What is a fair way to assign rooms to several housemates, and divide the rent between them? This is not just a theoretical question: many people have used the Spliddit website to obtain envy-free solutions to rent division instances. But envy freeness, in and of itself, is insufficient to guarantee outcomes that people view as intuitive and acceptable. We therefore focus on solutions that optim...

Obtaining a well distributed non-dominated Pareto front is one of the key issues in multi-objective optimization algorithms. This paper proposes a new variant for the elitist selection operator to the NSGA-II algorithm, which promotes well distributed non-dominated fronts. The basic idea is to replace the crowding distance method by a maximin technique. The proposed technique is deployed in wel...

In fair division of indivisible goods, $\ell$-out-of-$d$ maximin share (MMS) is the value that an agent can guarantee by partitioning goods into $d$ bundles and choosing $\ell$ least preferred bundles. Most existing works aim to all agents a constant fraction their 1-out-of-$n$ MMS. But this sensitive small perturbation in agents' cardinal valuations. We consider more robust approximation notio...

the awareness of administrative organization of rescue and relief operation from spatial and temporal dimensions is pre requirement of rescue and relief. this subject and existence of accessible transportation networks that can save their performance after emergency situations are the most important parameters in efficiency of rescue and relief operation. the position of firefighting stations a...

In the Dasgupta-Heal-Solow-Stiglitz model of capital accumulation and resource depletion we show the following equivalence: If an efficient path has constant (gross and net of population growth) savings rates, then population growth must be quasi-arithmetic and the path is a maximin or a classical utilitarian optimum. Conversely, if a path is optimal according to maximin or classical utilitaria...