In multi-agent collaborative search missions, task allocation is required to determine which agents will perform which tasks. We propose a new approach for decentralized task allocation based on a decentralized genetic algorithm (GA). The approach parallelizes a genetic algorithm across the team of agents, making efficient use of their computational resources. In the proposed approach, the agents continuously search for and share better solutions during task execution. We conducted simulation experiments to compare the decentralized GA approach and several existing approaches. Two objectives were considered: a min-sum objective (minimizing the total distance traveled by all agents) and a min-time objective (minimizing the time to visit all locations of interest). The results showed that the decentralized GA approach yielded task allocations that were better on the min-time objective than those created by existing approaches and solutions that were reasonable on the min-sum objective. The decentralized GA improved min-time performance by an average of 5.6% on the larger instances. The results indicate that decentralized evolutionary approaches have a strong potential for solving the decentralized task allocation problem.

Real-world multi-objective engineering design optimization problems often have parameters with uncontrollable variations. The aim of solving such problems is to obtain solutions that in terms of objectives and feasibility are as good as possible and at the same time are least sensitive to the parameter variations. Such solutions are said to be robust optimum solutions. In order to investigate the trade-off between the performance and robustness of optimum solutions, we present a new Robust Multi-Objective Genetic Algorithm (RMOGA) that optimizes two objectives: a fitness value and a robustness index. The fitness value serves as a measure of performance of design solutions with respect to multiple objectives and feasibility of the original optimization problem. The robustness index, which is based on a non-gradient based parameter sensitivity estimation approach, is a measure that quantitatively evaluates the robustness of design solutions. RMOGA does not require a presumed probability distribution of uncontrollable parameters and also does not utilize the gradient information of these parameters. Three distance metrics are used to obtain the robustness index and robust solutions. To illustrate its application, RMOGA is applied to two well-studied engineering design problems from the literature.

An entropy-based metric is presented to assess the diversity of solutions in a multi-objective optimization technique. This metric quantifies the 'goodness' of a solution set in terms of its distribution quality over the Pareto-optimal frontier. As a demonstration via a three-objective test example, the entropy metric is used as a means of comparing two multi-objective genetic algorithms.

The production problem in product design consists of determining technically feasible options and implementing collective decision making to decide which alternatives to produce. A problem with considering collective decision making in the production problem is that it may not be possible to define, a priori, a group utility function, due to the difficulty of making interpersonal comparisons of the members' preferences. Constructing a group utility function and solving the production problem may lead to unacceptable alternatives for some of the members. The distribution problem involves consideration of individual preferences in satisfying group decision-making situations. If production and distribution of the products are considered simultaneously, the preferences of the members are taken into account, explicitly leading to acceptable solutions. This approach also allows for explicit consideration of a company business strategy in determining which products to develop. A production-distribution approach is outlined and demonstrated for the design of a power electronics module product with a group of decision makers consisting of three customers and a manufacturer. In addition to explicit consideration of the customers' preference, some business strategies are also considered, leading to product alternatives acceptable to the customers and manufacturer.

An optimization strategy is presented that provides a frame-work in which optimization algorithms and heuristic procedures can be coupled to solve nonlinearly constrained design optimization problems. These problems cannot be efficiently solved by either approach independently. The approach is based on an optimization algorithm dealing with local monotonicity and sequential quadratic programming techniques with heuristic procedures which are statistically derived from observations obtained by applying the optimization algorithm to different classes of test problems.