as .\\ as shown schematically in Figure lb. The 

 station closest to S., is designated as S3 and 

 Vj is the link joining S^ and S;^. The 

 link .\', is not permitted to be either of 

 the links already connected to S.,- The gain cri- 

 terion is then calculated as g^ = c/.v, - rA',. If 

 this is negative, S.2 is designated as the other 

 neighbor of S, in the tour. If^, is positive, S4 is 

 designated as one of the tour neighbors of S;j as 

 shown in Figure Ic. If y2 were chosen to join S^ 

 with Si, the result would be a tour. The gain criter- 

 ion is then calculated asg? ^ dx2 - dy^. If^i + ^2 

 >0, the original tour could be improved by ex- 

 changing Xi and .V.2 with .v'l and y2, respectively. 

 This potential improvement, which results from 

 closing up the tour immediately (G'-' = g^ +^2'' is 

 then stored. Now S5 is chosen as the nearest 

 neighbor of S4, and _V2 is designated as the link 

 connecting the two stations. Station S5 is not per- 

 mitted to be either of the stations already con- 

 nected to S^. Figure Id shows there is only one 

 choice for station Se and the link X3 such that if Sg is 

 connected toSj, a tour remains. If S^ were chosen 

 as the other neighbor of S5 in the original tour, 

 closing up Sg to Sj would result in a tour of two 

 disconnected pieces (Figure le). The gain as- 

 sociated with closing up immediately (connecting 

 Sg with S, ) is then compared with that obtained by 

 joiningS4toS] (G* ). The link connecting Sg to S, is 

 designated asy j. The gain criterion is then calcu- 

 lated as §3 = dx-f, - dy:i. Ifg^ + g-z + gs^G'' <G* is 

 the best improvement thus far), there is no im- 

 provement, so the number of links ik ) to be profit- 

 ably exchanged is defined as k = 2. If^, +g., + g.^ 

 > G*, however, a new station S^ and link .V4 are 

 selected and the process is continued. 



A limited backtracking feature of the program 

 is included for the case when G- = (i.e., no im- 

 provement can be made). The link ^2 was chosen 

 ( Figure Id ) to join S-, to S4 as the closest station to 

 S4. When no improvement is made at some stage 

 (G* = 0), new links y2 are considered in order of 

 increasing length to a maximum of five choices. If 

 still no improvement is found, the fiveV] links are 

 examined in order of increasing length. When G" 

 cannot be improved, and the valued determined, a 

 new initial station S, is selected and the process 

 repeated. The procedure ends when all n stations 

 have been examined. A new random tour is gener- 

 ated, and each station is examined as an Sj again 

 in the same manner. This limited backtracking 

 significantly increases program effectiveness. 



The computational procedure has other features 



that improve the calculations and reduce running 

 time; such as limited foresight to the next links to 

 be broken, allowance for nonsequential link ex- 

 changes, and elimination from computation of 

 those links previously recorded in good tours. For 

 a more complete description of the algorithm, see 

 Lin and Kernighan (1973). 



Results 



Station Description 



Separate station grids lere used for areas east 

 and west of the Mississippi River Delta. A station 

 consisted of a rectangle, lat. 2'30" by long. 2'30", 

 within which three trawl tows were made. Sta- 

 tions were identified and located at the center 

 point of the rectangle. 



The station grid for the West Delta area con- 

 sisted of an area extending from long. 89°30'W to 

 91°30'W (Figure 2). The station gind for the East 

 Delta area consisted of a primary and secondary 

 zone extending between long. 88°00'W and 

 89^^30'W and long. 79°30'W and 88"00'W (Figure 

 3). Each area was limited by the 9.2-m (5-fm) and 

 92-m (50-fm) depth contours. Stations were 

 excluded from random selection in both areas be- 

 cause of navigation and trawling hazards, and 

 areas of known low groundfish densities. 



Random Selection 



Station number, latitude, and longitude were 

 stored in a master grid file for each area. Input to 

 station selection for the West Delta region was the 

 number of stations to be sampled. This region had 

 780 stations. For the East Delta area, the number 

 of stations must be specified separately for the 

 primary and the secondary zones — there were 555 

 stations in the primary zone and 139 in the sec- 

 ondary region. Station selection was performed by 

 a random number generator which selected sta- 

 tions based on the number required for each area. 



Crujse Track Optimizatit)n 



Requirements for an optimized cruise track 

 were different for the areas east and west of the 

 delta. A round-trip track was desired for the West 

 Delta area, while a one-way calculation was de- 

 sired for the East Delta area. The latter consisted 

 of the shortest route from a designated starting 

 point near Pascagoula. Miss., through each 

 selected station and ending at a point near the 

 mouth of the Mississippi River. 



708 



