What we do.

Ideation, Innovation, and Implementation. At Pell Innovations we know the importance of guarding your intellectual property in the early concept stages and keep our clients' proprietary information and/or trade secrets in strict confidence. We specialize in the optimization of complex problems through the use of robust Multi-objective Genetic Algorithms. Using this technique we can help businesses and individuals improve their products, systems, processes, and machines. We solve problems, period.

What is a Genetic Algorithm?

A Genetic algorithm (GA) is a search technique that mimics the evolutionary principles found in nature. To solve a particular design problem, a GA begins its search with a population of designs or "individuals" that have random input parameters. Each member of the population possesses a chromosome which encodes, in some fashion, the parameters of the individual design. Standard representations involve a string of digits, where each digit may take on a range of numerical values. In GA terms, the string of digits corresponds to the chromosome of an individual, whereas the digit corresponds to a single gene. A basic GA begins by systematically analyzing each individual in the population of designs according to set specifications and assigns it a fitness rating which reflects the designer's goal(s). This fitness rating is then used to identify the designs that perform better than others, enabling the genetic algorithm to determine which designs are weak and should be eliminated. The remaining, more desirable individuals provide genetic material (design parameters) that is then used to create an improved population of designs. This procedure is iterated over many generations until the algorithm converges to an optimum solution.

Why is a Multi-objective approach more robust?

In recent years, efficient methods have been developed to extend genetic algorithms such that multiple conflicting objectives may be optimized simultaneously. This is an important attribute, since real world problems often involve multiple objectives. Furthermore, true multi-objective optimization techniques highlight the fact that there are often many equally optimal solutions to a particular problem; without proper knowledge of these trade-off solutions, the designer is missing a range of opportunities that may be exploited. For example we show an optimization run with two competing objectives. We want to maximize the value of objective A and minimize the value of objective B. The black dots show the performance of an individual design that had its parameters automatically chosen and its performance evaluated by the genetic algorithm. Generation after generation, the population of designs (black dots) converges to a compromise optimal or "Pareto-optimal" front, shown in red. All of the designs that make up this front are equally optimal, since one is slightly better in one objective over the other.

A real world Pareto-optimal front is shown in the next figure, here we present an illustration of the range of Intel Pentium 4 computer processors that trade calculation speed for cost. Data from PCMark'04, a software program used to provide benchmark speed tests, is compared to retail prices for a range of Intel architectures. The goal for computer enthusiasts is to maximize computational speed for a minimum cost. Here we find a spectrum of Pareto-optimal designs, with extreme cases including the Pentium 4 3.8 GHz CPU, and the a 2.4 GHz CPU. Once again, in these two objectives no two designs lying on the dotted frontier may be considered superior over the other. This multi-objective consideration allows the designer to take part in higher level reasoning. For example, if the market strived only for minimal cost, we would be blindly led to the 2.4 GHz processor. The higher level perspective allows us to exploit the Pareto-front and select the 3.4 GHz CPU, a design that a provides only a 10% reduction in speed when compared to the 3.8 GHz CPU, while offering a significant cost reduction of nearly 57%. It is possible to extend this line of reasoning to more complex problems involving physical structures, systems, and processes for any number of objectives. This procedure maps out the design space and allows us to navigate the complex decision process involved in finding a truly optimum solution to a particular problem.

Typical Applications

• Scheduling
  
• Structural Design
  
• Route Planning
  
• Chemical Synthesis
  
• Facility Layout Design
  
• Machine Learning
  
• Shape Optimization
  

Additional Services

We also offer small businesses and individuals in the New England area the following services:

• Solid modeling and virtual prototyping in SolidWorks
  
  Rate: $60 / hour
• Finite Element Analysis (FEA)
  
  Rate: $60 / hour
• Patent Drawings
  
  Rate: $100 / sheet
• Small scale rapid prototyping
  
  Rates: call/email for quote
• Ideation & Invention. Some people think inside the box, some people think outside the box. For us, there is no box. We provide idea creation, invention and problem solving when other people cannot. For special projects only.
  
  Rates: call/email for quote
• Special discounts available for MTI award recipients.

Examples

           FEA             Machine Design        Art/Sculpture     Consumer Products    2D-3D Conversion