Multi-Objective Optimization Information Fusion and Its Applications for Logistics Centers Maximum Coverage

From past the development direction of logistics centers covering problem, the main solution is almost always relying on modern computer and gradually developed intelligent algorithm, at the same time, the previous understanding of dynamic covering location model is not "dynamic", in order to improve the unreasonable distribution of logistics centers deployment time, improve the service coverage, coverage as the optimization goal to logistics centers, logistics centers as well as each one can be free to move according to certain rules of "dot", according to the conditions set by the site moved to a more reasonable. The innovation of all algorithms in this paper lies in that the logistics centers themselves are regarded as the subject of free "activities", and they are allowed to move freely according to these rules by setting certain moving rules. Simulation results show that the algorithm has good coverage effect and can meet the requirements of logistics centers for coverage effect.

Greedy Genetic Algorithm for the Data Aggregator Positioning Problem in Smart Grids

In this work, we present a metaheuristic based on the genetic and greedy algorithms to solve an application of the set covering problem (SCP), the data aggregator positioning in smart grids. The GGH (Greedy Genetic Hybrid) is structured as a genetic algorithm, but it has many modifications compared to the classic version. At the mutation step, only columns included in the solution can suffer mutation and be removed. At the recombination step, only columns from the parent’s solutions are available to generate the offspring. Moreover, the greedy algorithm generates the initial population, reconstructs solutions after mutation, and generates new solutions from the recombination step. Computational results using OR-Library problems showed that the GGH reached optimal solutions for 40 instances in a total of 75 and, in the other instances, obtained good and promising values, presenting a medium gap of 1,761%.

Partial Covering of a Circle by 6 and 7 Congruent Circles

Background: Some medical and technological tasks lead to the geometrical problem of how to cover the unit circle as much as possible by n congruent circles of given radius r, while r varies from the radius in the maximum packing to the radius in the minimum covering. Proven or conjectural solutions to this partial covering problem are known only for n = 2 to 5. In the present paper, numerical solutions are given to this problem for n = 6 and 7. Method: The method used transforms the geometrical problem to a mechanical one, where the solution to the geometrical problem is obtained by finding the self-stress positions of a generalised tensegrity structure. This method was developed by the authors and was published in an earlier publication. Results: The method applied results in locally optimal circle arrangements. The numerical data for the special circle arrangements are presented in a tabular form, and in drawings of the arrangements. Conclusion: It was found that the case of n = 6 is very complicated, whilst the case n = 7 is very simple. It is shown in this paper that locally optimal arrangements may exhibit different types of symmetry, and equilibrium paths may bifurcate.

Allocation of Relief Centre for Flood Victims Using Location Set Covering Problem (LSCP)

The frequency of natural disaster has been increasing over the years, resulting in loss of life, damage to properties and destruction of the environment. Compared to other natural disaster, floods are the most significant natural hazard in Malaysia that affect thousands of people. It becomes of great concern especially, during these recent floods, several relief centers were experiencing problems when most of the flood’s victims needed to move to the other relief centers after the existing shelters were also affected by flood water. Furthermore, the relief centers were congested due to the large number of flood evacuees that were over the capacity provided. This study attempts to adapt an advance mathematical location-allocation models in making decision to locate and allocate flood victims during flood event. The Location Set Covering Problem (LSCP), with capacitated constraint is considered and solved using Excel Solver. The determination of safe locations for relief centres with respect to prone area is proposed by adding three new constraints which are the distance from river, elevation from sea level and rainfall amount. A flood case of Kuala Kuantan, Pahang in 2013 was used as the main study area for the analysis as well as the whole Kuantan district. Two scenarios of split and non-split allowed were tested for allocation process and result showed that the percentage allocation and number of relief centers involved increases when the distance increases accordingly. Hence, the model can be considered for better evacuation plan.

Uniform Random Covering Problems

Motivated by the random covering problem and the study of Dirichlet uniform approximable numbers, we investigate the uniform random covering problem. Precisely, consider an i.i.d. sequence $\omega =(\omega _n)_{n\geq 1}$ uniformly distributed on the unit circle $\mathbb{T}$ and a sequence $(r_n)_{n\geq 1}$ of positive real numbers with limit $0$. We investigate the size of the random set $$\begin{align*} & {\operatorname{{{\mathcal{U}}}}} (\omega):=\{y\in \mathbb{T}: \ \forall N\gg 1, \ \exists n \leq N, \ \text{s.t.} \ | \omega_n -y | < r_N \}. \end{align*}$$Some sufficient conditions for ${\operatorname{{{\mathcal{U}}}}}(\omega )$ to be almost surely the whole space, of full Lebesgue measure, or countable, are given. In the case that ${\operatorname{{{\mathcal{U}}}}}(\omega )$ is a Lebesgue null measure set, we provide some estimations for the upper and lower bounds of Hausdorff dimension.