Modular Design Problem Research Articles

Comparison of Multi-Objective Evolutionary Algorithms to Solve the Modular Cell Design Problem for Novel Biocatalysis

A large space of chemicals with broad industrial and consumer applications could be synthesized by engineered microbial biocatalysts. However, the current strain optimization process is prohibitively laborious and costly to produce one target chemical and often requires new engineering efforts to produce new molecules. To tackle this challenge, modular cell design based on a chassis strain that can be combined with different product synthesis pathway modules has recently been proposed. This approach seeks to minimize unexpected failure and avoid task repetition, leading to a more robust and faster strain engineering process. In our previous study, we mathematically formulated the modular cell design problem based on the multi-objective optimization framework. In this study, we evaluated a library of state-of-the-art multi-objective evolutionary algorithms (MOEAs) to identify the most effective method to solve the modular cell design problem. Using the best MOEA, we found better solutions for modular cells compatible with many product synthesis modules. Furthermore, the best performing algorithm could provide better and more diverse design options that might help increase the likelihood of successful experimental implementation. We identified key parameter configurations to overcome the difficulty associated with multi-objective optimization problems with many competing design objectives. Interestingly, we found that MOEA performance with a real application problem, e.g., the modular strain design problem, does not always correlate with artificial benchmarks. Overall, MOEAs provide powerful tools to solve the modular cell design problem for novel biocatalysis.

All capacities modular cost survivable network design problem using genetic algorithm with completely connection encoding

AbstractWe study the survivable network design problem (SNDP) for simultaneous unicast and anycast flows in networks where the link cost follows All Capacities Modular Cost (ACMC) model. Given a network modeled by a connected, undirected graph and a set of flow demands, this problem aims at finding a set of connections with a minimized network cost in order to protect the network against any single failure. This paper proposes a new Genetic Algorithm with an efficient encoding to solve the SNDP in networks with ACMC model (A-SNDP). Our encoding scheme is simple and allows large search space. Extensive simulation results on real large topology instances show that the proposed algorithm is much more efficient than the Tabu Search and other conventional Genetic Algorithm in terms of minimizing the network cost.

Effective Tool-Point Acceleration of Serial Chain Mechanisms Based on Basic Geometric Transformations

In this paper, a method to manage the actuator parameters of a serial chain mechanism composed of revolute joints to achieve improved responsiveness characteristics (acceleration capability) based on the basic geometric parameters of the mechanism is presented. Here, an analytic framework presented by the authors in an earlier work, which exploits the geometric structure of this type of mechanism is extended to address the tool-point mass and acceleration. The manipulator’s geometry is reduced to a set of lengths, which are representative of the mechanical gains associated with the manipulator and they, along with the transmission ratio of the actuators, are used to map the actuator parameters to their effective values at the tool-point where a direct comparison to the task requirements can be made. With this method, minimal computations are required to evaluate the system’s performance since only the forward kinematic computations are required. The effects of the actuator transmission ratio parameter on the effective tool-point force, mass, and acceleration are investigated for a six-DOF serial chain manipulator. Through this case study, it is demonstrated how the transmission ratio is managed to balance the system’s effective tool-point force and mass to obtain an optimal tool-point acceleration. In addition to the investigation of the effects of the actuator parameters, the method is shown to be useful in the solution of the configuration management or modular design problem since the exponential design space can be searched for a globally optimal solution with minimal computations. The goal of the configuration management problem is to quickly configure and/or reconfigure a robotic manipulator from a finite set of actuator modules.

Continuous Modular Design Problem: Analysis and Solution Algorithms

This article studies the continuous modular design (MD) problem. First, the article presents duality results for problem (MD) based upon the Wolfe duality theory for nonlinear programming. From these results, an optimality test for problem (MD) is derived that consists of solving a single, balanced transportation problem. Second, the article shows that two well-known optimization approaches, the generalized Benders decomposition and the separable programming approach of linear programming, each have the potential to solve efficiently large instances of problem (MD).

A genetic algorithm-based solution methodology for modular design

Combinatorial optimization problems usually have a finite number of feasible solutions. However, the process of solving these types of problems can be a very long and tedious task. Moreover, the cost and time for getting accurate and acceptable results is usually quite large. As the complexity and size of these problems grow, the current methods for solving problems such as the scheduling problem or the classification problem have become obsolete, and the need for an efficient method that will ensure good solutions for these complicated problems has increased. This paper presents a genetic algorithm (GA)-based method used in the solution of a set of combinatorial optimization problems. A definition of a combinatorial optimization problem is first given. The definition is followed by an introduction to genetic algorithms and an explanation of their role in solving combinatorial optimization problems such as the traveling salesman problem. A heuristic GA is then developed and used as a tool for solving various combinatorial optimization problems such as the modular design problem. A modularity case study is used to test and measure the performance of the developed algorithm.

On Modular Design of Field Robotic Systems

Robots are needed to perform important field tasks such as hazardous material clean-up, nuclear site inspection, and space exploration. Unfortunately their use is not widespread due to their long development times and high costs. To make them practical, a modular design approach is proposed. Prefabricated modules are rapidly assembled to give a low-cost system for a specific task. This paper described the modular design problem for field robots and the application of a hierarchical selection process to solve this problem. Theoretical analysis and an example case study are presented. The theoretical analysis of the modular design problem revealed the large size of the search space. It showed the advantages of approaching the design on various levels. The hierarchical selection process applies physical rules to reduce the search space to a computationally feasible size and a genetic algorithm performs the final search in a greatly reduced space. This process is based on the observation that simple physically based rules can eliminate large sections of the design space to greatly simplify the search. The design process is applied to a duct inspection task. Five candidate robots were developed. Two of these robots are evaluated using detailed physical simulation. It is shown that the more obvious solution is not able to complete the task, while the non-obvious asymmetric design develop by the process is successful.

Generalized bilinear programming: Part I. Models, applications and linear programming relaxation

The evolution of the bilinear programming problem is reviewed and a new, more general model is discussed. The model involves two decision vectors and reduces to a linear program when one of the decision vectors is fixed. The class of problems under consideration contains traditional bilinear programs, general quadratic programs, and bilinearly constrained and quadratically constrained extensions of these problems. We describe how several important applications from the literature, including the multiple modular design problem, can be modeled as generalized bilinear programs. Finally, we derive a linear programming relaxation that can be used as a subproblem in algorithmic solution schemes based on outer approximation and branch and bound.

The continuous modular design problem with linear separable side constraints

This paper describes a heuristic for designing a single module in the presence of linear side constraints and nonlinear requirements constraints. The objective is to minimize the total parts cost to satisfy demand for a set of end products. We model the problem as a nonconvex programming problem and show that the problem can be transformed into an equivalent convex problem. Due to the size of the potential applications we develop a heuristic procedure that is an extension of the Shaftel and Thompson algorithm. Closed form expressions are derived for determining feasible movement directions and step lengths. Computational results are promising since the CPU time required to run the heuristic is small and the solutions compared favorably with solutions generated by standard nonlinear programming software.

Multiple Modular Design Over a Finite Time Horizon

The demand for product variety is recognized to originate at the consumer level and is an influential factor in the make-up of a product line. The concept of modularity entails standardization of subassemblies as a cost saving device. This allows for product differenliation while maintaining low production costs. A multi-period multi-module generalization of earlier research on the Modular Design problem is given. In this model the realistic situation of fluctuating demands and costs through time is incorporated. A search method, employing some hueristic techniques, locates good solutions efficiently.

A Simplex-Like Algorithm for the Continuous Modular Design Problem

This paper derives an efficient solution procedure for solving the continuous version of the Evans modular design problem. The Kuhn-Tucker conditions are used to derive a dual problem that can be solved easily and whose dual variables indicate which equations should be tight. The technique retains a free-basic solution throughout so that fast solution routines can be employed that are quite similar to those for transportation problems. Computational experience shows that this technique works well on very large problems. We therefore have provided a solution technique for solving a nonlinear problem that has applications to various aspects of the design process.

A monotonic passy-like algorithm for the modular design problem

This paper presents a new algorithm for the continuous modular design problem. The method is based on and can be combined with preceding work by Passy, and Shaftel and Thompson.

Primal Decomposition of Mathematical Programs by Resource Allocation: II—Computational Algorithm with an Application to the Modular Design Problem

Part I of this paper presented a method for primal decomposition of large convex separable programs into a sequence of smaller subproblems. In this part, additional theory and development of a parametric subproblem-solution and step-size-determination technique completes the algorithm. A previously unsolved problem in the operations-research literature, the generalized modular design problem of Evans [Opns. Res. 18, 562–4 (1970)] is solved by the algorithm and numerical results provided.

Technical Note—An Integer Approach to Modular Design

This paper discusses the modular-design problem, as set up by David Evans, in which the module is made of several components: there exist Ei of the ith component in each module, and for every application j, D, modules will be needed to satisfy all component requirements. The problem is to design a module (i.e., choose Ē) such that the requirements are satisfied at a minimum cost of surplus components. Mathematically, the problem is: minimizeEi,Dj ∑i=1i=m eiEi ∑j=1j=ndjDj subject to EiDj ≧ Rij; EiDj are positive integers and ei, dj, are constants. The conclusion of the paper is that the two procedures outlined by Evans and by A. Charnes and M. Kirby for the noninteger case cannot be used to find the integer solution. An integer branch-and-bound technique is proposed that has been shown to be useful in the solution of small problems and that has potential use in larger problems.

Letter to the Editor—A Note on “Modular Design—A Special Case in Nonlinear Programming”

A generalization of the modular design problem is explained and posed as an unsolved problem in nonlinear programming.

Modular Design, Generalized Inverses, and Convex Programming

It is shown that the modular design problem [Formula: see text] can be transformed into a problem of minimizing a separable convex function subject to linear equality constraints and nonnegativities. This transformation is effected by using a generalized inverse of the constraint matrix. Moreover the nature of the functional and the constraints of the separable problem are such that a good starting point for its solution can be obtained by solving a particular transportation problem. Several possible methods for solving the separable problem are discussed, and the results of our computational experience with these methods are given. It is also shown that the modular design problem can be viewed as a special case of a large class of general engineering design problems that have been discussed in the literature.