This article studies a class of multirobot coordination problems where team robots aim to reach their goal regions with minimum time and avoid collisions obstacles other robots. A novel numerical algorithm is proposed identify the Pareto optimal solutions no robot can unilaterally reduce its traveling without extending others'. The consistent approximation in epigraphical profile sense guarante...

We consider bicriteria optimization problems and investigate the relationship between two standard approaches to solving them: (i) computing the Pareto curve and (ii) the so-called decision maker’s approach in which both criteria are combined into a single (usually non-linear) objective function. Previous work by Papadimitriou and Yannakakis showed how to efficiently approximate the Pareto curv...

The massive scale and variability of microarray gene data creates new and challenging problems of signal extraction, gene clustering, and data mining, especially for temporal gene profiles. Many data mining methods for finding interesting gene expression patterns are based on thresholding single discriminants, e.g. the ratio of between-class to within-class variation or correlation to a templat...

W settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct: (1) polynomial-time algorithms to determine exactly the number of Pareto optima and Pareto strategies; (2) a polynomial-space polynomial-delay prescribed-ord...

GENE_ARCH is an evolution-based Generative Design System that uses adaptation to shape energy-efficient and sustainable architectural solutions. The system applies goal-oriented design, combining a Genetic Algorithm (GA) as the search engine, with DOE2.1E building simulation software as the evaluation module. The GA can work either as a standard GA or as a Pareto GA, for multicriteria optimizat...

We provide axiomatic characterizations of two natural families of rules for aggregating equivalence relations: the family of join aggregators and the family of meet aggregators. The central conditions in these characterizations are two separability axioms. Disjunctive separability, neutrality, and unanimity characterize the family of join aggregators. On the other hand, conjunctive separability...

Many real-world control applications, from economics to robotics, are characterized by the presence of multiple conflicting objectives. In these problems, the standard concept of optimality is replaced by Pareto–optimality and the goal is to find the Pareto frontier, a set of solutions representing different compromises among the objectives. Despite recent advances in multi–objective optimizati...

The main method of solving multi-objective programming is changing multi-objective programming problem into single objective programming problem, and then get Pareto optimal solution. Conversely, whether all Pareto optimal solutions can be obtained through appropriate method, generally the answer is negative. In this paper, the methods of norm ideal point and membership function are used to sol...

This paper presents an adaptive weighted sum method for multiobjective optimization problems. The authors developed the bi-objective adaptive weighted sum method, which determines uniformly-spaced Pareto optimal solutions, finds solutions on non-convex regions, and neglects non-Pareto optimal solutions. However, the method could solve only problems with two objective functions. In this work, th...

Given several different new product development projects and limited resources, this paper is concerned with the optimal allocation of resources among the projects. This is clearly a multi-objective optimization problem (MOOP), because each new product development project has both a profit expectation and a loss expectation, and such expectations vary according to allocated resources. In such a...