We study the Pareto frontier for two competing norms ‖ · ‖X and ‖ · ‖Y on a vector space. For a given vector c, the Pareto frontier describes the possible values of (‖a‖X , ‖b‖Y ) for a decomposition c = a + b. The singular value decomposition of a matrix is closely related to the Pareto frontier for the spectral and nuclear norm. We will develop a general theory that extends the notion of sing...

Requirements prioritisation is a key decision making activity of the software development process, which relies on the capability of different decision-makers to identify the optimal candidate rankings of the requirements, in order to be able to perform a strategic choice among them. In this paper, we formulate such multi-decision-maker requirements prioritisation as a multi-objective optimisat...

this paper uses integrated data envelopment analysis (dea) models to rank all extreme and non-extreme efficient decision making units (dmus) and then applies integrated dea ranking method as a criterion to modify genetic algorithm (ga) for finding pareto optimal solutions of a multi objective programming (mop) problem. the researchers have used ranking method as a shortcut way to modify ga to d...

This study presents a methodology for quantifying the tradeoffs between sampling costs and local concentration estimation errors in an existing groundwater monitoring network. The method utilizes historical data at a single snapshot in time to identify potential spatial redundancies within a monitoring network. Spatially redundant points are defined to be monitoring locations that do not apprec...

Real life problems involve seldom only one criterion, but multiple criteria should be optimised at the same time. The criteria can even be conflicting each other, so the classical techniques used in single criteria optimization cannot be simply reused. Many ideas have been presented in the literature for addressing multiple criteria optimization problems; one of the ideas is to provide the so-c...

This paper proposes a novel multi-objective model for an unrelated parallel machine scheduling problem considering inherent uncertainty in processing times and due dates. The problem is characterized by non-zero ready times, sequence and machine-dependent setup times, and secondary resource constraints for jobs. Each job can be processed only if its required machine and secondary resource (if a...

River regulation alters the natural flow regime of streams with consequent impacts on terrestrial and aquatic habitats riparian zone. The severity such can be modulated by changing redistribution rules at water intakes reservoirs. Contrary to minimal-flow policies, non-proportional proportional policies result in variable environmental releases, namely Dynamic Environmental Flows (DEFs), which ...

The aggregation of objectives in multiple criteria programming is one of the simplest and widely used approach. But it is well known that these techniques sometimes fail in different aspects for determining the Pareto frontier. This paper proposes a new line search based approach for multicriteria optimization. The objectives are aggregated and the problem is transformed into a single objective...

The aggregation of objectives in multiple criteria programming is one of the simplest and widely used approach. But it is well known that this technique sometimes fail in different aspects for determining the Pareto frontier. This paper proposes a new approach for multicriteria optimization which aggregates the objective functions and uses a line search method in order to locate an approximate ...