Police patrol routing problem (PPRP) attracts researchers’ attention especially on artifitial inteligence. The challenge here is that a limited number of patrols cover a wide range of area that includes several hotspots. In this study, a new model for PPRP is proposed simulating the Solomon’s benchmark for vehicle routing problem with time windows. This model can solve this problem by maximising the coverage of hotspots with frequencies of high priority locations while ensuring the feasibility of routes. Two constructive greedy heuristics are developed to generate the initial solution of the PPRP: highest priority greedy heuristic (HPGH) and nearest neighbour greedy heuristic (NNGH). Experimental results show that the simulated Solomon’s benchmark is suitable to represent PPRP. In addition, results illustrate that NNGH is more efficient to construct feasible solution than HPGH.
One of the major problems in today’s economy is the phenomenon of tax evasion. The linear regression method is a solution to find a formula to investigate the effect of each variable in the final tax evasion rate. Since the tax evasion data in this study has a great degree of uncertainty and the relationship between variables is nonlinear, Bayesian method is used to address the uncertainty along with 6 nonlinear basis functions to tackle the nonlinearity problem. Furthermore, variational method is applied on Bayesian linear regression in tax evasion data to approximate the model evidence in Bayesian method. The dataset is collected from tax evasion in Malaysia in period from 1963 to 2013 with 8 input variables. Results from variational method are compared with Maximum Likelihood Estimation technique on Bayeisan linear regression and variational method provides more accurate prediction. This study suggests that, in order to reduce the tax evasion, Malaysian government should decrease direct tax and taxpayer income and increase indirect tax and government regulation variables by 5% in the small amount of changes (10%-30%) and reduce direct tax and income on taxpayer and increment indirect tax and government regulation variables by 90% in the large amount of changes (70%-90%) with respect to the current situation to reduce the final tax evasion rate.