Method For The Best Solutions Search in Multiobjective Decision Problems

T h i s pape r d e s c r i b e s a method f o r c o n s t r u c t i n g a d e c i s i o n r u l e p r o v i d i n g t h e i s o l a t i o n o f t h e most p r e f e r a b l e s o l u t i ons i n m u l t i o b j e c t i v e d e c i s i o n p r o b l e m s . The method i s based o n t h e i t e r a t i v e p r o c e d u r e f o r c o n s t r u c t i n g d e c i s i o n r u l e s . C r i t e r i a o f m e a n i n g f u l n e s s and c o n s i s t e n c y o f r e c e i v e d i n f o r m a t i o n a r e f o r m u l a t e d . The r e s u l t s a r e g i v e n o f a p p l y i n g t h e method t o s o l u t i o n o f t h e most p r e f e r a b l e a l t e r n a t i v e s s e a r c h p rob lems c o n c e r n i n g t h e m i n e s h a f t l a y o u t . I n t r o d u c t i o n D e c i s i o n t h e o r y w h i c h b e l o n g s t o the a r e a o f a r t i f i c i a l i n t e l l i g e n c e i s q u i c k l y d e v e l o p i n g . D e c i s i o n mak ing i s c l o s e l y r e l a t e d t o p r o b l e m s o l v i n g , t h o u g h t h e s e a r e n o t i d e n t i c a l p r o c e s s e s . P rob lem s o l v i n g i m p l i e s t h e s e a r c h o f means t o a c h i e v e t h e c l e a r l y v i s i b l e g o a l w h i c h n e v e r t h e l e s s canno t b e a c h i e ved d i r e c t l y [ 1 ] ; t h e d e c i s i o n p r o c e s s i n g e n e r a l i m p l i e s t h e s e a r c h o f a l l p o s s i b l e means o f a c h i e v i n g t h e Bet o b j e c t i v e , p r e f e r e n c e c o m p a r i s o n among them and c h o i c e o f t h e b e s t o n e . The most i m p o r t a n t s p e c i f i c o f d e c i s i o n m a k i n g p rob lems i s t h e p resence o f a d e c i s i o n m a k e r who has t o a c t i n t h e s i t u a t i o n w h i c h i s c h a r a c t e r i z e d b y l a c k o f i n f o r m a t i o n abou t t h e e n v i r o n m e n t , abou t t h e p o s s i b l e outcomes o f t h e d e c i s i o n s and about t h e v a l u e s o f some ou t comes . I t i s n o t o n l y t h a t o b j e c t i v e f u n c t i o n s ( o p t i m a l c r i t e r i a ) i n t h e s e p rob lems a r e n o t s t a t e d b u t a l s o t h e i r e x i s t e n c e i s n o t i n d i s p u t a b l e . The need t o s o l v e complex p r a c t i c a l p r o b l e m s and t h e i n t e r e s t t o s c i e n t i f i c p r o b l e m s accompaning them led to q u i c k deve lopment o f d e c i s i o n t h e o r y . I t i s v e r y i m p o r t a n t t h a t d e c i s i o n t h e o r y p o s t u l a t e s n o n e x i s t e n c e o f a d e c i s i o n t h a t c o u l d b e c o n s i d e r e d t h e b e s t one i n any a b s o l u t e s e n c e , b u t o n l y f o r a g i v e n d e c i s i o n maker i n c o n n e c t i o n w i t h t h e s e t o b j e c t i v e . Thus t h e two main p r o b l e m s o f t h e d e c i s i o n t h e o r y a r e a s f o l l o w s : 1) to subs t i t u te man in repeat ing rou t ine dec is ion problems (programmable problems); 2) to help man in complex and uncer ta in s i t ua t i ons to choose decis ions consistent w i t h h i s preference judgments us ing formal ized models and methods which al low avoid ing mistakes in long and complex chains of l o g i c a l arguments (unprogrammable problems). Decision theory must provide the basis f o r development of models and methods whereby a l l the in format ion on the problem, i nc l ud ing the dec is ion maker's preference judgements is used in order to decide which of the a l t e r n a t i v e courses of act ions is the bes t . When dec i s i o n problems are formal ized d i f f i c u l t questions such as analys is of complex and uncer ta in s i t u a t i o n s become concept u a l l y equivalent to simple problems tha t can be solved by "common sense". Present ly i t i s un i ve rsa l l y acknowledged tha t in most important r e a l l i f e decis ion problems the so lu t i on q u a l i t y cannot be estimated by one scalar -valued performance c r i t e r i o n . Here ar ises the problem of est imat ing and comparing a l t e rna t i ves tak ing i n t o cons ide ra t ion a great number of c r i t e r i a ( m u l t i c r i t e r i a o r mu l t i ob jec t i ve decision problems[2j. Themain d i f f i c u l t i e s in develop ing formal ized dec is ion methods which