# Efficient Sizing and Layout Optimization of Truss Benchmark Structures Using ISRES Algorithm
## 3 Improved Stochastic Ranking Evolutionary Strategy (ISRES)  
Using the penalty function method for certain issues can be successful; however, it is hard to determine what an optimal (or nearly optimal) value for it should be. If the value is too small, then infeasible solutions may not be penalized enough, allowing for them to be generated by the evolutionary algorithm. A \"small\" penalty function value implies a relatively low penalty applied to infeasible solutions. In such cases, the penalty may not be sufficient to discourage the generation of infeasible solutions by the evolutionary algorithm, potentially leading to suboptimal outcomes. Conversely, a value that is too high will cause feasible solutions to be found, but of poor quality. A \"large\" penalty function value indicates a higher penalty imposed on infeasible solutions. While this may effectively discourage the generation of infeasible solutions, excessively high penalties can lead to premature convergence to suboptimal feasible solutions. Moreover, a large penalty value can restrict the exploration of the search space, particularly in regions where feasible and infeasible solutions are intertwined or separated. To maximize the effectiveness of the exploration of infeasible regions, it is best to consider an appropriate value for the problem. Depending on the situation, different values may be necessary. Finding an optimal or near-optimal value for the penalty function is crucial for balancing the trade-off between penalizing infeasible solutions and promoting the exploration of the search space. The appropriate value depends on the specific characteristics of the optimization problem, such as the nature of the constraints and the distribution of feasible regions in the search space. A penalty value that is too small will suppress any exploration of unfeasible regions, even in the beginning of the evolution. This is especially ineffective for problems where feasible regions are disconnected from each other in the search space. Exploring infeasible regions can act as pathways linking two or more feasible areas. The key concern is how much exploration of infeasible regions (i.e., how large the value is) should be considered a reasonable amount. This is dependent on the problem. Even for the same issue, different stages of evolutionary search may need different values [47]. Different values can create different fitness functions; therefore, what is considered a fit individual under one fitness function may not be considered fit under another. Consequently, it is necessary to rank individuals in a population adaptively in order to find near-optimal solutions. To do this, [PERSON] and [PERSON] [47] introduced a novel rank-based selection method for ranking individuals, which does not involve the specification of a value. To assess the effectiveness and efficiency of this method, experimental studies have been conducted, and it can be seen as an exterior penalty approach [48]. Adaptively finding a near-optimal solution is the same as adaptively ranking individuals in a population. Therefore, the problem becomes how to sort individuals based on their objective and penalty scores. The SRES ranks the individuals without assigning a value. The authors who developed the SRES created an improved version of it named the ISRES. The ISRES presents a modified version of the optimization algorithm that uses the exponential averaging of trial step sizes. The Improved Stochastic Ranking Evolutionary Strategy (ISRES) algorithm, a refinement of the Stochastic Ranking Evolutionary Strategy (SRES), introduces a suite of enhancements tailored to enhance efficiency and efficacy in optimization endeavors. Foremost among these enhancements is the implementation of the exponential averaging of trial step sizes, fostering a more nuanced and adaptive exploration of the search space compared to the fixed step sizes utilized by the SRES.