به‌كارگيري دو الگوريتم فراابتكاري براي حل مسيله‌ي پوشش مجموعه در حالت غيرقطعي بودن دسترس پذيري به وسايط نقليه‌ي امدادي با رويكرد سيستم هاي صف زمان مبنا

SOLVING A SET COVERING PROBLEM IN THE UNCERTAINTY CONDITION OF AN EMERGENCY SYSTEM WITH A NON-STATIONARY QUEUING APPROACH USING TWO META-HEURISTICS

زمان رسيدن وسايط نقليه‌ي امدادي‌ يكي از مهم‌ترين پارامترها در مسيله‌ي پوشش مجموعه1 در حوزه‌ي امداد‌رساني است. با توجه به مسايل دنياي واقعي، و از آنجا كه هر نوع تسهيلي هميشه به‌طور قطعي در دسترس نيست، در اين نوشتار ارايه‌ي روشي مناسب براي مكان يابي بهينه‌ي مراكز امدادي با توجه به قيود هزينه‌ها هدف‌گيري شده است. با استفاده از سيستم هاي صف ناپايدار2 و همچنين زمان مبنا3 بودن (متغير‌بودن) نرخ هاي حوادث و امدادرساني، مسيله‌ي پوشش مجموعه بسط داده شده است. به‌منظور حل اين مسيله در ابعاد بزرگ روش بهبود‌يافته‌ي بهينه‌سازي انبوه ذرات (IPSO) و الگوريتم شبيه‌سازي تبريد (SA) استفاده مي‌شود. به‌منظور نشان‌دادن كارايي الگوريتم‌هاي پيشنهادي، تعدادي از مسايل در ابعاد كوچك توسط اين الگوريتم‌ها حل و سپس نتايج مربوطه با نتايج حاصل از روش حل دقيق شاخه و كران مقايسه مي‌شود.

Set covering problems have attracted the attention of many researchers in recent years, especially in emergency systems. One of the most important objectives in set covering problems is for emergency vehicles to be on time at accident locations in order to provide services. Based on real observations, service facilities (i.e., emergency vehicles) are not always available and they are provided under uncertain conditions. In these problems, after defining a customer location, facility centers are selected from candidate points to present services to customers efficiently. Hence, an appropriate method is investigated to localize the emergency centers, so that accident locations may receive appropriate services. In this paper, a new approach, based on queuing systems, is presented for developing set covering problems, in which the arrival rate of the emergency services and service rate vary at different time intervals, as shown by ?(t) and µ(t), respectively. These are categorized as non-stationary queuing systems, with time-varying rates, which is a probability variable depending on traffic conditions, accidents, weather conditions, vehicle failure, route conditions, and so on. To approximate the arrival and service rates in non-stationary M(t) /M(t) /1 queuing systems, their average rates can be considered to determinate the probability of available facilities. Since exact solutions of the set covering problems belonging to the category of NP-hard problems are not practical on a large scale, two meta-heuristic algorithms, namely: Improved Particle Swarm Optimization (IPSO) and Simulated Annealing (SA), are presented and the results are compared with branch and bound algorithms in small size problems. At the end, a number of test problems on a large scale are solved and the efficiency of the foregoing algorithms is evaluated. The results have shown that IPSO obtained high quality solutions with reasonable computational time and accuracy compared tothe SA algorithm.