CAN GENETIC ALGORITHM OPTIMIZE SUBMARINE CONCEPT DESIGN?

Darwin natural selection as tool for optimization with actual case study.

In contemporary marine concept design optimization, engineers seek cutting-edge solutions that meet stringent performance, safety, and environmental standards. The process often involves a combination of innovative methodologies and experience/common sense to achieve optimal results. One widely adopted approach is the spiral method, which emphasizes iterative refinement through successive cycles of design, evaluation, and adjustment.

However, it's crucial to acknowledge that while the spiral method facilitates progress and adaptation, it doesn't guarantee the discovery of the absolute best solution. This limitation stems from the inherent constraints within the project domain, such as time, resources, and the complexity of variables influencing marine design.

METAHEURISTIC BIO-INSPIRED ALGORITHM

To overcome these limitations and enhance optimization efforts, engineers often turn to advanced algorithms.

In this article we are going to explore the bio-inspired metaheuristic algorithms. These algorithms mimic natural processes and biological phenomena to efficiently explore vast solution spaces and find near-optimal solutions. Examples include genetic algorithms, swarm intelligence algorithms like particle swarm optimization, and nature-inspired methods such as the plant growth simulation algorithm and human-based optimization.

GENETIC ALGORITHM

The genetic algorithm, pioneered by John Holland in 1975, stands out as one of the? powerful optimization technique. Drawing inspiration from the principles of natural selection and genetics, genetic algorithms employ concepts such as crossover, mutation, and selection to iteratively evolve a population of potential solutions towards optimal or near-optimal designs.

In a genetic algorithm, we work with a group of potential solutions called a population. Each member of this population represents a possible solution and is characterized by a genome that encodes its traits. Typically, the genome is initially assigned random values to represent a diverse set of potential solutions.

At any given point during the algorithm's execution, the entire collection of solutions is referred to as a generation. The initial generation, often labeled as generation 0, consists of these randomly generated solutions.

So now that we have our initial population, we need to start the natural selection by simulating the survival of the solutions. This is achieved through the use of a fitness function, which evaluates the performance or "fitness" of each solution.?

After assessing the fitness of the entire population, the focus shifts to selecting parents who will produce offspring for the subsequent generations of solutions. This selection process can take various forms such as tournament selection or roulette selection. Solutions with higher fitness values are favored for selection as parents, reflecting their greater likelihood of contributing to the next generation of solutions.

The iteration continues until Generation 1 reaches a predetermined threshold of species.?

However, this process may encounter two significant issues: insufficient species diversification and potential loss of optimal solutions during crossover.

To address the diversification challenge, which manifests itself as the concentration of search efforts within a limited area of the design domain, the mutation process comes into play. Mutations occur randomly, with a set probability, causing a random alteration in one chromosome of the genome of certain species. This mechanism facilitates the exploration of new solutions that may not have been accessible with the initial gene pool alone.

To prevent the loss of optimal solutions during the crossover process, elitism plays a crucial role. This mechanism involves copying some of the fittest solutions from the previous generation into the new generation. By preserving these top-performing solutions, elitism ensures that promising genetic material continues to contribute to the evolutionary progress of the population.?

The genetic process continue until the target generation number is reached.

Ok, but is it something that is applicable to the engineering world? To demonstrate its practicality, let's delve into a case study. Please note that the upcoming paragraphs will contain technical details.

CASE STUDY: INTRODUCTION AND MODEL

In this multi-objective optimization process, the solution was subjected to a NSGA-II algorithm to identify the Pareto Front. NSGA-II is an extension of the Genetic Algorithm that incorporates dominance and crowding distance parameters.

While a detailed explanation of these parameters is beyond the scope of this article, in essence:

A given solution 1 dominates solution 2, when minimization is searched, if

?i : fi(x1)≤f(x2)

? i : fi(x1) < f(x2)

The same thing could be established for maximization dominance changing the sign of the inequation.

The crowding distance metric quantifies the extent to which a solution is separated from the rest of the population. Similar to how mutation operates, crowding distance serves to diversify the solutions. A higher crowding distance implies a greater likelihood of being chosen for reproduction, as it indicates a solution's distinctiveness within the population.

In this particular case study, two key performance indicators were identified as objectives for the optimization problem: minimizing the advance resistance of the submarine and maximizing the critical buckling pressure of the submarine shell.

OBJECTIVE 1: ADVANCE RESISTANCE

Considerations regarding propulsive performance are pivotal in submarine design. Typically, the drag resistance (R_av) experienced by a body moving through a fluid medium is influenced by factors such as fluid density, in this context seawater density (ρ_w), velocity (v), and the total wetted surface area of the body, along with coefficients representing frictional, form, and residual components.

For simplicity in implementing the optimization problem, the R_av equation from "Fundamentals of Submarine Concept Design" (1992) by Capt. H.A. Jackson has been chosen as a basic expression.

Where:

rho_w: water density

V: submarine advance speed

Cf: frictional resistance coefficient (def. from ITTC '57)

d_Cf: residual resistance coefficient (def. from ITTC'57)

WS: wetted surface, funtion of Cwsf and Cwsa (refer to "Fundamentals of Submarine Concept Design" for details)

OBJECTIVE 2: CRITICAL PRESSURE FOR BUCKLING

For the maximization problem, the Windenburg and Trilling equation, also known as the DTMB equation when applied to steel material (Poisson ratio=0.3), has been chosen due to its simplicity and effectiveness. This equation is specifically designed to evaluate the pressure at which buckling instability occurs in cylindrical structures when subjected to external pressure. It provides a straightforward means of assessing the critical buckling pressure, which is crucial for ensuring the structural integrity of cylindrical components such as submarine shells.

Where:

E: Young modulus

h: shell thickness

L: length of unsupported shell

D: mean cylinder diameter

RESULTS

The parameters utilized in the NSGA algorithm are presented in the table below. However, to achieve a significant Pareto front, these parameters required some tuning.

The code was written in python. Processing occurred on a computer with an AMD 3900X processor and a total RAM capacity of 36 GB at 3600 MHz. The size of the initial population and the number of generations were maintained at appropriate levels for the purpose of this study. Furthermore, the final population underwent filtering to eliminate clones or solutions that were very closely similar. Processing took 22 seconds.

The solutions comprising the Pareto front represent the optimal outcomes for this specific optimization scenario. It's important to note that while genetic algorithm optimization can efficiently explore the solution space and identify trade-offs between competing objectives, it does not replace the expertise and intuition of a skilled designer. A designer seeking well-balanced initial solutions would likely prioritize analyzing the solutions found along the Pareto front. This underscores the complementary nature of genetic algorithm optimization and human design intuition, emphasizing the importance of integrating both approaches in the design process for optimal results.

I am a Marine Engineer and Naval Architect based in Lucca, Italy, with over four years of experties on Submarine and Defence System design. Recently I am focusing on Project Engineering, by employing a systematic approach and leveraging my interdisciplinary skills.