. During the study, various optimization algorithms were tested: screening, the multi-objective genetic algorithm (MOGA), and the adaptive multi-objective algorithm [19; 20; 21]. At step 1, each section was divided into three zones along its length: the root zone, the middle zone, and the overlapping zone. The length zones of the second section are shown in Figure 5. Within each section, the constraints presented in Table 1 were implemented. For top diagonal and low diagonal rovings within each of the zones, a separate parameter was used to describe diameters. Lateral longitudinal rovings were supposed to have a diameter per length zone. Top longitudinal and low longitudinal rovings were characterized by a parameter per frame spacing within the middle zone, and a parameter per length zone within the root zone and overlapping zone. Thus, the number of parameters was reduced by a factor of 7 from 465 to 67. Figure 5 shows the second section of the boom with the description of the rovings. Based on the preliminary research involving various algorithms, the screening method (quasi Monte Carlo) was chosen for further solution. This method, compared to the others, showed consistently shorter times to find the best value. The method is effective at determinint the most probable area for finding extremal functions. The Hammersley distribution was chosen as a quasi-random distribution [22]. The Hamersley distribution is two dimensional. In the first dimension, it represents Vander [PERSON]'s distribution of several equal intervals. Consistent use of this method allowed the determination of ranges of admissible parameter values. At step 2, the number of parameters was first increased up to 168 to refine the solution. Each section was divided into the same three zones as used in the first step, but, contrary to the first step, top diagonal and low diagonal rovings of the middle zone were supposed to possess various diameters within each frame spacing. The same was assumed for longitudinal rovings in the middle zone. However, to improve convergence and reduce calculation time, the following parameters of diagonal and longitudinal rovings were linked:  
* Low diagonal to low longitudinal. * Top diagonal to top longitudinal. * Low diagonal to low longitudinal. Diameters of diagonal rovings within each spacing were assumed to be equal to half the diameter of the longitudinal rovings in the same frame spacing. Using these links, the number of parameters was reduced to 89. The imposition of links between diagonal and longitudinal rovings led to the need of increasing lower and upper bound values for the parameters to ensure strength and stability by at least 25%. The search method used was screening. Step 2 of the optimization procedure results in the weight of the CM boom being 1154 kg, which is a weight reduction of 16% with respect to the initial structure. At step 3, the Jaya algorithm [23] was applied to refine the parameters values, taking the results of step 2 as the initial configuration. The Jaya algorithm is an optimization method that has been rapidly developing in recent years. It combines the advantages of both evolutionary algorithms and methods based on swarm intelligence. It is based on screening out the worst solutions and replacing them with the best ones. The method is iterative and shows high efficiency in solving optimization problems.