Waste　disposal　facilities　are　kinds　of　typical　＂semi-desirable　facilities＂.　Some　incompatible　objectives　such　as　cost　and　obnoxious　effect　etc.　should　be　considered　in　the　process　of　location　and　other　related　decisions　of　these　facilities.　The　location-routing　problem　in　waste　logistics　network　in　cities　is　one　kind　of　typical　periodic　location　routing　problem　(PLRP),　for　different　population　centers　can　be　visited　by　different　frequency　in　certain　period,　however,　the　multi-objective　optimization　of　this　problem　is　short　of　research.　A　multi-objective　PLRP　is　studied　in　this　paper,　which　combines　the　practical　situation　of　waste　logistics　network　in　cities.　A　new　method　is　proposed　measuring　negative　effect　based　on　the　concept　of　dispersion　distance;　a　mixed　integer　programming　model　concerning　two　objectives　of　average　total　cost　and　average　negative　effect　is　raised;　a　multi-objective　evolutionary　algorithm　is　devised　to　solve　location-allocation　problem,　visiting　scheduling　problem　and　vehicle　routing　problem　simultaneously.　The　global　algorithm　strengthens　an　extension　local　search　deepening　the　search　of　feasible　collection　and　transportation　plans;　a　sub-algorithm　termed　DRECW-LS　which　strengthens　the　diversification,　randomization　and　local　search　based　on　ECWA　solves　the　periodic　location-routing　problem.　The　computing　example　shows:　the　algorithm　can　solve　analogous　large　size　problems　and　shows　excellent　quality　and　computing　efficiency.