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this work proposes a novel approach, called the -algorithm, that addresses the challenge of modeling and evaluating multiobjective formulations. as a contribution to multiobjective optimization theory, it introduces a novel algorithm to continuously generate optimal solutions in a decentralized design context. it generalizes the well-established algorithms of uzawa, powell, and dantzig to the multiobjective setting. the approach, called -algorithm, is shown to be an efficient way to address the problem of implementing multiobjective planning without making assumptions of the objectives. instead it works by performing a simple linear projection of the problem into a space where strong duality holds (i.e., in which the cost is zero) and where both the primal and dual solutions are zero. for a linearized version of the problem, the algorithm may be described as follows: using the concept of a parameter space of parameters, -algorithm determines the most-preferred solution by performing a hybrid form of search using particle swarm optimization over the parameter space. when solving a multiobjective problem, the dimensionality of the parameter space increases linearly with the number of objectives. therefore, as the number of objectives increases, the algorithm becomes exponential in this space.
analytic in-situ approaches to decomposing global policy-making problems into smaller, more tractable sub-problems, and algorithmic approaches to solving them, are an increasingly popular tool for interactive decision support. here, we take a holistic approach, combining multiple interactive optimization methodologies with advanced technologies in order to more efficiently learn the characteristics of the problem, visualize and further investigate solutions, and flexibly switch between fully automated interactive methodologies and fully automated search algorithms.
this work proposes a novel approach, called the -algorithm, that addresses the challenge of modeling and evaluating multiobjective formulations. as a contribution to multiobjective optimization theory, it introduces a novel algorithm to continuously generate optimal solutions in a decentralized design context. it generalizes the well-established algorithms of uzawa, powell, and dantzig to the multiobjective setting. the approach, called -algorithm, is shown to be an efficient way to address the problem of implementing multiobjective planning without making assumptions of the objectives. instead it works by performing a simple linear projection of the problem into a space where strong duality holds (i.e., in which the cost is zero) and where both the primal and dual solutions are zero. for a linearized version of the problem, the algorithm may be described as follows: using the concept of a parameter space of parameters, -algorithm determines the most-preferred solution by performing a hybrid form of search using particle swarm optimization over the parameter space. when solving a multiobjective problem, the dimensionality of the parameter space increases linearly with the number of objectives. therefore, as the number of objectives increases, the algorithm becomes exponential in this space.
analytic in-situ approaches to decomposing global policy-making problems into smaller, more tractable sub-problems, and algorithmic approaches to solving them, are an increasingly popular tool for interactive decision support. here, we take a holistic approach, combining multiple interactive optimization methodologies with advanced technologies in order to more efficiently learn the characteristics of the problem, visualize and further investigate solutions, and flexibly switch between fully automated interactive methodologies and fully automated search algorithms.
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