Dynamic　vibration　absorbers　(DVAs)　are　widely　used　in　engineering　practice　because　of　their　good　vibration　control　performance.　Structural　design　or　parameter　optimization　could　improve　its　control　efficiency.　In　this　paper,　the　viscoelastic　Maxwell-type　DVA　model　with　an　inerter　and　multiple　stiffness　springs　is　investigated　with　the　combination　of　the　traditional　theory　and　an　intelligent　algorithm.　Firstly,　the　expressions　and　approximate　optimal　values　of　the　system　parameters　are　obtained　using　the　fixed-point　theory　to　deal　with　the　H　infinity　optimization　problem,　which　can　provide　help　with　the　range　of　parameters　in　the　algorithm.　Secondly,　we　innovatively　introduce　the　particle　swarm　optimization　(PSO)　algorithm　to　prove　that　the　algorithm　could　adjust　the　value　of　the　approximate　solution　to　minimize　the　maximum　amplitude　by　analyzing　and　optimizing　the　single　variable　and　four　variables.　Furthermore,　the　validity　of　the　parameters　is　further　verified　by　simulation　between　the　numerical　solution　and　the　analytical　solution　using　the　fourth-order　Runge-Kutta　method.　Finally,　the　DVA　demonstrated　in　this　paper　is　compared　with　typical　DVAs　under　random　excitation.　The　timing　sequence　and　variances,　as　well　as　the　decreased　ratios　of　the　displacements,　show　that　the　presented　DVA　has　a　more　satisfactory　control　performance.　The　inerter　and　negative　stiffness　spring　can　indeed　bring　beneficial　effects　to　the　vibration　absorber.　Remarkably,　the　intelligent　algorithm　can　make　the　resonance　peaks　equal　in　the　parameter　optimization　of　the　vibration　absorber,　which　is　quite　difficult　to　achieve　with　theoretical　methods　at　present.　The　results　may　provide　a　theoretical　and　computational　basis　for　the　optimization　design　of　DVA.